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I am trying to figure out a way to calculate the number of calories burnt running. Before I do on to explain how I am doing this, I realize that there are many calculators out there that will do this for me, my interest is in finding out how this is calculated. I have had some conversations with a friend of mine that knows enough on this subject and his argument is that it does not matter how fast you are moving, what matter is how much you weight and the distance you travelled. In other words by his take, you would burn the same amount of calories by walking a mile in 60 minutes or running that mile in 12 minutes.

I had read many posts that support either side of this issue, some agree with the statement above others say that it is innacurate and that straining yourself, accelerates your heart rate (thus your metabolism) and you end up burning more calories in the end.

So i thought I'd try to figure out the physics behind the issue. These are the formulas I am using:

Work (joules) = Force (N) * Distance (m)

Force (N) = Acceleration (m/s^2) * Mass (Kg)

Acceleration (m/s^2) = (2 * Distance) / Time^2 (s)

These are the units of convertion I am using

1 Mile ~= 1609 Meters

1 calorie ~= 4.18400 joules

1 pound = 0.45 Kg

This is a sample calculation.

Test Weight = 200lbs = 90.71Kg

Distance Travelled = 1 Mile = 1609 meters

Time spent = 31 minutes = 1860 seconds

Acceleration = 3218.688 (m) / 3459600 (s^2) = 0.000930364 (m/s^2)

Force = 0.000930364 (m/s^2) * 90.7184 (Kg) = 0.084401152 (N)

Work = 0.084401152 (N) * 1609.344 (m) = 135.8304876 (J)

Calories = 135.8304876 / 4.18400 = 32.46426565

Ok so, with those numbers if the calculations are correct, i could say that if I ran for 31 minutes at any speed rate that would amount the distance to a mile I would burn 32.46 calories. However, if i keep everything else the same except that this time I took 60 minutes to reach the mile (more like a slow walk). Then my numbers are:

Acceleration = 3218.688 (m) / 12960000 (s^2) = 0.000248356 (m/s^2)

Force = 0.000248356 (m/s^2) * 90.7184 (Kg) = 0.022530419 (N)

Work = 0.022530419 (N) * 1609.344 (m) = 36.25919404 (J)

Calories = 36.25919404 / 4.18400 = 8.666155

Does this disprove that the whole concept of weight & distance will constantly give you the same results as far as calories used regardless of speed travelled? or are my calculations incorrect?

My friend pointed me to this calculator http://www.bodybuilding.com/fun/calories.htm and although they use speed to calculate calories burned (probably used to calculate distance) you can see that if you enter in 200lbs as the weight and 60 minutes as the time (select popular cardio exercises) in the results page: it says that running 10 mph (6 min/mile) burns 1524 calories and running 5 mph (12 min/mile) burns 762 calories, and it makes sense since at @5mph you cover half of the distance. My two questions here are how come my calculations do not reflect that? should't travelling a mile in 60 minutes only half the 32 calories burn at 31 minutes and produce a result of 16? Also I've tried to compare the same numbers as bodybuilding.com for instance running 5 miles in 60 minutes, and my numbers come back as only 216 calories used but bb.com comes back as 762. I also just noticed that using the bodybuilding.com calculator with the same numbers as before (200lbs and 60minutes) walking, @2.5 mph, burns 286 but running 5 mph (12 min/mile) burns 762 calories since the distance covered walking is half of that covered when running, shouldn't the calories burned be 381? Is there a different way to calculate all of this that does not include the formulas above?

Any help at all would be appreciatted. Thanx!

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# Calories used running

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