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# Metabolic Calculations in Action: Part 1

Bushman, Barbara A. Ph.D., FACSM, ACSM-CEP, ACSM-EP, ACSM-CPT

Author Information
ACSM's Health & Fitness Journal: 5/6 2020 - Volume 24 - Issue 3 - p 6-10
doi: 10.1249/FIT.0000000000000562
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Question:ACSM’s Guidelines for Exercise Testing and Prescription, 10th edition, has a table of “metabolic calculations.” Knowing how to use the equations to answer questions like calorie cost or target workload can be confusing. How can the calculations be used to answer exercise-related questions?

AThe metabolic equations allow for the estimation of energy expenditure during walking, running, cycling (leg and arm), and stepping as outlined in Table 6.3 of ACSM’s Guidelines for Exercise Testing and Prescription, 10th edition (GETP10), titled “Metabolic Calculations for the Estimation of Energy Expenditure (V̇O2 [mL·kg−1·min−1]) during Common Physical Activities” (1). An adaptation of the metabolic calculations is included in Box 1, showing the information from the table in GETP10 in the form of equations.

#### Box 1. Metabolic equations.

The list below displays the information from Table 6.3 of ACSM’s Guidelines for Exercise Testing and Prescription, 10th edition, as equations, including the oxygen cost at rest plus the oxygen cost of the activity (1). The unit of measure for the V̇O2 outcome is milliliters per kilogram per minute (mL.kg-1.min-1). The units of measure for each of the activity attributes are noted below; verifying the correct values is key to accurately using the calculations.

• Walking:
• Running:
• Leg cycling:
• Arm cycling:
• Stepping:

Note:

S = speed in meters per minute or m.min-1 (this is the same as m/min; to convert from miles per hour to meters per minute, multiply by 26.8; to convert from meters per minute to miles per hour, divide by 26.8)

G = grade (expressed as a decimal; e.g., 5% grade would be entered as 0.05)

M = body mass in kilograms (to convert from pounds to kilogram, divide by 2.2; to convert from kilogram to pounds, multiply by 2.2)

W = work rate in kilogram meters per minute or kgm.min-1 (this is the same as kgm/min; to determine, multiply the kilogram resistance on the flywheel by the revolutions per minute (rpm) by meters per revolution (m/rev); note that the m/rev for a Monark bike is 6 m, for a Tunturi or Bodyguard bike is 3 m, and for a Monark arm ergometer is 2.4 m)

f = frequency in steps per minute (one step is considered stepping up with each foot and then back down with each foot)

H = step height in meters (to convert from inches to meters, multiply by 0.0254; to convert from meters to inches, divide by 0.0254)

The V̇O2 estimations in Box 1 include the following components (2):

• Rest: For each of the activities, rest is part of the equation, with the assumption that 1 MET is 3.5 mL·kg−1·min−1. For more on what “MET” represents, see Box 2 (3).
• Horizontal: This component reflects the oxygen cost to move the body horizontally. During walking, this is about 0.1 mL oxygen for each kilogram body mass for each meter of horizontal distance; during running, this is doubled, given the greater displacement between each step. These values are reflected in the constant of 0.1 and 0.2 within the horizontal component for walking and running, respectively. For leg cycling, this component reflects the cost of unloaded cycling (i.e., moving the legs without any resistance on the flywheel) and is assumed to be 3.5 mL·kg−1·min−1. Note that because of the smaller muscle mass, no cost is attributed to unloaded arm cycling. For stepping, this reflects the oxygen cost of approximately 0.2 mL oxygen per four-step cycle, resulting in the constant of 0.2 for the horizontal component.
• Vertical/resistance: This component reflects the oxygen cost of raising body mass against gravity for walking and running. During walking, this is about 1.8 mL·kg−1·min−1, and for running, this is 0.9 mL·kg−1·min−1. For cycling (leg and arm), this component is the oxygen cost for working against the resistance, or external load, of the ergometer. For leg ergometry, the constant is 1.8, and for arm ergometry, the constant is 3, reflecting the lower efficiency of using the arms (consider the contraction of accessory muscle needed to stabilize the torso). For stepping, there are two constants. The 1.8 mL·kg−1·min−1 reflects the cost of stepping up (i.e., vertical assent), and the 1.33 reflects the oxygen cost of stepping down (i.e., deceleration against gravity).

Adding these components provides an estimation of oxygen consumption, assuming the person is in steady state (1,2). See Box 3 for an example of an equation that can be used to estimate V̇O2max for the Bruce protocol given the non–steady-state nature of maximal exercise (4).

#### Box 2. What is a MET?

MET is the abbreviation for metabolic equivalent and is “the ratio of the work metabolic rate to the resting metabolic rate” and “is roughly equivalent to the energy cost of sitting quietly” (3). One MET is equal to 3.5 mL·kg−1·min−1. To see MET value for many activities, consult this web site: https://sites.google.com/site/compendiumofphysicalactivities/home (3). MET level can also be determined once the oxygen consumption is calculated using the metabolic equations by dividing the outcome in mL·kg−1·min−1 by 3.5 (e.g., 35 mL·kg−1·min−1 = 10 METs).

#### Box 3. Estimating V̇O2max from GXT: Bruce protocol.

Overestimating may result when using the equations in Box 1 with non–steady-state activity such as a maximal exercise test; using the speed and grade attained at the end of a maximal test would not be appropriate to estimate V̇O2max (2). Instead, prediction equations have been developed to estimate maximal oxygen consumption based on test performance. The following calculation can be used with the standard Bruce protocol; “time” reflects how long the individual was able to continue with the test (4) (numbers in bold are constants):

For example, if a test ended with maximal effort midway through the fifth stage (i.e., at the 13:30 mark), then the time entered into the equation would be 13.5 minutes (as 30 seconds is 0.5 of a minute: 30 ÷ 60 = 0.5):

The fifth stage of the Bruce protocol involves running at 5.0 mph with an 18% grade. When calculating the oxygen consumption for that workload using the running equation from Box 1, there would be an overestimation (calculation yields 52.0 mL·kg−1·min−1).

## CALCULATING ESTIMATED OXYGEN CONSUMPTION AND CALORIC EXPENDITURE

A simple use of the metabolic equations is to determine the estimated oxygen uptake for a particular activity. For walking and running, knowledge of the speed and grade (incline) of the treadmill is required; the only difference between the two equations are the constant values related to the horizontal (0.1 and 0.2, respectively) and vertical (1.8 and 0.9, respectively) components (1,2).

For example, consider a person who weighs 65 kg and who is running on a treadmill at 8.5 mph, with a 1% grade. The first step is to select the running equation:

To solve for V̇O2, the speed must be converted from miles per hour to meters per minute by multiplying 8.5 by 26.8 (8.5 × 26.8 = 227.8 m·min−1). The grade must be expressed as a decimal; thus, 1% grade is entered into the equation as 0.01 (shift the decimal over two places). With these values, the equation can be solved (bolded numbers are the constants; ensure the correct order of calculations by completing calculations in parentheses first):

The calculated V̇O2 can be used to estimate the caloric cost given that 1 L oxygen consumption (1LO2) requires approximately 5.0 kilocalories per minute (kcal·min−1) (2). The first step is to convert the V̇O2 determined from the equation, where the unit of measure is mL·kg−1·min−1, to L·min−1 (i.e., oxygen consumption without regard to body weight). To do this, take the V̇O2 in mL·kg−1·min−1 and divide by 1000 to convert from milliliters to liters and then multiply by body weight in kilograms:

Then, with the given relationship that 1 L oxygen requires approximately 5 kcal·min−1, convert from liters per minute to kilocalories per minute as follows:

For a 40-minute workout, the total caloric expenditure would be 664 kcal (calculated as 16.60 kcal·min−1 × 40 min = 664 kcal). See Box 4 for an alternative way to determine kilocalories per minute (2).

#### Box 4. Using METS to estimate kcal·min−1.

A simple way to estimate the calorie cost of an activity is to use this equation (numbers in bold are constants) (2):

Consider a person who weighs 80 kg walking at a 3.7-MET level (e.g., walking 3.0 mph with a 1% grade):

If the person walked for 40 minutes, the estimated calorie cost would be 207 kcal.

For leg or arm cycling, knowledge of the work rate and the individual’s body weight is required (1,2). For example, consider a person (body weight 70 kg) cycling on a Monark leg ergometer (i.e., stationary bike) at 50 rpm with resistance on the flywheel of 2.0 kg. The first step is to select the leg cycling equation:

The next step is to determine the work rate in kilogram meters per minute (kgm·min−1). Given that the number of meters per revolution (m/rev) for a Monark leg ergometer is 6 m, to determine kgm·min−1, multiply the kilogram resistance by the revolutions per min by the distance per revolution. For this example:

With this information, along with the person’s body weight (given as 70 kg), enter the values into the equation to determine oxygen consumption (bolded numbers are the constants; ensure the correct order of calculations by completing calculations in parentheses first):

The steps to determine caloric cost for a given workout are the same as shown with the running example. First convert to L·min−1:

Then, convert from liters per minute to kilocalories per minute:

If the cycling workout was 40 minutes in duration, this would require approximately 314 kcal (7.85 kcal·min−1 × 40 min = 314 kcal).

For stepping activity, knowledge of the step height and the step rate (steps per minute) is required (1,2). One step is defined as a four-part activity: lifting one leg onto the step, followed by the other leg, and then returning back down with the one leg and then the other (e.g., one step includes stepping up with the right foot, then stepping up with the left foot, followed by stepping down with the right foot, and then stepping down with the left foot). To help with the pacing, music with a beat set to four times the step count would allow for a foot contact with each beat (e.g., if the target is 20 steps·min−1, then select music with a beat at 80 beats per minute so each foot contact occurs on a beat: 20 × 4 = 80). Consider a person who weighs 50 kg stepping at a rate of 20 steps·min−1 on a 10-inch step. First, select the stepping equation:

Note that 10 inches is equal to 0.25 m, determined by converting from inches to meters (rounded to the nearest hundredth): 10 × 0.0254 = 0.25. Enter the values into the equation to determine oxygen consumption (bolded numbers are the constants; ensure the correct order of calculations by completing calculations in parentheses first):

If this activity is done for 40 minutes, the calorie cost would be estimated 194 kcal (following the steps from the prior examples, convert to L·min−1: 19.47 mL·kg−1·min−1 is equal to 0.97 L·min−1 (19.47 ÷1000 × 50); then convert to kcal·min−1: 0.97 L·min−1 would require 4.85 kcal·min−1 (.97 × 5); and in the final step, multiply the kcal·min−1 by the number of minutes: 4.85 × 40 = 194 kcal).

Other applications of the metabolic calculations may involve determining what activities are needed to achieve a target intensity (2). This can be helpful in setting up an exercise program for an individual. In this situation, the V̇O2 is known and an aspect of the activity is to be determined (e.g., speed, grade, or resistance on flywheel).

For example, a 28-year-old male (weight 80 kg) has a V̇O2max of 46 mL·kg−1·min−1. This is considered in the “fair” classification for cardiorespiratory fitness per GETP10 (1). To provide guidance for his leg cycling exercise, a target in the moderate-intensity range of oxygen uptake reserve (V̇O2R) was selected: 55% V̇O2R. GETP10 defines moderate intensity as 40% to 59% V̇O2R and vigorous intensity as 60% to 89% V̇O2R; for more on V̇O2R, see Box 5 (1).

#### Box 5. What is V̇O2R?

V̇O2R refers to oxygen uptake reserve and is calculated as follows (1):

V̇O2R = [(V̇O2max – V̇O2rest) × target intensity] + V̇O2rest

V̇O2rest is assumed to be 3.5 mL·kg−1·min−1. The target intensity is expressed as a decimal (e.g., 75% is entered into the equation as 0.75).

To calculate 55% V̇O2R, assuming V̇O2rest is 3.5 mL·kg−1·min−1 (i.e., 1 MET):

Thus, the target intensity is 26.88 mL·kg−1·min−1; this is the V̇O2 value used in the leg cycling equation, along with his body weight of 80 kg, to solve for the work rate (W) (bolded numbers are constants):

[subtract 7 from both sides of the equation]

[divide both sides of the equation by 1.8 and multiply by 80]

He indicates being comfortable with a pedal rate of 60 rpm when on a Monark cycle ergometer (this type of cycle ergometer has a known 6 m/rev as noted in Box 1). To give him guidance on the resistance to place on the flywheel, consider the three contributors to the kgm·min−1 work rate: kg resistance, rpm, and m/rev.

Or more simply shown:

This information can be used as a starting point, with heart rate and rating of perceived exertion used to refine the exercise prescription (1,5). Similar calculations can be done for walking and running, with the understanding that a choice must be made for either the speed or the grade, solving for the other variable; for stepping, the step count or step height would need to be selected, solving for the other variable (2). This example will be continued in the July/August issue along with additional applications using the metabolic equations.

## CONCLUSION

The use of the metabolic equations requires attention to units of measure as well as the order of calculations. With an understanding of the components that contribute to oxygen consumption for various exercises under steady-state conditions, estimated caloric costs and target workloads can be calculated.

## References

1. American College of Sports Medicine. ACSM’s Guidelines for Exercise Testing and Prescription. 10th ed. Philadelphia (PA): Wolters Kluwer; 2018. p. 472.
2. American College of Sports Medicine. ACSM’s Guidelines for Exercise Testing and Prescription. 7th ed. Baltimore (MD): Lippincott Williams & Wilkins; 2006. p. 366.
3. Ainsworth BE, Haskell WL, Herrmann SD, et al. The Compendium of Physical Activities Tracking Guide. Healthy Lifestyles Research Center, College of Nursing & Health Innovation, Arizona State University. [cited 2019 Dec 6] Available from: https://sites.google.com/site/compendiumofphysicalactivities/.
4. Foster C, Jackson AS, Pollock ML, et al. Generalized equations for predicting functional capacity from treadmill performance. Am Heart J. 1984;107:1229–34.
5. Bushman BA. Determining the I (Intensity) for a FITT-VP aerobic prescription. ACSMs Health Fit J. 2014;18(3):4–7. [cited 2019 Dec 6] Available from: https://journals.lww.com/acsm-healthfitness/Fulltext/2014/05000/Determining_the_I__Intensity__for_a_FITT_VP.4.aspx.