## Is there a way to calculate how much calories are burnt when you run?

Question

I want formulas. I know that kinetic energy equals 1/2mv2, could it be calculated with this? Let s say for instance that I run 500 meters in a time 500 seconds. How would I calculate it then and what formula would i use?

Update: I am not interested in running and burning calories in real life. I’m just curious about the formula

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General Physics
4 years
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## Answer ( 1 )

Two people doing the same race in the same time could have greatly different amounts of food energy used.

There are complicated formulae on the web using heart rate but I know that one of them is wrong.

The one published for females shows that the heavier a woman is the LESS energy is used.

Clearly this is incorrect. But most heart rate monitors are programmed like this and give incorrect results when the female setting is chosen.

To get to the amount of energy used in moving is a little easier.

You have a leg which is a distributed mass which must be swung and accelerated for each stride.

The human body is incapable of returning this energy as the leg slows so to get the energy you have expended just work out the number of strides taken.

Then the “average” velocity of the leg at each stride

And the mass of the leg. Do 1/2 m v^2 for each leg at each stride.

So far this is “easy”

But you do need to add in the amount of “bounce” How much your body raises and lowers on each stride.

Now if you want to work out the calories used you need to know your efficiency.

That might be below 14% for an unfit person up to perhaps 28% for an athlete in training.

Which means that for every Joule used to move the muscles you require somewhere between 3 and 7 joules of food.

I don’t run. But I train on a bike a lot.

My efficiency has gone from around 20% up to around 26% so the same ride at the same speed takes about 75% of the calories that it did early in the training period ( as measured by VO2 measures ).

More efficient style and equipment means that I use only around 70% of the energy in various losses.

So that according to the heart rate monitor an hours hard riding used to take around 700 calories.

Now the same ride in an hour takes about 450 calories.

Riding faster and harder means I do it in less time so it might reach about 550 calories for a full paced ride.

Now how does this relate? If your body was a similar size and mass to mine ( 75 kg) and you were a similar fitness then you are using about 100 calories for each 10 minutes of hard high intensity activity.

Or perhaps 60 calories in the same time for a laid back easy jog.