Metabolic Equations
How many calories do you burn when you walk 3 miles? Because exercise is an important step
in weight loss, it is important to be able to quantify caloric costs of a given activity. Below are
equations that have been validated by the American College of Sports Medicine to accurately
quantify caloric cost.
Each equation has two components: a horizontal phase and a vertical phase. These
components, plus our metabolic cost at rest, combine to form the overall caloric cost of an
activity. The first step to calculate the cost of an activity is to estimate VO2 and expressed it in
ml of oxygen/kg of mass/min of activity (ml/kg/min). From this, we can derive calories.
Walking equation: VO2= (0.1é + (1.8 àé + 3.5. Where S = speed, G = grade.
S= speed in meters/min. Convert by multiplying speed in mph by 26.8 (a constant).
Thus, 3.2 mph would be converted to 85.76 meters/min (3.2*26.8 = 85.76).
G= grade in decimal form (i.e., 5% grade is 0.05); if 0% grade, then vertical=0
We will use the walking equation for any speeds less than 1.9 3.75 mph. Above 5.0
mph we will use the running equation listed below.
Running equation: VO2= (0.2 é+ (0.9 àé + 3.5. Where S = speed, G = grade. See
above.
Walking example 1: Calculate the VO2 for someone walking 3.2 mph and a 6% grade.
Step 1 is to convert speed: 26.8*3.2 = 85.76.
Step 2: .1*85.76 = 8.57. This is the speed component of the equation.
Step 3: 1.8*85.76*.06 = 9.26. This is the second part of the equation (1.8 *S*G).
Step 4: 8.57 + 9.26+ 3.5 = 21.34 ml/kg/min.
Don forget, we have to add in the metabolic cost at rest. This equals 3.5
Once we know the metabolic cost (ml/kg/min), we can estimate total kcals burned.
In the walking example 1, if our subject weighed 140 lbs and walked for 40 minutes, then we
can estimate that our subject burned 271 kcals. To do this, we need to do the following:
1.
2.
3.
4.
5.
Convert weight to kg. This is done by dividing pounds by 2.2. So 140/2.2 = 63.63.
Multiply our metabolic cost by the body weight. 21.3 * 63.63 = 1357 ml/min.
Divide our new metabolic cost by 1000, to get L/min. 1357/1000 = 1.357.
For every liter of oxygen consumed we burn 5 kcals. So 1.357 * 5 = 6.78 kcals/min.,
Our subject exercised for 40 min. So 6.78 * 40 = 271 kcals burned for the intensity
and duration of exercise.

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