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# Calculating Caloric Expenditure

Optimize client workouts by using the ACSM metabolic equations to determine exercise intensity and caloric expenditure.

By Jeffrey Janot, PhD

May 31, 2005

A common inquiry clients often make is, “How many calories am I burning during this exercise?” How do you answer that question? Do you take an educated guess based on a client’s heart rate? Do you rely on the numbers on the treadmill? You can provide a more accurate assessment by calculating exercise intensity.

In general, you can determine intensity by employing heart rate methods, such as percent heart rate maximum (%HRmax) or percent heart rate reserve; by teaching clients subjective measures, such as the rating of perceived exertion (RPE) or talk test; or by converting workload or intensity to oxygen consumption (VO_{2}). The last method is the most individualized and accurate one because it is based specifically on the metabolic demands of exercise (Swain & Leutholtz 2002).

Using heart rate to calculate intensity is not as accurate, because increases in heart rate are not always attributable solely to increases in exercise intensity or energy demand; heart rate can be affected by other factors, such as stress, medications, caffeine, dehydration, etc. Subjective measures also have their limitations, since it requires some experience with RPE and the talk test to monitor intensity accurately with these methods. In essence, VO_{2} is the best indicator of exercise intensity because it is tied closely to energy expenditure. The higher the intensity, the more oxygen clients consume and the more calories they burn.

VO_{2}reserve (VO_{2}R) is the difference between VO_{2}max and resting VO_{2}. (VO_{2}R provides a more accurate estimate of actual exercise intensity than VO_{2}max precisely because it takes rest into account.) Resting VO_{2} is constant for everyone and is equal to 3.5 milliliters per kilogram of body weight per minute. VO_{2}max is predicted from a submaximal test you administer to your client. (For a quick review of submaximal test options, refer to “Cardiorespiratory Fitness Testing,” Parts I and II, in the September and November–December 2004 PFT 101 columns.) VO_{2} or VO_{2}max can be reported in liters of oxygen consumed per minute (L/min), milliliters of oxygen consumed per minute (ml/min), or milliliters of oxygen consumed per kilogram of body weight per minute (ml/kg/min).

Once you have determined a client’s VO_{2}max, you can calculate VO_{2}R by subtracting resting VO_{2} (3.5 ml/kg/min) from VO_{2}max. When calculating VO_{2}R, as when calculating heart rate reserve, it is best to determine an intensity range that includes a low end and a high end. Use the low end of the range (40%–50%) for sedentary or low-fit clients and the high end (70%–85%) for fitter, more experienced exercisers. To get the target VO_{2} range for an individual client, you would multiply the VO_{2}R by the percentages of choice and then add resting VO_{2} to each number.

Here is an example:

You have a 25-year-old active client with a VO_{2}max of 55 ml/kg/min. For this client, you would most likely use a VO_{2} range of 70%–85% and calculate as follows:

VO_{2}R: 55 − 3.5 = 51.5 ml/kg/min

client’s low end: (51.5 × 0.70) + 3.5 = 39.55 ml/kg/min

client’s high end: (51.5 × 0.80) + 3.5 = 44.7 ml/kg/min

The target VO_{2} range for this individual is 39.55–44.7 ml/kg/min.

These values can now be used to calculate workloads for a variety of exercise modalities by using the ACSM metabolic equations. See “Calculations for Common Activities” on page 33.

Calculating caloric expenditure from VO_{2} is easy. Simply convert the client’s VO_{2} value to kilocalories (kcal) per minute. The VO_{2} value you are using must be in liters, however, and since the VO_{2} values calculated using the metabolic equations are in milliliters, you must convert them. Here’s how:

1. Multiply the VO_{2} value in ml/kg/min by the client’s weight in kilograms. You will be left with a VO_{2} value in ml/min.

2. Divide this value by 1,000 to convert VO_{2} to L/min.

Once VO_{2} is in liters, you can calculate how many kcal clients are expending during exercise. For every liter of oxygen consumed, approximately 5 kcal are burned, so kcal can be determined from VO_{2} by using this conversion factor. Here’s a quick example:

Your client is exercising at a VO_{2 }of 2 L/min. Multiply 2 L/min by 5 kcal/L. Your client is burning 10 kcal/min. To get total kcal burned during exercise, simply multiply 10 by the total number of minutes of exercise.

The most effective and accurate way of designing an appropriate exercise intensity level and calculating caloric expenditure is through the use of VO_{2}. However, the number of calculations required may limit use of this technique to individual clients. When determining appropriate exercise intensities and calculating caloric expenditure in a group setting, other methods should be used. In the next PFT 101 article, we will practice using VO_{2}R and the ACSM metabolic equations in real-life case studies.

ACSM metabolic equations are available for five primary activities (ACSM 2000; Heyward 2002). Here we will discuss four of them: walking, running, cycling or leg ergometry, and stepping. There are two reasons to use the metabolic equations: (1) to calculate a VO_{2} for a given workload or work rate and then convert VO_{2} into caloric expenditure per minute, and (2) to calculate a workload or work rate intensity from a VO_{2} value (Swain & Leutholtz 2002). In the equations below, VO_{2} is calculated in milliliters per kilogram per minute (ml/kg/min), and 3.5 is a constant that refers to resting oxygen consumption.

Walking

VO_{2} = (0.1 x speed) + (1.8 x speed x grade) + 3.5

This equation is appropriate for fairly slow speed ranges—from 1.9 to approximately 4 miles per hour (mph). Speed is calculated in meters per minute (m/min). The numbers 0.1 and 1.8 are constants that refer to the following:

0.1 = oxygen cost per meter of moving each kilogram (kg) of body weight while walking (horizontally)

1.8 = oxygen cost per meter of moving total body mass against gravity (vertically)

Running

VO_{2} = (0.2 x speed) + (0.9 x speed x grade) + 3.5

This equation is appropriate for speeds greater than 5.0 mph (or 3.0 mph or greater if the subject is truly jogging). Speed is calculated in m/min.

The constants refer to the following:

0.2 = oxygen cost per meter of moving each kg of body weight while running (horizontally)

0.9 = oxygen cost per meter of moving total body mass against gravity (vertically)

Cycling or Leg Ergometry

VO_{2} = [1.8 (work rate) ÷ body mass in kg] + 7

This equation is appropriate for power outputs of 300–1,200 kilogram meters per minute (kgm/min) and speeds of 50–60 revolutions per minute (rpm). Since the power output that needs to be plugged into the equation is in kgm/min, and many exercise bikes measure in watts, you may need to convert watts to kgm/min (1 watt = 6 kgm/min). The constants refer to the following:

1.8 = oxygen cost of producing 1 kgm/min of power output

7 = oxygen cost of unloaded cycling plus resting oxygen consumption

Stepping

VO_{2} = [0.2 (step rate)] + [1.33 x 1.8 (height in meters x step rate)] + 3.5

This equation is appropriate for stepping rates of 12–30 steps/min and for step heights ranging from 1.6 to 15.7 inches. Since the height that needs to be plugged into the equation is in meters, you must convert inches to meters (1 inch = 0.0254 meters). The constants refer to the following:

0.2 = oxygen cost of moving horizontally during stepping

1.8 = oxygen cost of moving vertically during stepping

1.33 = correction factor for positive and negative (up and down) component of stepping

In essence, VO_{2} is the best indicator of exercise intensity because it is tied closely to energy expenditure.

*Source: ACSM 2000.*

**Have a question about caloric expenditure?** Ask it here.

### References

American College of Sports Medicine (ACSM). 2000. *ACSM’s Guidelines for Exercise Testing and Prescription* (6th ed.). * *Baltimore: Lippincott Williams & Wilkins.

Heyward, V. 2002.* Advanced Fitness Assessment and Exercise Prescription *(4th ed.). Champaign, IL: Human Kinetics.

Swain, D., & Leutholtz, B. 2002.* Exercise Prescription: A Case Study Approach to the ACSM Guidelines *(1st ed.). Champaign, IL: Human Kinetics.

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