# Calculate burned calories (Running) without heart rate [duplicate]

I need some formulae to calculate the burned calories for jogging. The information I have would be: gender, weight, age, pace (speed), fractional grade, and time.

What I have now is the following formulae:

``````VO2 = 0.2 * speed + 0.9 * speed * fractional_grade + 3.5
kcal/min = 5 * weight * VO2/1000
// weight in kg, speed in meters/minute
``````

Does anyone has a better formulae that also takes gender and age into account?

• Jun 21, 2015 at 18:44

Running calorie burn doesn't change so much with age and gender. Because its about the work you did physically.

There is a non-linear relationship between walking speed and rate of calorie burn. Essentially what this means is that total calorie burn while walking depends on both the distance that you walked and the speed at which you were walking. This makes calorie burn while walking slightly different from calorie burn while running, which is only distance dependent (i.e. while running it doesn't matter what speed you run a given distance, you will burn the same amount of calories as long as the distance is the same). That's why this walking calorie burn calculator must take into consideration both walking time and walking distance, whereas our Running Calorie Burn Calculator only requires distance as an input.

## Method

For a walking surface grade between -5% to +5% inclusive, this walking calorie burn calculator is based on equations (shown below) derived by ShapeSense.com from experimental data displayed in Figure 3 of the study titled "Energy Cost of Running," by R Margaria, P Cerretelli, P Aghemo, and G Sassi (note that the data on walking energy expenditure was originally printed in the study titled "Sulla fisiologia, e specialmente sul consumo energetico, della marcia e della corsa a varie velocita ed inclinazioni del terreno," by R. Margaria). The experimental data gathered by Margaria measured calorie burn of subjects walking at various speeds and on various surface grades. It was found that there is a non-linear relationship between walking speed and rate of calorie burn, as opposed to calorie burn while running, which displays a linear relationship between speed and rate of calorie burn.

For a walking surface grade between +6% to +15% inclusive, this walking calorie burn calculator is based on the American College of Sports Medecine (ACSM) metabolic equation for walking oxygen consumption (i.e. VO2), with a subsequent conversion from VO2 to calorie burn included by ShapeSense.com. These equations are shown below.

This walking calorie burn calculator will not return a calorie burn estimate for walking speeds below 1 kilometre per hour (0.62 miles per hour) or above 7.5 kilometres per hour (4.66 miles per hour).

## Walking Calorie Burn Equations

For -5% grade: CB = [0.0251 x KPH3 - 0.2157 x KPH2 + 0.7888 x KPH + 1.2957] x WKG x T
For -4% grade: CB = [0.0244 x KPH3 - 0.2079 x KPH2 + 0.8053 x KPH + 1.3281] x WKG x T
For -3% grade: CB = [0.0237 x KPH3 - 0.2000 x KPH2 + 0.8217 x KPH + 1.3605] x WKG x T
For -2% grade: CB = [0.0230 x KPH3 - 0.1922 x KPH2 + 0.8382 x KPH + 1.3929] x WKG x T
For -1% grade: CB = [0.0222 x KPH3 - 0.1844 x KPH2 + 0.8546 x KPH + 1.4253] x WKG x T
For 0% grade: CB = [0.0215 x KPH3 - 0.1765 x KPH2 + 0.8710 x KPH + 1.4577] x WKG x T
For +1% grade: CB = [0.0171 x KPH3 - 0.1062 x KPH2 + 0.6080 x KPH + 1.8600] x WKG x T
For +2% grade: CB = [0.0184 x KPH3 - 0.1134 x KPH2 + 0.6566 x KPH + 1.9200] x WKG x T
For +3% grade: CB = [0.0196 x KPH3 - 0.1205 x KPH2 + 0.7053 x KPH + 1.9800] x WKG x T
For +4% grade: CB = [0.0208 x KPH3 - 0.1277 x KPH2 + 0.7539 x KPH + 2.0400] x WKG x T
For +5% grade: CB = [0.0221 x KPH3 - 0.1349 x KPH2 + 0.8025 x KPH + 2.1000] x WKG x T
where

CB = Calorie burn (in calories)
KPH = Walking speed (in kilometres per hour)
WKG = Weight (in kilograms)
T = Time (in hours)

For +6% to 15% grade: CB = [0.1 x MPM + 1.8 x MPM x FG + 3.5] x WKG x T x 60 x 5 / 1000 where

CB = Calorie burn (in calories) MPM = Walking speed (in meters per minute) FG = Walking surface grade (expressed as a fraction, i.e. 6% = .06) WKG = Weight (in kilograms) T = Time (in hours) The units for the constant 3.5 are milliliters of oxygen per kilogram per minute. The units for the constant 60 are minutes per hour. The units for the constant 5 are calories per liter of oxygen The units for the constant 1000 are milliliters of oxygen per liter of oxygen.

## Resources

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

Margaria, R., 1938. Sulla fisiologia, e specialmente sul consumo energetico, della marcia e della corsa a varie velocita ed inclinazioni del terreno. Atti Accad. Naz. Lincei Classe Sci. Fis. Mat. Nat. Serie VI 7, 299–368.

American College of Sports Medecine: ACSM's Metabolic Calculations Handbook, 2007, Baltimore, MD. Also available online at: ACSM Metabolic Equations

• KPH is the walking speed, but what is the difference between KPH3, KPH2 and KPH? Jul 4, 2015 at 19:30
• @user3852496 the answer appears badly pasted in, essentially the digits should be superscripted / written as: kph^3, kph^2, kph, where ^ is the mathematical symbol for: to the power eg. kph^3 = kph * kph * kph Jul 21, 2015 at 15:01