# 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.

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.

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 :)

Pretty late to the party on this one but thought it was worth adding that the JavaScript behind the runners world calculator is pretty simple. Looking at the function toolSubmit (which is called when the "Calculate" button is clicked) it's clear that it calculates calories burned as:

calories burned = distance run (kilometres) x weight of runner (kilograms) x 1.036


This is rounded to a whole number and then formatted as the message displayed in the browser.

• Ha, interesting. Presumably the constant (1.036) is based on something like the MET tables mentioned in fitness.stackexchange.com/a/25564/7397 – DilithiumMatrix Aug 29 '17 at 22:48
• @DilithiumMatrix perhaps it's using the MET tables, but I'd bet a 3.6% discriminant is an act of laziness more than anything else. It's likely the programmer was given a set of distances, weights and calories and they just changed this constant by +/- 0.1% until it fit reasonably well. These kind of sets are what drives a lot of calorie logic on treadmills. It's worth taking away from this that a lot of these calculators are really poorly written. This one was just easy to see how poorly written it is. – edwardc Nov 11 '18 at 9:55

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.