## Inputs

 Distance Round Trip (miles): Elevation Gain (ft) Bodyweight (lbs) Backpack Weight (lbs) Terrain Scaling (1-2, normal to all very rough)

### Downhill

Work Ratio relative to Flat Walking
Equivalent Number of Flat Miles
Base Calories Burned (kcal)

Some background is explained in this post. Basically this is a rough estimate of the workload and calories burned during a hike.

For terrain, assume a value of 1 unless you have a feeling that the terrain you are hiking on really adds on more work that normal. In that case, you might want to scale the energy by some factor - say 1.1 (10% increase), but this is highly speculative. (I have disabled the 'terrain' option for now and set it at 1)

I personally would trust the uphill estimates pretty well, but the downhill may be underestimated.

UPDATE #1: I think generally we all feel the downhill could be quite underestimated. The study & equation I used did the research on a treadmill, where friction on downhill is quite consistent and this is not the case in reality. For now, I am going to assume that one mile downhill (at any grade) is equivalent to walking a flat mile. Even though this isn't the best assumption (probably more work descending 20% grade than flat, but less at 10%), it's probably a decent guess until I get a lot of data collected.

Summitpost discussion / debate on the topic

1. curious if you've thought to take speed into consideration...

2. Of course you burn calories more quickly with faster speeds, but then you finish more quickly as well...

Efficiency-wise, there are speed differences, especially between walking and running. Within various walking speeds, there are also differences. On flat terrain, for most people, the most efficient speed to walk a mile is ~ 3 mph, while 2 or 4 mph will take more energy. However, from what I know these studies are done 0% grade, and from my own experience I believe the efficient speed changes as a function of grade, so it's really hard to properly take speed into account.

1. By the laws of physics, work (ie calories burned) is force X distance. Speed is NOT a factor. Only think that effects the calories you burn is how far you travel (vertical and horizontal distance) and how much weight you carry (your weight + pack weight). If you hike 10 miles and 5000 vertical feet, you will burn the same amount of calories whether you do it in 1 hour or 10 hours.

2. By the law of biomechanics, speed does play a factor in changing mechanical efficiency of human movement, i.e. human calories expended to perform global mechanical work. So it is a factor, albeit a minor one.

3. see this article on caloric after-burn as a function of workout intensity:

http://www.runnersworld.com/weight-loss/running-v-walking-how-many-calories-will-you-burn

jb

4. You guys are framing the question wrong. People aren't some simple idealized shape that obeys basic newtonian physics. Yes, work=force*distance. However, you have to take into account how gait changes with speed. As walking speed changes the muscles required for balance/propulsion vary, which dynamically alters efficiency. There is a walking speed that is maximally efficient, and then efficiency will decline below/above that speed. From what I remember, this is around 2-3 mph depending on a person's physical characteristics (height/leg length...). Therefore, speed has a great deal to do with efficiency. If you don't believe me, then just try speed walking across the room vs. trying to walk as slow as possible vs. a normal speed.

5. Anonymous, everything you point out I already mentioned in my post above. It's not the wrong question and perhaps your reading comprehension is subpar. Yes speed matters as I've mentioned but to account for it you have to have a relationship at all various grades, not just flat! That relationship will change at each gradient (potentially the difference will be reduced).

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7. I am an engineer, so I'll clear this up for you guys...

The equation, W = F * D, is dependent on your velocity and the angle of your climb, and here is why..

F = m * a, m = mass, a=acceleration. If you do a force balance and determine the net force working on you as you climb, you have to consider a few forces...

Force of gravity, force of friction, and the force you apply as you climb. At constant velocity, your forces balance out to zero. The energy used, on the other hand, increases as you apply this force for a distance (hence force x distance).

Gravitational acceleration is constant, BUT the angle you are climbing changes how you fight this force. The force of gravity needs to be "fought" more as your angle of climb changes, because you have less ground to rebound your acceleration (for every action, there is an equal but opposite reaction). Since the angle decreases how much the ground absorbs your acceleration, you have to balance that out with other forces, such as more work done by your hike. In addition, your fighting gravity more directly as you climb in elevation. So, the force of gravity plays a massive factor.

Also, your frictional loss and other resistances tend to be functions of your velocity, so the faster you walk, the more you have to overcome to stay at a constant velocity.

So, to wrap things up, we can go through the math.

At constant velocity, your forces balance out (Newton's law... an object in motion tends to stay in motion...)

SO:

Fnet = F gravity + F walking + F other resistances such as friction and wind resistance

Force = m * a

acceleration due to gravity is g (9.81 m/s^2). It works in the opposite direction of your movement, so we will denote this as g. Gravity is where your incline comes into play. As your angle increases, the force of gravity increases. Inversely, gravity helps you out as you're going downhill, so the g becomes positive, thus less work required.
SO:

F= m * g * sin (angle of climb)
The sin function is in there due to trigonometry, which is difficult to explain if you have never learned it, but it has to do with angles and triangles.

If we assume constant velocity, your body is actually not accelerating, so F walking drops out. If you're actually physically putting work in to accelerate or decelerate, then that will increase or decrease. In addition, your frictional losses and resistances are dependent on your velocity, so that will increase as well.

SO

W = Fnet * D. As you increase in slope, your Fnet increases due to the gravity equation, as you accelerate for reasons other than gravity, your Fnet will increase, and if your velocity increases, your Fnet will slightly increase due to friction. If you are going downhill, you will have less of an Fnet due to the direction of gravity (switching from positive to negative).

8. Condescending engineer is condescending. And wrong. Nutrition and calorie expenditure is way more complicated than a few basic physics formulas. Speed as a factor has much more to do with individual capacity for aerobic workload. The body is very efficient at shunting oxygen where it needs to go, but there's really only so much it can handle. When it fails at getting oxygen to muscles, you build up lactic acid and other metabolites from anaerobic metabolism.

Sorry, you sound like an asshole when you point at F = M*A (a formula learned by most high schoolers) and then proceed to overexplain a point and miss the most salient features.

9. I agree with Anonymous there: W = F.D is not adequate. It completely ignores the work done by muscle fibers, which occurs everywhere in your body, at different rates and stresses. You can't use F = ma for chemical transport or work inside the body.

10. I think every intelligent commenter on here agrees on two basic points:
1) the base physics are straightforward. F=mass x acceleration, W=mass x distance, etc.
2) the difficult part of estimating caloric expenditure has to do with human biomechanics and how all the different factors play into overall process(muscle mass and composition, VO2max, age, weight, sex, height, speed, slope, what I ate for breakfast this morning, etc. etc.).

For everyone else who can't get beyond concept of treating this an idealized mass moving in an over-simplified Newtonian physics class exercise, try to imagine the human body as simply an engine with an efficiency curve that relates power output/power input

ps - also an engineer ;)

11. Wow, Anthony Liberator is a complete idiot.

12. Both walking and running are so very inefficient as means of moving the human body forward that you can't readily assume basic physics will give you the correct answer. Take running. Try running on the spot. Notice that you are not moving forward but you are expending a lot of energy. That's because you are bouncing up and down, lifting your entire body up a couple of inches and then letting it fall. You are also lifting your chunky legs up and down. So there you are, running on the spot and not going anywhere - but still getting very out of breath. Cycling is far more efficient at using the human body to make forward motion - have a look at how many calories you burn moving on an exercise bike for 10km compared to using a treadmill. Even with cycling you are using a lot of energy just moving your legs up and down (and spinning the front wheel). You could create a bio-mechanical model for walking or running to gauge the efficiency in different situations, but probably measuring some typical cases is best.

3. Would a heart rate monitor help to verify these results? I'm not sure how I feel about HRM, but people swear by them. Thanks for the calculator! I've been looking for something that measures distance and altitude versus just time (I'm a slow hiker)

4. Question- the downhill portion is listed as the same energy use as walking flat. But don't you have to take into consideration the POTENTIAL ENERGY on the downhill portion as well? You are expending energy to slow yourself down (otherwise you would be going very fast by the end of your hike: MGH=1/2MV^2). It only makes a little bit of difference, but it should add up to a a few hundred calories on a significant hike, no?

1. I would think an estimate of walking flat on the downhill side is a good estimate. I agree with the prior comment that you expend energy to slow yourself down, however, there is less energy required to propel yourself forward as compared to flat walking... thereby cancelling out the energy expending in "braking" as you descend.

2. Anthony, are you a Bioengineer perchance? Human beings work off chemical energy, we're not an internal combustion engine. Energy expenditure still obeys the laws of physics, but there are more factors involved than the way you make it seem. Grand scheme of things, energy is conserved and it may seem intuitive to think of it simply as energy out regardless of HOW the work is done... but that's not a real life scenario.

The same way a car's fuel efficiency changes as it speeds up or slows down (Yes, cars get more efficient at around 50-60 mph, then start to lose efficiency if it goes lower or higher to air resistance). Human beings also have to account for different factors, we don't work in a vacuum, nor are we as efficient at producing work with energy as cars or rigid bodies.

5. Great questions.

@Anon #1: I use a HRM a lot, and recently I purchased a Garmin Forerunner 305, so I hope to "validate" the results by comparing across heart rates. But that will take a while. Heart rate does fluctuate but tends to be reasonable accurate especially as exertion gets higher - however it will also be affected by altitude so that would have to be considered.

@Anon #2: I agree with your rational...you can take a look at the paper that I referenced in the link in the first sentence - that is where I got the equation for work vs grade. In that study, they found a relationship for the downhill as well (all measured on a treadmill). Energy costs decreases until about a -10% grade, then begins increasing. On a real trail with less friction (and more muscle co-activation), I don't think the equation would hold. I would think going down a 20% grade would take more energy than the equation predicts. But the problem is I don't know (nor does anyone) really what the relationship is in realistic situations, so I am just using the standard flat mile rate, even though I don't believe it is that accurate.

6. My initial observations heart rate vs walking downhill: When the slope gets steep (20 - 25%), my heartrate slightly increases relative to 10-15% AND I am walking slower. Accumulated over the same distance, energy intake would increase on steeper downhill grades.

7. Really interesting, thank you!

How do fitness level or RHR factor into these types of calculations? You said there is individual variation, but is there any rough estimate, or percent correction that can be applied?

My RHR is ~42-44, and I log >50 miles, 12,000-18,000 ft delta elevation per week on trail. My caloric intake is typically ~2300/day, so it seems like I should have starved to death by now by the calculations here... LOL. I'd assume it was valid for me to straight factor down by what is no net weight change for me, but was wondering if there is any rough rules of thumb.

Also, are there any male/female differences for these types of calculations?

Thanks!

8. Hi,

I think its a complex issue not totally understood (and certainly not by me!). Here's a link at some articles with really good info:

http://www.bodyrecomposition.com/fat-loss/the-energy-balance-equation.html

http://www.bodyrecomposition.com/research-review/role-of-nonexercise-activity-thermogenesis-in-resistance-to-fat-gain-in-humans-research-review.html

There are a lot of variables that can change even when you think you've estimated how many calories you are burning / consuming. I don't think your RHR will affect your caloric expenditure during exercise much (although your resting metabolic rate will affect your RHR), since since exercise workload is dependent on things like bodyweight and efficiency. Fitness level will increase efficiency some, so if you maintain the same mileage over time, those miles might come from slightly fewer calories.

Outside of bodyweight distribution, I'm not sure how much gender affects estimates, but it could.

9. Very cool. Have you done any calculations to determine what kind of metabolic increase, in terms of calories, continues after a hike?

10. Love this, have not seen anything like it. How do you think calories burned would differ for women vs. men?

11. @Chris: there won't be much. unless doing intervals. lots of high intensity training could yield a decent metabolic increase post-hike, but I'd guess most people don't hike that way! but if you feel "warmer" than usual after a hike, you might have elevated metabolism. You could definitely "feel" like there is b/c you will be hungry from the deficit you created during the hike.

12. @Anon: There will be a difference due to bodyweight for sure. I don't know if there is significant differing "efficiencies" of hiking between genders that could make an additional difference

13. just found this on a google search --very cool. Just finished a 5 mile RT hike with an elevation gain of 1200 feet,burned about 700 calories. hooray!

14. I'm not sure gender per se would make a difference, but shouldn't height factor in? I'm 5' tall, and I obviously need to take more steps per mile than someone who is 5'9" (and fewer than someone who is 4'9"). Granted, I'm only bringing this up because this is such a marvelous calculator! Cool to see factors for elevation gain and weight carried.

15. Thanks for posting this... Most of the calorie calculators I've seen simply ask for the "number of minutes hiked" which is pointless... Hiking for an hour with 2000ft elevation gain is a completely different beast than walking a trail that only gains 200ft over the course of two miles.

FWIW - I know that I definitely burn more calories descending than if I were walking a flat course the same distance. It absolutely takes extra effort to keep oneself in control as you're making your way downhill.

1. It is very true, especially if there are scrambles to descend or a lot of rock to navigate.

16. I'm surprised its so hard to find a good scientific answer to this seemingly common question. The above calculator is best I've seen but its author admits limitations. I invite anyone with the motivation to see if perhaps NASA has done the relevant basic research in the course of determining exercise needs on-orbit. or maybe the Army has the data?

17. When you put a RT distance in, is that assuming you are doing an in and out hike rather than a loop? So, if RT is 9 miles you would add together the uphill and downhill calories to get total? or is this an "OR" relationship (either 9 miles all uphill or 9 miles all downhill)? Just want to make sure I'm looking at this correctly.

18. How would you factor in Age and Gender? Calories expended in any exercise is adjusted usually with those attributes.

19. I think something is wrong in the Incline calculation......taking an extreme example...you hike 2.12 miles (4.24 round trip) and gain 2 miles or 10560 feet in elevation. The calculator shows this as a 95 degree incline when 90 degrees or straight up is the max (in my example the incline would be 70 degrees. I view this as a right angle triangle problem where the hiking distance is the hypotenuse. Does this comment make sense or am I misunderstanding the problem?

1. It's percent grade, not degrees

20. I have worn a HRM for many years. I keep journals of each hike/climb (or bike ride) or other outing with elapsed time, min & max HR, and calories burned. (based on age, weight, gender inputs)
Over this time, consistent results emerge. For me, it was about 400 calories per hour uphill, and 150-200 down.
I even did splits occasionally with ascent & descent to ascertain expenditure downhill.
In a gym, on a elliptical, the machines reports far higher calorie burn than my HRM for same workout. They base it only on whatever you input- it has no way of knowing your fitness level.

21. "I'm not sure gender per se would make a difference, but shouldn't height factor in? I'm 5' tall, and I obviously need to take more steps per mile than someone who is 5'9" (and fewer than someone who is 4'9"). Granted, I'm only bringing this up because this is such a marvelous calculator! Cool to see factors for elevation gain and weight carried."

Yes you take more steps per mile, but they are not equal in effort to a tall person's steps. But you are right there might be a difference, and that would go with measuring % gross mechanical efficiency at different speeds. For instance, with running, research as found the optimal running speed for % efficiency is dependent on height - taller people have optimal efficiencies at different speeds than shorter people.

All that to say - there is going to be a difference. But it won't be major, perhaps a few % adjustment. Someday I'll look if there's any good data on that, and add it to the model.

22. @Erick: You input the total miles, and it assumes 1/2 are going for uphill, and 1/2 going for downhill.

23. "How would you factor in Age and Gender? Calories expended in any exercise is adjusted usually with those attributes."

A large portion of the effects of age and gender will be on the absolute amount of work / power performed, which is accounted for here via the explicit hike statistics and bodyweight. Now there will be some effect still, and if I go thoroughly through the research literature, I could add corrections for both. I would guess there would be slight decreases in expenditure with increasing age and female from male, but I'm not sure yet. Again, these differences would be a few % change in the estimates.

24. "I think something is wrong in the Incline calculation......taking an extreme example...you hike 2.12 miles (4.24 round trip) and gain 2 miles or 10560 feet in elevation. The calculator shows this as a 95 degree incline when 90 degrees or straight up is the max (in my example the incline would be 70 degrees. I view this as a right angle triangle problem where the hiking distance is the hypotenuse. Does this comment make sense or am I misunderstanding the problem?"

I am reporting the "percentage" % incline, which is different from the "angle" (degrees). % incline is defined as rise / run, or vertical distance / horizontal distance (x 100%)

25. Question here:

Is this the number of calories burned above and beyond the normal number of calories burned while sitting or is it the total calories burned?

In other words, let's see my calculation above shows that I burned 2000 calories on a hike. Is that 2000 calories above and beyond the calories burned if I had spent the time sitting on the couch or do I need to subtract my calories burned while sedentary to figure out how much weight I should have lost?

In my example above, I might burn 500 calories just sitting for a few hours. So would the actual calories burned on the hike really be 1500 calories--not 2000 because I'd be burning 500 anyway?

26. It took me a few minutes to figure out that I was supposed to add the uphill and downhill columns together. It would be helpful to add this to the instructions. Otherwise, thanks for the neat tool!

27. Question/Request:
I love the calculator - use it ever time I hit the trails. Is there anyway to add a extra digit space in the mileage? (now it seems like it accepts only 3 characters).

Thanks again!

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29. "I might burn 500 calories just sitting for a few hours. So would the actual calories burned on the hike really be 1500 calories--not 2000 because I'd be burning 500 anyway?"

Correct. For weight loss purposes, you often want to know how many *extra* calories you burned and that's how you'd go about it. Eg, if you have a 2000 kcal metabolism you burn 85 kcal every hour, and perhaps 100 kcal/hr during your waking hours. Subtract that from this produces.

30. @Sept 27: This is an estimate of caloric expenditure ABOVE resting expenditure.

31. It is interesting that I can estimate my total calories burned another way: I walk about 4 mph on level ground, and I can use the calculator at www.myfitnesspal.com to calculate calories burned per hour for my weight. For the two walks I have compared, if I multiply the time it takes me to take a walk at what _feels_ like 4 mph (but is actually slower because of the steep trails) by calories burned walking 4 mph on level ground, I get w/in 5% of what this calculator gives me. This is for medium-steep trails of the SF Bay Area with no backpack.

32. I've heard that using trekking poles increases calories burned on a hike. Here's a link that references an article on the topic. http://www.livestrong.com/article/313832-does-using-trekking-poles-really-burn-more-calories/. So would there be a way of calculating calories burned with poles?

33. I think its not clear - on steeper trails hiking poles may actually reduce energy expenditure. On level ground, yeah swinging your arms with more weight will increase expenditure (but not 40%!). Overall, I'd guess it would increase expenditure, but as a function of the trail grade. I'm not sure there's enough data to properly estimate it, but I'd have to look further.

34. interesting - for my own interest I've just calculated something - I noticed when I'm tired I would rather walk a few steps further around a kerb than step up on it, so I wondered the calorie difference.

from a quick google I've found/calculated these ballpark figures -

walking on flat ground - about 0.03 calories per step
climbing stairs - about 0.11 calories per step up (0.05 down)

So - a rough comparison of 0.11/0/03 suggests one step up (say a kerb) costs the energy equivalent of about 4 steps on the flat - which accords with my feeling, that when I'm tired I'd rather walk a few more steps on the flat than to lift/step up on a kerb.

So the suggestion is one stair step up uses the energy equivalent of about 4 steps on flat ground.

35. For those interested in this topic, I recommend an article in the July-August 2011 issue of ADIRONDAC, the journal of the Adirondack Mountain Club. The article, "Counting Calories" by Stuart Kelley appears on page 21 discusses the issue. Kelley supplies a nomograph to calculate calories burned on a round trip hike given the elevation gain. He gives his assumptions in the text.

36. The calculator is great fun. Thanks for doing the work to develop it and put it online.

Should non-pack, non-body weight be counted as body weight or pack weight? Boots, clothing, etc.

37. Great tool! It would be awesome if you could add a metric option as well for non-US visitors. Right now I have to make the conversion myself and that is ok, but if it was incoporated in the tool it would be really neat.

38. Hey thanks for the handy post! I did a bike tour from Anchorage Alaska down to Tijuana Mexico, and afterwords I was extremely interested in trying to figure out how many calories we had actually been burning per day--and I know how frustrating it can be trying to account for EVERY little variance that could effect the calorie burn.

"My RHR is ~42-44, and I log >50 miles, 12,000-18,000 ft delta elevation per week on trail. My caloric intake is typically ~2300/day, so it seems like I should have starved to death by now by the calculations here... LOL. I'd assume it was valid for me to straight factor down by what is no net weight change for me, but was wondering if there is any rough rules of thumb."

I personally have experienced this "phenomenon." I haven't ever really nailed down a definite number for average calories burned on an average day on our bike tour--but we were riding into strong headwinds every day, uphill and downhill on STEEP Alaskan/Canadian inclines, each carrying about 100 lbs. of gear and food on our bikes for an average of 75 miles per day over the course of about 12 hours each day. All I know is that we ate as much SPAM, Oreos, Nutterbutters, Twizzlers (and other high calorie foods) as we could handle, and we still each lost 30 lbs by the end of our tour. I started out with something like 26% body fat and 35% muscle, and ended up with 12% body fat and 47% muscle by the end. So in response to the above comment, it would SEEM like you would starve to death with a huge caloric burn like that, but somehow, your body adapts. Depending on which generic calculator you choose, it looks like we burned about 7000-10,000 calories per day. Supposedly, one burns a lb. of fat for every 3000 calories. It just doesn't seem like it adds up. One day I'll actually do the math to see how that measures up lol.

Until then, I am just happy to have your calculator here. :)

1. Sounds like an epic tour!

39. "Should non-pack, non-body weight be counted as body weight or pack weight? Boots, clothing, etc."

I would imagine the important thing is that you count the total weight somewhere--whether you put the weight of your clothes etc on your body weight, or in with packed weight. Usually when you are calculating caloric burn, you are taking into account the total amount of work output, which is directly related to how much weight you are moving around--including clothes, pack, water, etc.--not just how much you weigh naked.

1. I think the calculator weights (no pun intended) pack weight and body weight differently when doing the calorie calc; 200+20 pound pack <> 220 and no pack.

2. pack weight seems to be weighted less than body weight, which could make sense because less body mass means less energy dissipated as heat. i can put a 10lb weight in my pack but that 10lb weight will be inert and not experience a metabolic increase that your body would during exertion.

bw

40. Sorry for the delay in response. I haven't updated this blog in a year, and there's plenty more to add! The backpack is weighted slightly less than bodyweight, based on studies that estimated how much increase in energy expenditure there was for varying pack weights. Again, an approximation.

I will work on adding a metric calculator, plus some additional fun stuff.

1. +1 for metric calculator. Very interesting post )).

41. Sorry, just kinda new to this kind of stuff. Anyways, can anyone tell me what exactly is "base calories burned" in the calculator above? And is this "base calories burned" same as the BMR?

1. Sorry for the confusion. The "adjusted" calories is accounting for backpack weight, which is calculated slightly differently than bodyweight.

42. I just went down Mt. Meeker's south face (30-50% slope) and I'd rather walk 5 flat miles than do that single mile of descent over--I'm going to eat some extra pork rinds for the additional calories I think I may have burned.

On another note, it's said the Pike's Peak ascent is roughly as hard as a flat marathon, and your calculator matches that assertion pretty closely. Of course, nothing but easy trail <=15% on that hike.

-jb

43. Love your calculator - I've been doing over 30 miles a week hiking on day hikes. I am pretty skinny already but would like to know how much to eat to stay fit but not lose weight or muscle. This is helpful.

44. This calculator says I burn 200 calories less than all the other ones.

45. Have you done a simple physics analysis to compute the energy (in calories) that it would take to raise your weight vertically (elevation gain)? This is the minimum additional calories you would burn above your normal burn rate on level ground. You could then compute the percent increase in work versus wahat you consume walking on the level. This could then be converted into additional effective miles hiked. Using the reverse calculation on the downhill would have some problems as a fair amount of energy is consumed slowing yourself on each step to counter the effects of gravity. Your or anyone elses thougths? Is their someone with fresher physics ability than I that could do a sample computation? CK

46. Hi CK,

Yes I have done that on my own a bit for some single-instance calculations, but have not added that to the calculator. That's not a bad idea though to help give people a sense of the added mechanical work. However the pure physics approach does not included the gross mechanical efficiency - essentially the relationship between metabolic energy in (calories / minute) and mechanical energy out (watts) which will be ~ 25%, but will vary as a function of the grade.

47. no time/ speed this is so off

48. Have you calculated the effect of adding extra weight to a backpack causes in additional hiking time/

49. The pure physics approach, MGH*muscle efficiency, results in numbers that are quite similar to this and actual experimental data. Keep in mind muscle efficiency and movement efficiency is not exactly the same (you waste some energy just balancing, taking unnecessary steps, etc, so the use of 15-20% total efficiency is probably most reasonable for relatively steady climbs. Keep in mind in very cold conditions your body will spend a large amount of energy staying warm in addition to gaining elevation, and at high altitude you will burn that much more based on your heart and lung increased rates.

Thus summit day on Everest is commonly referred to as a 10-15,000 calorie day, while the same elevation gain at sea level on a nice day would be much closer to the simple MGH*efficiency calculation, or about 1,500 calories for a 175lb male.

1. Pure physics does not include an estimate for muscle efficiency or mechanical efficiency. Actual efficiency of uphill climbing will be higher than 15% (and higher than 20% if the trail isn't too loose).

I am interested in the very high altitude expenditure though. Do you have any references for those caloric estimates? I've been looking for that.

50. This may be a dumb question, but when I read a guide for a hike or a trail, I always assumed the distance cited was "as-the-crow-flies" from the start to the end of the trail, not the actual distance of the trail itself. So if I walk a trail that says it's 3.2 miles long, my GPS may read that I actually walked something like 6 miles (depending on the number of switchbacks, turns, etc). I've never tested this, so it may be an incorrect assumption.

My question is though, when you input distance into the calorie calculator, do you use a straight distance as-the-crow-flies from lowest to highest elevation, or do you input the actual amount of miles you hiked?

1. You should input the actual amount of miles.

51. Wow, this is interesting! Used my Garmin Forerunner 305 and heartrate monitor this morning on a hike. Went 5.7 miles roundtrip ascending 3350 ft. The garmin didn't seem to adjust for ascent or heart rate vs a flat hike. It said I burned 249 calories going up and 232 coming down. That couldn't be right!? Yesterday I took a hike for 3.18 miles ascending 1320 feet and it said I burned 250 calories (I forgot my HR monitor so it didn't have that information). Your calculator results 824 going up and 240 coming down on today's hike. Fascinating! Thanks for posting this!

1. No way you burned 249 calories going up 3350 ft! What was the time duration and your average heartrate on the uphill for each hike?

2. Ze,
I found your calculator working again with internet explorer, Yay!
I also noticed you had posted this question last fall, so I thought I would answer it.
It took me 2 hours 25 minutes round trip. My max hr was 165 and average 127 for the round trip. I didn't use the lap function on the garmin, so I can't say for sure the HR on the ascent alone, but looking at the graph, I'm confident my average going up was around 140.
Hope that's helpful information regarding the use of tools like the garmin, versus your calculations.
Thanks again,
Courtney

52. You calculate Average Grade [%] as:

Why do you divide distance by 2?

53. fyi, I have compared the results of this hiking calculator to my own estimates and those from the exercise walkers at the gym - the kind that go up to very high angles. I'm not sure which algorithm the exercise machines use, but the results of this calculator are within 10% almost always of the calculations I have used, and also of the gym machines. The gym exercise machines are great for burning a high amount of calories in less than half the time of the typical hikes I can endure. Thank you for your cool website, which I use daily!

1. The numbers shown by those machines have been thoroughly discredited, self promotion/profit, check Stanford,UCB, CSU, adinfinitum....

2. using somesuch treadmill at the gym set to a 20% grade, the display estimated ~200 calories/inclined mile (and its estimate varied a bit as a function of speed); this calculator suggests i was burning more like 375 calories/inclined mile. of course, the heart rate monitor in the hand grips said i was at 195 bpm (even though i was hardly exerting myself at 3.2 mph), which means i'm probably dead and don't need to worry about exercising anymore.

wb

54. There isn't technology capable of even making a reasonable estimate. Well, the tech is there, the cost would be horrendous. Heat expense, water, friction, temperature, etc, etc,.... I applaud your effort, I believe you could find a'very' moving average. Cheers!

55. I am not sure that this equation can take into account rolling hills. I may gain only 1000 feet of elevation, But I could go back and forth between 900ft and 1000ft 5 times. If that is the case it would really have to be calculated as 1500 ft of elevation. So to get an accurate reading don't we need to add elevation every time we head downhill and essentially re-climb a hill? Not to be critical this thing is actually quite helpful, I just figured I'd bring it up.

1. Hi Richard,

Yes you are supposed to enter the cumulative elevation gain. So you should put in the 1500 ft value.

56. I just scanned through the discussions above and didn't see anything specifically discussing eccentric muscle motion, for example lowering a 100 pound weight one foot. From a simplistic interpretation of physics, some would say doing this burns no energy; however, it should be obvious from experience that the resistance used in lowering the weight certainly tires the muscles! How can you measure the calories burned in this way?

1. Yes to eccentric calorie burning. It takes force to hold an object in place, or lower it slowly. Force = Mass*Acceleration.
I Hike an very difficult 6 mile trail yesterday, and sweated major on the down hill. Thighs and calves were working hard to resist gravity - burning actually.

57. Just did pikes peak... Up 7400 to 14100 It seems to me above 12k ft you burn a lot more cal. I could hike this at sea level and do 1k ft 7 times and I know it would be much easier. Am I all wet on thinking this?
Btw .... I love your sight and have shared it with many of my friends.

1. with the lower oxygen pressure, you might be using up more glycogen in your muscles than at sea level. That could certainly account for the increased exhaustion, but that's just a guess.

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59. Hi,

I read through the description page and the provided paper, yet I don't fully understand how everything works.
Am I required just to use the 'Adjusted Calories Burned' as a final estimate or use the sum of 'Base' and 'Adjusted'? If first is the case (use only the adjusted), then correct me if I'm wrong, but you calculate the calories burned in assumption of 'Flat Miles' and then scale the results according to climb to get the adjusted calories?

Also are you planning to release the second version of this calculator anytime soon? (asking as this one can't take more than 3 symbols in milage field [14. is as much as I can type so, for instance, 13.6 and 14.4 is then ~14 which is just an extra error :/ ].

All in all thanks for doing work in this field and providing this useful tool as there's definitely lack of them on the internet. Hopefully you can help me with my questions.

Cheers,
Ben

1. Sorry for the extremely late reply. The "Base" considers just your bodyweight, while the "Adjusted" includes the backpack. This is confusing for no good reason so I apologize!

The Equivalent Flat Miles is just an estimate of how many miles it would take you to burn the same number of calories as the Adjusted estimate.

60. Everyone thinking that Speed has anything to do with calories burned hiking. It doesn't, not with running either. The reason is that wind resistance is negligible for walking and running. Same person burns the same calories running a mile as walking a mile.

Speed is a factor for BICYCLES, that is Correct. But not for walking, or even running.
- Rocket Scientist. Bazinga.

P.S. Love the blog.

61. Someone asked about the weight of boots - I recall reading that 1 lb on the foot = x lbs on the back. Not sure of the exact number. This is because the foot is raising and lowering the boot with every step. So I would include the weight of boots in body weight. I also read somewhere a very long time ago that in winter hiking, the additional clothing worn adds to the caloric burn, due to it's resistance/confining nature. So I was told to keep food in my pocket and eat continuously in order to maintain energy for heat and climbing.

1. You are correct, this is something to consider. Heavier boots will have a larger effect than just adding their weight. For instance, a 1 lb increase in boot weight might be equivalent to 5 lbs additional backpack weight.

62. I would assume that the calories burned WOULD change depending on your pace, specifically whether you're working in an aerobic or anaerobic state. The body uses energy differently depending on the workout intensity/speed, and will use more or less energy to move your body the same distance. It's a difference in efficiency, much like a car.

1. There are multiple things in play. You are right about changing from aerobic to anaerobic, but that doesn't change total calories burned (there is a blog post on this). Movement efficiency does change some at different speeds, but it is hard to quantify for uphill / downhill and not that big of a difference.

63. I found this post while following up on a trail conversation between a physicist and an engineer coming off Mt Washington last weekend. The opening gambit: "why don't I get just as hot descending as ascending, when the potential energy that I added on the way up, I dissipated on the way down". Where does all that energy go on the way down? Have fun with this. (and your descent == flat trail assumption clearly cannot be correct)

1. It can be correct. The simple physics view ignores musculoskeletal mechanics. The human body cannot descend downhill without expending energy.

Imagine the body as a car. The car has a gas pedal, and a "brake pedal" that really also use gas to move you in the reverse direction. With each step, the human body is hitting the reverse pedal to slow down...then accelerate again, then slow down...each time using energy.

Unless you want to jump off a building, then you can descend with using up an energy.

64. Any chance of you producing a version of your calculator to download and use on a PC ?

1. I'm working on an app version.

2. It would be great if your calculator could be used by 'WalkJogRun' as they attempt (very badly) to estimate calorie usage for created routes, but appear to do it without taking ascent into account even though they do calculate ascent and descent.

Re calorie usage on decent. It is quite obvious that energy is expended as the body fights against gravity (the only efficient way to descend is to descend from a rooftop at a gradient of -90 degrees, whilst making no lateral progress) . Any walker knows that the thigh muscles get a good workout on steeper downhill terrain and are thus consuming energy.

I did expect that there is a quite linear relationship between gradient and extra energy requirement. However, people who scree-run and fell-run will often tell you that theirs is a more efficient method of descent (they use their speed and skill to descend quicker, resisting gravity far less than someone moving very slowly holding their weight for long periods between downward steps). In the end, I believe that downhill calorie consumption is largely controlled by the individuals skill level.

65. Thanks for doing doing this.

I also read through all the comments. I enjoyed all those who didn't like what they read (the results they got), those who failed to read at all, those who over think this stuff, but most of all I enjoyed the intelligent discussion.

Thanks again for taking the time to put this together and to maintain it.

1. You're welcome!

66. I made up a list of my 55 favorite hikes in Rocky Mountain NP a few years ago, but never had a real scientific way to sort them before I found your website. After calculating the amount of calories I use for each hike, I had to rearrange my hikes. Thanks a lot for coming up with this calculator. The only recommendation I would have is to allow tenths of miles for hikes over 10 miles to avoid having to do interpolation.

67. I don't dispute that this is a reliable way to calculate calorie use, but after looking at the results I got from comparing 55 of my favorite hikes in Rocky Mountain National Park, I'd have to say I'm a little skeptical that it's a good way to compare hikes. In the past, I have equated walking one mile on flat ground to about a 300-foot gain in altitude. Using this calculator, if I walked a total of one mile with a gain of 500 feet, I would use the same number of calories as if I had walked 2 miles on flat ground. The problem is that I know that it takes a lot more effort for me to climb uphill 500 feet in a half-mile and then work my way back down to where I started than it does for me to cruise along for a couple of miles on flat ground. It may be an altitude thing, because the higher you are, the more effort it takes to go uphill. But if you're at 11,000-foot altitude, I think most people would think twice before taking a one-mile shortcut that would take them 500-feet up and down.

1. Intensity will certainly be higher (esp. at altitude) and you will be done sooner. But the total number of calories burned will be similar. What if you ran that 1.5 miles?

68. Being on a low cal diet right now, down about 50% of normal, I've read that your metabolism will decrease as you starve. I wonder if this plays any part in calculating calories burned?

1. You are correct, but it shouldn't matter too much in this context. The drop in bodyweight will have a significant effect.

69. I am planning on hiking the John Muir Trail in September (2014) and would be interested in the Calories burned per each day so I can determine the food I will need. My question is since the calculator is based on round trip, do you have the equation that I can use to determine the thru-hike expenditure?
Thank you,

Gary Schlageter
gary@opensystem.com

1. I'm also interested in how to use your web-calculator for a non-round-trip hike. Thanks!

2. Hi Gary,

We'll see if I can to it, but in the meantime, you could do this slightly tedious method:

Let's say it's a one way hike of 50 miles, 12000 ft gain, 4000 ft loss

Divide your total miles by 2 = 25 miles

Enter 25 into the Distance. Enter your upward gain (12000 ft) into the elevation. Grab the Uphill Calories burned.

Then, change the elevation gain to the elevation loss value for your hike (4000 ft, make it positive). Grab the Downhill Calories burned.

Sum the 2 calories burned values.

70. I'm not sure if you know about 'Naismiths rule', but this has been used for a very long time as a very rough and ready calculation of expected time of hike based on distance and height gain. The calculation is 1 hour for every 3 miles distance plus 1 hour for every 2000 feet of ascent - many people conclude that Mr Naismith was a very fit bugger!

Anyway, as a test I plugged in a 6 mile flat walk and a 6 mile walk with 2000 feet ascent into your calculator. According to Naismith the one with ascent should take 50% more time to complete than the flat walk (3 hours versus 2 hours). It is quite reassuring that your calculator gives, for my weight, a calorie use of 1342 for the hill walk versus 824 for the flat one - an increase of 62%. i.e. the calorie use given by your calculator is quite closely in step with the extra time required according to Naismiths rule.

71. Thanks for the calculator. I get about 118 calories per level mile plus 20 per 100 feet of gain. I have always wondered about how to adjust my hiking logs for elevation change.

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73. Hi Zé,
Do you mind sharing your calculation formula and how it was produced?

74. Thank you. Great job with with the calculator. My observations over 40 years is that efficiency appears to play a bigger role on the trails and fells than on a normal ground level walk. I also suspect that there is a wider range of individual skill and subsequent efficiency while depending than ascending. As Nigel C stated about fell running that is undoubtedly less energy consuming way of descent but takes skill to carry it of. As they flow down hill leaning forward stacked over their feet. Very impressive but a thing of the past for me. My 62 year old preference for easy does it and staying vertical is undoubtedly more energy consuming. I am less efficient year by year as my skill declines with decreasing balance and reaction time. But gravity is getting stronger yea that's the answer :-) Thanks again.

1. Hello, I so totally agree! Especially walking down I have the feeling it has a huge impact...

75. Hey, Thanks for the calculator. It's so much better than the one that comes with my fitness program Cheers!

76. Thanks a bunch for making this and putting it up. It helps supplement my approximations of food I will need on my really long treks!

77. Without getting too nerdy, my general experience based on many calculators and personal weight loss over 5 years is that climbing steep grades (700-800 ft/mi) at a brisk pace (3-4mph, 15-17min/mi) and running back down them at a moderate pace (8min/mile) burns about 30-35% more calories than running on flat terrain at 7-8mph. I would definitely add 10-20% to the counter here for a moderate downhill run. Hope this helps!

78. So i only need to eat 13 3000 calorie meals to walk 900 miles mostly uphill (aka barefooting the mountains of norway) at ~2mph... This is vastly less than i thought would be needed

1. If you type in 900, it is assuming round trip mileage. If you then only look at the uphill data, that is basically for 450 miles.

79. I like this calculator. It's a good incentive for my wife and I to get out walking. Despite the physics I have my doubts about the accuracy however. I walked the CMD Arete route up Ben Nevis back in May. Ice axe crampons. the works. I was shattered when I finished took me 8.5 hours of constant hard graft to reach the summit and 3 hours to trek back down. total route is 11 miles and 1700m of climbing. A few weeks back I walked 22 miles on Dartmoor and did 1050m of accents. That walk was a doddle in comparison. Only took 8.5 hours in total. Yet the calculator says I burned far more calories on that walk. Trust me I burned far more on Ben Nevis. I would assume it's the terrain that made the difference, so would suggest that is a big factor in this calculation.

1. You are right it does not account for terrain. I have much personal experience with what you described! I originally added a scaling factor for terrain, but I simply don't have the empirical data to support what coefficients to attribute to different terrains.

80. Thanks for this page! One question - I entered nine miles round trip, but the results say uphill 9 miles and downhill 9 miles. Shouldn't it be 4.5 miles for each?

81. Does elevation have any bearing, meaning if my hike is 4000 or above, my heart seems to be working a bit harder.

82. This is fucking retardedly off. I hiked 9 miles with 75lb pack and you're telling me I burned 600 calories?!

I would burn 100 cals per mile just walking with NO backpack. Thats 900 cals WITHOUT my 75lb pack.