# Energy expenditure (calories burned) equation for running

There are numerous online calorie calculators for running (e.g. from runners world). What is the underlying formula for calculating energy expenditure while running? This post has an excellent answer for the analog of calories burned throughout the day.

-
– arober11 Jul 3 '15 at 18:49
– arober11 Jul 3 '15 at 18:49
– arober11 Jul 3 '15 at 19:59
– arober11 Jul 3 '15 at 20:17

Worth noting, without data from an ECG (heart rate monitor) and face mask based gas analyzers, along with details of the gradient, wind speed, and surface there aren't any accurate equations.

The best you can do is to estimate a VO2 (mL·kg-1·min-1) figure, and convert that into a Kcal one:

Kcal/Min ~= respiratoryExchangeRatio * massKg * VO2 / 1000

Note: respiratoryExchangeRatio is 5.0 for blood sugars, but drops to 4.86 for freeing energy from fat, so if the run is of more than a few min's use this.

Personally I prefer the ACMS Running VO2max equation, as it's relatively simple, will give a number that's accurate within: +/-14.5%, though the conversion to Kcal will multiply the error by a bit, and it's recommended in the paper: Energy Expenditure of Walking and Running: Comparison with Prediction Equations, Hall et Al, 2003

For running, the Léger equation and ACSM prediction model appear to be the most suitable for the prediction of running energy expenditure.

So we have:

VO2 = (0.2 * metersMin) + (0.9 * metersMin * fractionalgrade) + 3.5

on the flat, this equates to:

VO2 = (0.2 * metersMin) + 3.5

The Léger equations is simpler, but does not account for gradient:

V̇O2 = 2.209 + 3.1633 * kph

Though a not dissimilar degree of accuracy is claimed by the MET tables and formula, and is even simpler:

Kcal ~= METS * bodyMassKg * timePerformingHours

Where MET is short for Metabolic Equivalent of Task, and is just an abstract way to quantify the relative energy cost of an activity, a number of sites offer MET estimates for specific activities eg.

-
This is fantastic! Thanks so much – DilithiumMatrix Jul 22 '15 at 14:08

I googled a bit and stumbled upon the following formula. The source claims it's from Journal of Sports Sciences.

Men use the following formula:

Calories Burned = [(Age x 0.2017) + (Weight x 0.09036) + (Heart Rate x 0.6309) -- 55.0969] x Time / 4.184.

Women use the following formula:

Calories Burned = [(Age x 0.074) -- (Weight x 0.05741) + (Heart Rate x 0.4472) -- 20.4022] x Time / 4.184.

Calculation

For example, here’s my formula based on a 49 year old male weighing 155 for a workout where my heart rate averages about 148 bpm throughout a 60-minute FitCamp workout.

[(49 x 0.2017) + (155 x 0.09036) + (148 x 0.6309) – 55.0969] x 60/4.184 =

[9.8833 + 14.0058 + 93.3792 – 55.0969] x 14.3403 = 891.47 calories (or 15 kcal/min)

This is the most comprehensive (and quite recent) formula I could find, which takes in account many factors that others don't (age, heart rate etc.). Hope it helps :)

-
This looks great! Thanks. I just don't get why there aren't more comparable things for running explicitly. – DilithiumMatrix Mar 27 '14 at 17:11
I'd double check the formula above, as a quick Google shows the supposed male formula being used in an all female study: COMPARISION OF ENERGY EXPENDITURE DURING WALKING AND RUNNING ON TRACK BEFORE AND AFTER TRAINING IN YOUNG HEALTHY ADULT WOMEN, Note: both the site and the paper are vague as to the origin of the formula. – arober11 Jul 3 '15 at 18:58

It depends, there are quite a few different formulas available, depending on who was doing the research, and when it was performed. To some extent, the method used to determine the calories burned can have an effect on the formula.

http://www.stanford.edu/~clint/Run_Walk2004a.rtf

That is a link to a published study from Syracuse University, comparing several different methods of calculating calorie burn. If you are looking at a watch, treadmill or other device that is measuring it for you, somewhere in their literature they should be describing what method they are using.

-