# Prediction Equations for Running Energy Expenditure

## Introduction

A common question poised to me since I'm "the math guy who is a fitness nerd" is: "How can I tell how many calories I'm burning?" Well this article will tackle what I have found or extrapolated from some of the literature available to me specifically on running.

## Method 1: National Strength and Conditioning Association

Using Table 4.2 found on page 76 of the NSCA’s Guide to Tests and Assessments running can be estimated if you know: (1) speed in meters/min, (2) percent grade as a decimal, and (3) weight in kg. Respectively denoted S, G, and W in the equation below.

Calories/min≈0.005*W*(0.2*S + 0.9*S*G + 3.5)

Example: A 180lb. (81.65kg) person ran a 16:00 2mi (3,218.688m) on a track (G=0). Therefore:
Calories≈16*0.005*81.65*(0.2*201.168 + 0.9*201.168*0 + 3.5)≈286

## Method 2: Metabolic Equivalent of Tasks

The 2011 Compendium of Physical Activities has come out with a large amount of data to determine calories for various exercises. Section 12 focuses on running. Using a Sextic Regression produces the below estimation with an R^2≈0.9972285. S is speed in MPH.

MET≈0.000537581699302*S^6 - 0.028452488685417*S^5 + 0.603305681198265*S^4 - 6.51203242807151*S^3 + 37.4611917042903*S^2 - 106.824410216861*S + 123.207132971046

The equation to apply METs to find out out calories is:

Calories/min=MET*(Weight in kg)/60

Therefore, the combined equation is:

Calories/min(0.000537581699302*S^6 - 0.028452488685417*S^5 + 0.603305681198265*S^4 - 6.51203242807151*S^3 + 37.4611917042903*S^2 - 106.824410216861*S + 123.207132971046)*(Weight in kg)/60

Example: A 180lb. (81.65kg) person ran a 16:00 2mi (3,218.688m) on a track. Therefore:

Calories≈16*(0.000537581699302*7.5^6 - 0.028452488685417*7.5^5 + 0.603305681198265*7.5^4 - 6.51203242807151*7.5^3 + 37.4611917042903*7.5^2 - 106.824410216861*7.5 + 123.207132971046)*81.65/60≈247

I should note that the American College of Sports Medicine has a slightly modified version of the formula above.1 Instead of dividing by 60 you multiply by 0.0175. So, it's 5% flat increase comparatively. In the example the total calories would've come out to 259.

## Method 3: Traditional Rule of Thumb

I have seen this method in various books, even at one point in a military physical fitness regulation (I'd link it if I knew which one). The method is you burn 1 calorie for every kg of bodyweight per km walked or ran. So, actually it's a two for one deal!

Example: A 180lb. (81.65kg) person ran a 16:00 2mi (3,218.688m) on a track. Therefore:

Calories≈3.218688*81.65≈263

## Method 4: American Council on Exercise

The American Council on Exercise has a Physical Activity Calorie Counter Calculator on their website. Putting a good amount of data through it in August 2018 and using various regression equations I found that a Power Regression was the best fit. See the short PDF here. The equation uses weight in pounds and speed in MPH.

Calories/min≈0.01232*W*(S^1.003)

Example: A 180lb. (81.65kg) person ran a 16:00 2mi (3,218.688m) on a track. Therefore:

Calories≈16*0.01232*180*(7.5^1.003)≈268

## Conclusion

As you can see the numbers vary a bit and you should expect it to do so. They are all based on certain data sets and humans have an expected deviation amount. Thus, the estimations should as well. Regardless, you now have four methods to choose from to give you some estimation for your caloric burn from running.

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