Simple Conversions
1. Convert mph to m · min-1.
4 mph × 26.8 = 107.2 m · min-1
2. Convert ml · min-1 to L · min-1.
4,000 ml · min-1/1,000 = 4.0 L · min-1
Convert L · min-1 to kcal · min-1.
4.0 L · min-1 × 5 = 20 kcal · min-1
3. Convert METs to ml · kg-1 · min-1.
5 METs × 3.5 = 17.5 ml · kg-1 · min-1
4. Convert lb to kg.
175 lb/2.2 = 79.5 kg
5. Convert in. to cm.
15 in. × 2.54 = 38.1 cm
Convert cm to m.
38.1 cm/100 = 0.381 m
6. Convert lb to kg.
120 lb/2.2 = 54.5 kg
Convert ml · kg-1 · min-1 to ml · min-1.
42 ml · kg-1 · min-1 × 54.5 kg = 2290.9 ml · min-1
Convert ml · min-1 to L · min-1.
2,290.9 ml · min-1/1,000 = 2.29 L · min-1
7. Convert kgm · min-1 to watts.
1,200 kgm · min-1/6 = 200 W
8. Convert lb to kg.
165 lb/2.2 = 75 kg
Convert L · min-1 to ml · min-1.
4.5 L · min-1 × 1,000 = 4,500 ml · min-1
Convert ml · min-1 to ml · kg-1 · min-1.
4,500 ml · min-1/75 kg = 60 ml · kg-1 · min-1
Convert ml · kg-1 · min-1 to METs.
60 ml · kg-1 · min-1/3.5 = 17.1 METs
9. Convert mph to min · mile-1.
60 min/6.2 mph = 9.7 min · mile-1
10. Convert kcal to L of O2.
50 kcal/5 = 10 L of O2
11. Convert METs to kcal · kg-1 · hr-1.
9 METs × 1 = 9 kcal · kg-1· hr-1
Convert kcal · kg-1 · hr-1 to kcal · hr-1.
9 kcal · kg-1 · hr-1 × 70 kg = 630 kcal · hr-1
Convert kcal · hr-1 to kcal · min-1.
630 kcal · hr-1/60 min = 10.5 kcal · min-1
Cardiovascular Dynamics
1. Convert ml · kg-1 · min-1 to ml · min-1.
32 ml · kg-1 · min-1 × 60 kg = 1,920 ml · min-1
Calculate Q (ml · min-1) = VO2/a-v O2 difference.
Q = 1,920 ml · min-1/12 ml O2/100 ml
= 192,000/12
= 16,000 ml · min-1 or 16 L · min-1
Calculate SV = Q (ml · min-1)/HR (bpm).
SV = 16,000 ml · min-1/160 bpm
= 100 ml/beat
2. Calculate MAP = [(systolic BP – diastolic BP)/3] + diastolic BP.
MAP = [(125 – 78 mmHg)/3] + 78 mmHg
= 93.7 mmHg
3. Calculate MVO2 = HR × systolic BP/100.
MVO2 = 85 bpm × 135 mmHg/100
= 114.7 mmHg/min
4. Calculate VO2max = HR × SV × a-v O2 difference.
VO2max (ml · min-1) = 180 bpm × 140 ml/beat × 15 ml/100 ml
= 3,780 ml · min-1 or 3.78 L · min-1
Target Body Weight and Weight Loss
1. Calculate the FFM = BM × %FFM.
FFM = 210 lb × 0.65
= 136.5 lb
Calculate target BM = present FFM/%FFM goal.
target BM = 136.5/0.75
= 182 lb
2. Calculate weight loss = present BM – target BM.
weight loss = 210 – 182 lb
= 28 lb
3. Convert METs to kcal · kg-1 · hr-1.
6 METs × 1 = 6 kcal · kg-1 · hr-1
Convert present BM in lb to kg.
210 lb/2.2 = 95.5 kg
Convert kcal · kg-1 · hr-1 to kcal · hr-1.
6 kcal · kg-1 · hr-1 × 95.5 kg = 573 kcal · hr-1
Convert kcal · hr-1 to kcal · min-1.
573 kcal · min-1/60 min = 9.6 kcal · min-1
Calculate kcal per workout.
9.6 kcal · min-1 × 30 min/workout = 288 kcal/workout
Calculate kcal per week.
288 kcal/workout × 5 = 1,440 kcal/week
Calculate kcal deficit for weight loss.
28 lb × 3,500 = 98,000 kcal
Calculate number of weeks to accumulate kcal deficit.
98,000 kcal/1,440 kcal/week = 68 weeks
Target Heart Rate
1a. Karvonen method: THR = [% exercise intensity × HRR] + HRrest
Calculate the age-predicted HRmax.
220 – 32 years = 188 bpm
Calculate HRR = HRmax – HRrest.
188 – 68 = 120 bpm
Calculate 60% of HRR.
120 × 0.60 = 72 bpm
Calculate target HR.
72 + 68 = 140 bpm
1b. %HRmax method: THR = [% exercise intensity × HRmax]
0.60 × 188 = 113 bpm
1c. For this client, the Karvonen method yields a target HR that is 27 bpm higher than the value with the %HRmax method.
2. The %VO2R method is equivalent to the %HRR method; therefore, use
THR = [% exercise intensity × HRR] + HRrest.
Calculate the age-predicted HRmax.
220 – 45 = 175 bpm
Calculate HRR = HRmax – HRrest.
175 – 74 = 101 bpm
Calculate 55% of HRR.
110 × 0.55 = 56 bpm
Calculate target HR.
56 + 74 = 130 bpm
Metabolic Calculations (Using ACSM Equations)
1. Use ACSM running equation: VO2 = [S × 0.2] + [S × G × 0.9] + 3.5
Convert mph to m · min-1.
7 mph × 26.8 = 187.6 m · min-1
Calculate first term of equation (VO2 for speed).
VO2 = 187.6 m · min-1 × 0.2
VO2 = 37.5 ml · kg-1 · min-1
Calculate second term of equation (VO2 for speed and grade).
VO2 = 187.6 m · min-1 × 0.0 (% grade) × 0.9
VO2 = 0.0
Calculate the gross VO2 by adding the resting VO2 to the first two terms.
VO2 = 3.5 + 37.5 + 0.0 ml · kg-1 · min-1
VO2 = 41.0 ml · kg-1 · min-1
2. Use the ACSM leg ergometry equation: VO2 = [W/M × 10.8] + 3.5 + 3.5
Convert BM in lb to kg.
162/2.2 = 73.6 kg
Substitute known values into equation, and solve for power output in watts (W).
41 ml · kg-1 · min-1 = [W/73.6 kg × 10.8] + 3.5 + 3.5
34 ml · kg-1 · min-1/10.8 × 73.6 kg = W
W = 231.7
Convert W to kgm · min-1.
231.7 W × 6 = 1,390 kgm · min-1
Solve for resistance (kg) setting: power output (kgm · min-1) = kg × 6 m × rpm.
1,390 kgm · min-1 = kg × 6 m × 80 rpm
1,390/480 = 2.9 kg
3. Use ACSM stepping equation: VO2 = [f × 0.2] + [f × ht × 1.8 × 1.33] + 3.5
Calculate first term of equation.
VO2 = 0.2 × 24 steps/min
VO2 = 4.8 ml · kg-1 · min-1
Convert 8 in. to m.
8 × 2.54/100 = 0.203 m
Calculate the second term of equation.
VO2 = 24 steps/min × 0.203 m × 1.8 × 1.33
VO2 = 11.7 ml · kg-1 · min-1
Calculate the gross VO2 by adding resting VO2 to the first two terms of equation.
VO2 = 4.8 + 11.7 + 3.5
VO2 = 20.0 ml · kg-1 · min-1
Convert ml · kg-1 · min-1 to METs.
20.0 ml · kg-1 · min-1/3.5 ml · kg-1 · min-1 = 5.7 METs
Convert BM in lb to kg.
135 lb/2.2 = 61.4 kg
Calculate kgm · min-1 = BM (kg) × 24 steps/min × 0.203 m/step.
61.4 × 24 × 0.203 = 299 kgm · min-1
4. Use ACSM arm ergometry equation: VO2 = [W/M × 18.0] + 3.5
Convert 8 METs to ml · kg-1 · min-1.
8 METs × 3.5 = 28 ml · kg-1 · min-1
Substitute known values into equation, and solve for power output in watts (W).
28 ml · kg-1 · min-1 = [W/77 kg × 18.0] + 3.5
24.5 ml · kg-1 · min-1/18.0 × 77 kg = 104.8 W
Convert W to kgm · min-1.
104.8 × 6 = 628.8 kgm · min-1
Solve for resistance (kg) setting: power output (kgm · min-1) = kg × 2.4 m × rpm.
628.8 kgm · min-1 = kg × 2.4 m × 60 rpm
628.8/144 = 4.4 kg
5. Use the ACSM running equation: VO2 = [S × 0.2] + [S × G × 0.9] + 3.5
Substitute known values into equation, and solve for speed (S).
30 ml · kg-1 · min-1= [S × 0.2] + [S × 0.0 (level running) × 0.9] + 3.5
(30 – 3.5)/0.2 = 132.5 m · min-1
Convert m · min-1 into mph.
132.5 m · min-1/26.8 = 4.9 mph
6. Use ACSM running equation: VO2 = [S × 0.2] + [S × G × 0.9] +3.5
Convert mph to m · min-1.
6 mph × 26.8 = 160.8 m · min-1
Calculate the first term of equation.
VO2 = 160.8 m · min-1 × 0.2
VO2 = 32.2 ml · kg-1 · min-1
Substitute known values into equation.
40 ml · kg-1 · min-1 = 32.2 ml · kg-1 · min-1 + [S × G × 0.9] + 3.5
40 – 3.5 – 32.2 = 4.3 ml · kg-1 · min-1
Substitute known values into second term of equation.
4.3 ml · kg-1 · min-1 = 160.8 m · min-1 × grade × 0.9
Solve for % grade.
4.3/144.7 = .029 or 3% grade
7. Use the ACSM leg ergometry equation: VO2 = [W/M × 10.8] + 3.5 + 3.5
Calculate power output in kgm · min-1.
power output = 2.5 kg × 6 m × 70 rpm
power output = 1050 kgm · min-1
Convert power output to watts (W).
1,050 kgm · min-1/6 = 175 W
Substitute known values into ACSM equation.
VO2 = [175 W/75 kg × 10.8] + 3.5 + 3.5
VO2 = 32.2 ml · kg-1 · min-1
Convert ml · kg-1 · min-1 to L · min-1.
32.2 × 75 kg/1,000 = 2.42 L · min-1
Convert L · min-1 to kcal · min-1.
2.42 L · min-1 × 5 = 12.1 kcal · min-1
Divide kcal expenditure by kcal · min-1.
300 kcal/12.1 kcal · min-1 = 25 min
8. Convert BM in lb to kg.
150 lb/2.2 = 68.2 kg
Calculate net VO2 in METs.
5 METs – 1 MET (resting VO2) = 4 METs
Convert METs to kcal · kg-1 · hr-1.
4 METs × 1 = 4 kcal · kg-1 · hr-1
Calculate kcal · hr-1.
4 kcal · kg-1 · hr-1 × 68.2 kg = 273 kcal · hr-1
Convert kcal · hr-1 to kcal · min-1.
273 kcal · hr-1/60 min = 4.5 kcal · min-1
9. Convert min · mi-1 to mph.
60 min/25 min · mi-1 = 2.4 mph
Convert mph to m · min-1.
2.4 mph × 26.8 = 64.3 m · min-1
Use ACSM walking equation: VO2 = [S × 0.1] × [S × G × 1.8] + 3.5
Calculate the first term of the equation.
VO2 = 64.3 m · min-1 × 0.1
VO2 = 6.43 ml · kg-1 · min-1
Calculate the second term of the equation.
VO2 = 64.3 × 0.0 (level walking) × 1.8
VO2 = 0.0 ml · kg-1 · min-1
Calculate gross VO2 by adding resting VO2 to first two terms.
VO2 = 6.43 + 0.0 + 3.5
VO2 = 9.9 ml · kg-1 · min-1
Convert VO2 to METs.
9.9 ml · kg-1 · min-1/3.5 ml · kg-1 · min-1 = 2.8 METs
Calculate the net VO2.
2.8 METs – 1 MET (resting VO2) = 1.8 METs
Convert METs to kcal · kg-1 · hr-1.
1.8 METs × 1 = 1.8 kcal · kg-1 · hr-1
Calculate the net kcal · hr-1.
1.8 kcal · kg-1 · hr-1 × 55 kg = 99 kcal · hr-1
Convert kcal · hr-1 to kcal · min-1. 99 kcal · hr-1/60 min = 1.7 kcal · min-1