Q: *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?

A: Part 1 of the answer to this question appeared in the May/June 2020 issue of *ACSM’s Health & Fitness Journal®* (^{1}). Items covered in part 1 include the background of the metabolic equations, the estimation of oxygen consumption (V̇O_{2}) and caloric expenditure, and an introduction to calculating target workload. In part 2, additional insights into calculating target workload and using the equations within exercise prescription will be explored. As in part 1, an adaptation of the content 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 (V̇O_{2} [mL·kg^{−1}⋅min^{−1}]) during Common Physical Activities” (^{2}) is provided for reference (see Box 1).

#### Box 1. Metabolic equations.

The list below displays information from Table 6.3 of *ACSM’s Guidelines from Exercise Testing and Prescription,* 10th edition, as equations, including the oxygen cost at rest plus the oxygen cost of the activity (^{2}). The units of measure are noted below; verifying that the correct values is key to accurately using the calculations. The outcome V̇O_{2} is expressed in mL·kg^{−1}⋅min^{−1}.

- Walking: VO
_{2} = 3.5 + (0.1 × *S*) + (1.8 × *S* × *G*)
- Running: V̇O
_{2} = 3.5 + (0.2 × *S*) + (0.9 × *S* × *G*)
- Leg cycling: V̇O
_{2} = 3.5 + 3.5 + (1.8 × W ÷ M)
- Arm cycling: V̇O
_{2} = 3.5 + (3 × W ÷ M)
- Stepping: V̇O
_{2} = 3.5 + (0.2 × f) + (1.33 × 1.8 × H × f)

Where S is speed in meters per minute (to convert from mph to m⋅min^{−1}, multiply by 26.8; to convert from m⋅min^{−1} to mph, divide by 26.8); G is grade (expressed as a decimal; *e.g*., 5% grade would be entered as 0.05); M is body mass in kilograms (to convert from pounds to kg, divide by 2.2; to convert from kg to pounds, multiply by 2.2); Work rate (W) is kilogram meters per minute (to determine, multiply the kg resistance on the flywheel by the 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 is frequency in steps per minute (one step is considered stepping up with each foot and then back down with each foot); and H is step height in meters (to convert from inches to meters, multiply by 0.0254; to convert from meters to inches, divide by 0.0254).

## BRIEF REVIEW

Each of the equations in Box 1 includes estimated V̇O_{2} at rest (assumed to be 3.5 mL·kg^{−1}⋅min^{−1}) plus estimated V̇O_{2} for the given activity (^{2,3}). For walking and running, this includes the oxygen cost to move forward horizontally as well as to raise the body vertically against gravity. For arm and leg ergometry, this includes the oxygen cost of working against the resistance on the flywheel; for leg ergometry, the cost of unloaded cycling (*i.e*., movement of the legs without resistance) also is added. For stepping, this includes the oxygen cost of moving forward onto the step and the vertical cost of elevating the body against gravity and then decelerating against gravity when lowering the body back to the original position. The total estimated V̇O_{2}, expressed in units mL·kg^{−1}⋅min^{−1}, assumes the person is in steady state (^{2,3}).

When calculating estimated V̇O_{2}, care must be taken to ensure the appropriate units of measure are used (^{2}). For walking and running, knowledge of the speed (m⋅min^{−1}) and the incline (expressed as a decimal) is required. For leg and arm ergometry, the individual’s body weight (kg) and the work rate (kgm⋅min_{−1}) are needed. For stepping, knowing the step count (steps per minute) and the step height (m) is necessary. Conversion factors related to these units of measure are included in the footnotes of Box 1.

When V̇O_{2} has been calculated, one application is to estimate the caloric cost of an activity given that 1 L of oxygen consumption (1LO_{2}) requires approximately 5.0 kcal⋅min^{−1} (^{3}). This allows for the determination of the caloric expenditure for a given workout and also can be used to determine the number of minutes required to expend a given number of calories.

In addition to calculating VO_{2}, the metabolic equations may be used to determine exercise attributes needed to achieve a target intensity within an exercise prescription (^{2}). With a known VO_{2} target, guidance on the activity can be established, such as speed or grade on the treadmill, resistance on the flywheel of an ergometer, or step height or cadence for stepping.

## PUTTING THE METABOLIC CALCULATIONS TO USE

In part 1, an example was given for a 28-year-old male (body weight, 80 kg) with a V̇O_{2max} of 46 mL·kg^{−1}⋅min^{−1}. For a male of this age, the cardiorespiratory fitness classification is considered “fair” according to ACSM (^{2}), and a moderate-intensity target of 55% oxygen uptake reserve (V̇O_{2}R) was chosen; this equates to a target V̇O_{2} of 26.88 mL·kg^{−1}⋅min^{−1}. For a recap of how to calculate V̇O_{2}R, see Box 2.

#### Box 2. Calculating percent oxygen uptake reserve (% V˙O_{2}R).

Within an exercise prescription, moderate- or vigorous-intensity aerobic activity is recommended for most healthy adults; moderate intensity is considered to be 40% to 59% V˙O_{2}R, and vigorous intensity is in the range of 60% to 89% V˙O_{2}R (^{2}). For individuals who are deconditioned, lower intensity (such as 30% to 39% V˙O_{2}R) may provide conditioning benefits (^{2}).

To calculate %V˙O_{2}R, the individual’s V˙O_{2max} and V˙O_{2rest} must be known. V˙O_{2max} may be available from a graded exercise test or could be estimated from a submaximal assessment (*e.g*., Astrand–Ryhming cycle ergometer test) (^{2}). V˙O_{2rest} is assumed to be 3.5 mL·kg^{−1}⋅min^{−1} (*i.e*., 1 MET). The calculation for %V˙O_{2}R is as follows:

%V˙O_{2}R = [(V˙O_{2max} – V˙O_{2rest}) × target intensity] + V˙O_{2rest}

For the 28-year-old male in the example with a V˙O_{2max} of 46 mL·kg^{−1}⋅min^{−1}, for whom a target of 55%V˙O_{2}R was selected, the calculation would be as follows:

55%V˙O_{2}R = [(46–3.5) × 0.55] + 3.5 = 26.88 mL·kg^{−1}⋅min^{−1}.

Guidance on work rate for specific activities can be calculated to match this target intensity of 26.88 mL·kg^{−1}⋅min^{−1}. Part 1 included calculations related to leg cycling. To continue with this example for a walking exercise prescription, either the speed or the grade must be selected, solving for the other attribute. The client indicates he is comfortable walking at 4.2 mph (to convert to m⋅min^{−1}, multiply 4.2 by 26.8: 112.56 m⋅min^{−1}), so the next step is to solve for grade (consider the order of calculations with multiplication within parentheses occurring first):

Start by selecting the correct formula from Box 1:

V̇O_{2} = 3.5 + (0.1 × *S*) + (1.8 × *S* × *G*).

Then insert the known values for speed (112.56 m⋅min^{−1}) and target V̇O_{2} and then solve for grade (numbers in bold are constants):

26.88 = 3.5 + (0.1 × 112.56) + (1.8 × 112.56 × *G*) [next multiply within parentheses]

26.88 = 3.5 + 11.26 + (202.61 × *G*) [then add the 3.5 and 11.26]

26.88 = 14.76 + (202.61 × *G*) [then subtract 14.76 from both sides of the equation]

12.12 = 202.61G [then divide both sides by 202.61]

0.06 = *G* [finally, shift the decimal over by two places to express as a percentage: 6%]

Thus, the grade would be set at 6% when walking at a speed of 4.2 mph. This information can be used as a starting point, with heart rate (HR) and perceived exertion used to refine the exercise prescription (^{2}) (see Box 3 for information on ACSM recommendations). For more background related to setting intensity, see the *Wouldn’t You Like to Know* article “Determining the I (Intensity) for a FITT-VP Aerobic Prescription” (^{4}).

#### Box 3. Refining exercise prescription intensity with HR and RPE.

HEART RATE

When a measured maximal HR (HR_{max}) is unavailable, estimation of HR_{max} can be used, with the realization that use of an estimated HR_{max} may result in over- or underestimation (^{2}). One of the most common estimates is “220 − age,” although others also are available that may be more targeted to specific group on which they are based (^{2}).

With either a measured HR_{max} or calculated HR_{max} estimate, the next step is to calculate the percent HR reserve (% HRR), which follows a similar formula as % V̇O_{2}R: [(max – rest) × %] + rest. As with V̇O_{2}R, moderate intensity is considered to be 40% to 59% HRR and vigorous intensity is 60% to 89% HRR; for deconditioned individuals, lower intensity (30% to 39% HRR) may provide benefit (^{2}).

For the 28-year-old male in the example used throughout this article, his estimated HR_{max} would be 192 beats per minute (calculated as 220–28 = 192). Given that he has an HR_{rest} of 70 beats per minute, a target HR range can be determined. For an exercise prescription, typically a range is provided rather than a single HR value given the variability normally seen in response to exercise (^{2}). If a target of 50% to 60% HRR is selected, the calculation would be as follows:

% HRR = [(HR_{max} – HR_{rest}) × %] + HR_{rest}

For the lower limit (note that the percentage is expressed as a decimal):

50% HRR = [(192–70) × 0.50] + 70 [complete subtraction within parenthesis first]

50% HRR = [(122) × 0.50] + 70 [next complete multiplication within the brackets]

50% HRR = [61] + 70 [finally add the remaining two values]

50% HRR = 131

For the upper limit:

60% HRR = [(192–70) × 0.60] + 70 [complete subtraction within parenthesis first]

60% HRR = [(122) × 0.60] + 70 [next complete multiplication within the brackets]

60% HRR = [73] + 70 [finally add the remaining two values]

60% HRR = 143

Thus, to help provide guidance for the workout, he would seek to keep his HR within a range of 131 to 143 beats per minute.

**PERCEIVED EXERTION**

Another way to adjust exercise intensity is with the use of perceived exertion. The Borg RPE scales can be used (^{2}). Another option is a simple 0 to 10 relative scale; 0 reflects sitting at rest, and 10 is one’s highest effort level. On this scale, moderate intensity is 5 or 6, and vigorous intensity is 7 or 8 (^{5}). Perception related to breathing and HR is reflected in relative intensity. The “talk test” can assist with understanding these relative levels. In general terms, at a moderate intensity, individuals would have the ability to talk but not sing during the activity (^{5}). When increasing to vigorous intensity, the expectation would be that no more than a few words could be said without the need to pause to take breath (^{5}). Research into the ability of the talk test to guide intensity supports the achievement of steady state when subjects were able to “speak comfortably” as supported by measured HR within 60% to 85% HRR, RPE of moderate intensity, and blood lactate near resting levels (^{6}). When subjects were able to speak, but not entirely comfortably, the subjects were at metabolic threshold (^{6}). Once subjects were not able to speak comfortably, the intensity was considered to be high and above metabolic threshold (^{6}).

For an exercise prescription focused on stepping, the same general procedures would be followed where one of the exercise attributes is predetermined while the other is calculated. If cadence is set, then the height would be calculated. This might be applicable in situations where stackable risers are available, allowing the height to be adjusted. For the following example, the step height is set at 10 inches (to convert to meters, multiply by 0.0254: 10 × 0.0254 = 0.25 m) so the cadence will be calculated (consider the order of calculations with multiplication within parentheses occurring first):

Start by selecting the correct formula from Box 1:

V̇O_{2} = 3.5 + (0.2 × *f*) + (1.33 × 1.8 × *H* × f)

Then insert the known value for step height (0.25 m) and target V̇O_{2} and then solve for step frequency (numbers in bold are constants):

26.88 = 3.5 + (0.2 × f) + (1.33 × 1.8 × 0.25 × f) [next, multiply within parentheses]

26.88 = 3.5 + (0.2 × f) + (0.60 × f) [then subtract 3.5 from both sides of the equation]

23.38 = 0.2f + 0.60f [then add 0.2 and 0.60]

23.38 = 0.80f [finally, divide both sides by 0.80]

29 = f

Thus, the step frequency is 29. Frequency refers to a four-step sequence (stepping up with each foot and then back down with each foot), so if music were used to help maintain the proper cadence, a rhythm with a beat of 116 (calculated as 29 × 4 = 116) would allow for a foot contact with each beat. As noted with the walking example, this is a starting point; use of HR and/or perceived exertion can be used to adjust the prescription as needed.

In addition to target intensity, the recommended duration of exercise can be computed. ACSM notes a reasonable target of 1000 kcal per week of moderate-intensity physical activity for adults (^{2}). To continue with the example for the 28-year-old male, the number of minutes at his target intensity of 26.88 mL·kg^{−1}⋅min^{−1} would require about 93 minutes per week to expend 1000 kcal. Recall the relationship between oxygen consumption and caloric expenditure: 1LO_{2} requires about 5 kcal⋅min^{−1} (^{3}); this can be used to determine caloric cost per minute when exercising at the target intensity. The steps are as follows for the client:

First, convert mL·kg^{−1}⋅min^{−1} to L⋅min^{−1}:

26.88 mL·kg^{−1}⋅min^{−1} × 1 L/1000 mL × 80 kg body weight = 2.15 L⋅min^{−1}

Then convert from L⋅min^{−1} to kcal⋅min^{−1}:

2.15 L⋅min^{−1} × 5.0 Kcal/1LO_{2} = 10.75 kcal⋅min^{−1}

To achieve the target caloric expenditure of 1000 kcal for the week:

1000 kcal·week^{−1} / 10.75 kcal⋅min^{−1} = 93 min·week^{−1} [note that by dividing by kcal·min^{−1}, the kcal “cancel out,” and the result will be the number of min·week^{−1}]

The target intensity was toward the upper end of moderate (in the example, 55% V̇O_{2}R was selected based on fitness level; moderate intensity is considered 40% to 59% V̇O_{2}R), and thus the time to achieve 1000 kcal is lower than the 150 min typically noted for moderate-intensity activity (^{2}).

## CONCLUSION

The metabolic equations have many applications for the fitness professional. An understanding of the equations, for use with exercise in steady-state conditions, can allow for the determination of caloric cost as well as the development of an exercise prescription. The use of additional methods of monitoring intensity such as HR or perceived exertion can be used to modify the prescription to achieve moderate to vigorous targets.