# Running Calorie Burn Calculator

This running calorie burn calculator estimates the calories that you burn while running any given distance. The calculator takes into consideration the grade of the running surface that you are on (i.e. the incline or decline), whether you are running on a treadmill or not, and your fitness level. The incline or decline of the running surface is taken into consideration because more calories are burned as the incline of the running surface increases, and less calories are burned as the decline of the surface increases (until -10% grade, beyond which any further decline will cause an increase in calorie burn, similar to the effect of increasing the incline). Whether or not you are running on a treadmill is taken into consideration because treadmill runners do not need to overcome air resistance and therefore consume slightly less energy than those running on solid ground. Fitness level (measured through VO2max estimation) is taken into consideration because there is a known negative correlation between VO2max and energy cost of running (i.e. with increased fitness, or VO2max, you will burn less calories to run a given distance).

## Method

This running calorie burn calculator is based on equations (shown below) derived by ShapeSense.com from experimental data gathered by R Margaria, P Cerretelli, P Aghemo, and G Sassi for their study titled "Energy Cost of Running." The experimental data gathered by Margaria et al. measured calorie burn of subjects running on a treadmill at various speeds (from 9 to 22 km/hr) and running surface grades (from 20% decline to 15% incline). It was found that the net calories burned per kilogram of body weight per kilometer run is independent of speed, and depends only on the incline or decline of the running surface and the cardiorespiratory fitness level (measured through VO2max) of the runner. There is, therefore, no need to take running speed into consideration when estimating calories burned while running. You simply need to know the total distance run, the weight of the runner, and the incline or decline of the running surface. If the cardiorespiratory fitness level of the runner is known it will allow you to further refine your estimation of calorie burn because there is a known negative correlation between VO2max and energy cost of running. For this running calorie burn calculator, cardiorespiratory fitness level is estimated through VO2max estimation, based on the runner's 20 second resting heart rate, per the relationship defined by N Uth, H SÃ¸rensen, K Overgaard, and PK Pedersen in their study titled "Estimation of VO2max from the ratio between HRmax and HRrest--the Heart Rate Ratio Method." For the Uth et al. estimation of VO2max an age based estimation of maximum heart rate is made according to the method suggested by H Tanaka, KD Monhan, and DG Seals in their study titled "Age-predicted maximal heart rate revisited."

Apart from the running calorie burn considerations discussed above, this running calorie burn calculator also takes into consideration the absence or presence of air resistance while running, based on whether or not the runner is on a treadmill (i.e. no air resistance to overcome) or solid ground (i.e. air resistance must be overcome). A study titled "The influence of wind resistance in running and walking and the mechanical efficiency of work against horizontal or vertical forces," by LG Pugh, has shown that there is an increased energy cost of running on a solid surface, as opposed to on a treadmill, due to air resistance. Therefore, apart from the considerations described in the first paragraph above, this running calorie burn calculator also takes into consideration whether or not the runner is on a treadmill.

## Equations

### Running Calorie Burn Equations

*For - 20% ≤ % Grade ≤ - 15%:*

- CB = (((-0.01 x G) + 0.50) x WKG + TF) x DRK x CFF

*For - 15% < % Grade ≤ - 10%:*

- CB = (((-0.02 x G) + 0.35) x WKG + TF) x DRK x CFF

*For - 10% < % Grade ≤ 0%:*

- CB = (((0.04 x G) + 0.95) x WKG + TF) x DRK x CFF

*For 0% < % Grade ≤ 10%:*

- CB = (((0.05 x G) + 0.95) x WKG + TF) x DRK x CFF

*For 10% < % Grade ≤ 15%:*

- CB = (((0.07 x G) + 0.75) x WKG + TF) x DRK x CFF

where

CB = Calorie burn (in calories)

G = Grade of the running surface (expressed as an integer number, i.e. -10)

WKG = Weight (in kilograms)

DRK = Distance run (in kilometers)

CFF = Cardiorespiratory fitness factor (see description below)

TF = Treadmill factor (see description below)

### Determination of Cardiorespiratory Fitness Factor (CFF)

The intent of the cardiorespiratory fitness factor (CFF) used within this running calorie burn calculator is to account for fitness level of the runner since, according to the Margaria et al. study, "athletes can perform better not so much because of their greater skill as for their greater capacity for oxygen consumption." Essentially, a runner with a high VO2max will burn approximately 5% to 7% fewer calories while running than a runner with a low VO2max. To determine the cardiorespiratory fitness factor, CFF, an estimation of VO2max is required. VO2max is estimated based on the runner's resting heart rate, per the relationship defined by Uth et al., as shown below:

VO2max = 15.3 x (MHR/RHR)

where

VO2max = Maximum oxygen consumption (in mL•kg^{-1}•min^{-1})

MHR = Maximum heart rate (beats/minute) = 208 - (0.7 x Age)

RHR = Resting heart rate (beats/minute) = 20 second heart rate x 3

Once VO2max is known, the cardiorespiratory fitness factor, CFF, is assigned as follows:

*For VO2max ≥ 56 mL•kg*

^{-1}•min^{-1}:- CFF = 1.00

*For 56 mL•kg*

^{-1}•min^{-1}> VO2max ≥ 54 mL•kg^{-1}•min^{-1}:- CFF = 1.01

*For 54 mL•kg*

^{-1}•min^{-1}> VO2max ≥ 52 mL•kg^{-1}•min^{-1}:- CFF = 1.02

*For 52 mL•kg*

^{-1}•min^{-1}> VO2max ≥ 50 mL•kg^{-1}•min^{-1}:- CFF = 1.03

*For 50 mL•kg*

^{-1}•min^{-1}> VO2max ≥ 48 mL•kg^{-1}•min^{-1}:- CFF = 1.04

*For 48 mL•kg*

^{-1}•min^{-1}> VO2max ≥ 46 mL•kg^{-1}•min^{-1}:- CFF = 1.05

*For 46 mL•kg*

^{-1}•min^{-1}> VO2max ≥ 44 mL•kg^{-1}•min^{-1}:- CFF = 1.06

*For VO2max < 44 mL•kg*

^{-1}•min^{-1}:- CFF = 1.07

### Determination of Treadmill Factor (TF)

The intent of the treadmill factor (TF) used within this running calorie burn calculator is to account for the presence or absence of air resistance. If the runner is on a treadmill he or she does not experience air resistance while running and therefore burns fewer calories than a runner that is running on solid ground. For a person running at a typical casual runner's pace of 2.5 meters per second (9 km/hr, or 5.6 mph) it can be shown, based on data collected by LG Pugh for the study titled "The influence of wind resistance in running and walking and the mechanical efficiency of work against horizontal or vertical forces," that the energy cost of air resistance while running on solid ground is *roughly* 0.84 calories per kilometer (this is equivalent to approximately an extra 1.2% calorie burn relative to a runner on a treadmill). The value of 0.84 calories per kilometer *assumes* a typical running speed of 2.5 m/s and no wind (i.e. the extra calorie burn is caused by the runner having to "push" through still air while at running 2.5 m/s).

*For a runner on a treadmill:*

- TF = 0

*For a runner on solid ground at an assumed typical running speed of 2.5 m/s:*

- TF = 0.84

Margaria R, Cerretelli P, Aghemo P, Sassi G. Energy cost of running. J Appl Physiol. 1963 Mar;18:367-70.

Uth N, SÃ¸rensen H, Overgaard K, Pedersen PK. Estimation of VO2max from the ratio between HRmax and HRrest--the Heart Rate Ratio Method. Eur J Appl Physiol. 2004 Jan;91(1):111-5.

Tanaka, H., Monhan, K.D., Seals, D.G., Age-predicted maximal heart rate revisited. Am Coll Cardiol 2001; 37:153-156.