ACSM Metabolic Equations (HPRED 1410, Dr Bailey, Appendix D, Guidelines)

1. 1
ACSM Metabolic Equations
(HPRED 1410, Dr Bailey, Appendix D, Guidelines)
ACSM metabolic equations are typically used for two purposes:
1. To calculate oxygen consumption and from this, the energy expenditure
of a given exercise.
2. To calculate the target workload for a client on the specific mode used.
Note that each equation will have the following components:
VO2 = horizontal component + vertical component + resting component
Walking
Walking: VO2 = H + V + R
Walking: VO2 = 0.1(speed) + 1.8 (speed) (fractional grade) + 3.5
0.1 ml x kg-1
x min-1
= O2 cost of horizontal movement
1.8 ml x kg-1
x min-1
= O2 cost of vertical ascent
Speed = speed in m x min-1
Running
Running: VO2 = H + V + R
Running: VO2 = 0.2 (speed) + 0.9 (speed)(fractional grade) + 3.5
0.2 ml x kg-1
x min-1
= O2 cost of horizontal motion
0.9 ml x kg-1
x min-1
= O2 cost of vertical ascent cost

2. 2
Stepping
Stepping: VO2 = H + V + R
Stepping: VO2 = 0.2 (stepping rate) +1.33 x 1.8 (step height)(step freq) +3.5
= 0.2 (stepping rate) + 2.4 (step height)(step freq) +3.5
1.8 ml x kg-1
x min-1
= O2 cost of vertical ascent
1.33 = O2 cost of stepping down (vertical descent)
(1.33 includes the positive component of stepping up (1.0), and the negative
component of stepping down. (0.3)
step height = step height in meters, step freq = stepping frequency in min-1
Leg and Arm Ergometry
Note that there is no horizontal or vertical component here. All we see is the
resistive component (V) from the ergometer.
Leg Ergometry
Leg Ergometry: VO2 = V (resistive) + R
Note: 1. There is no horizontal component in leg ergometry
2. The vertical component is actually a resistive component.
Leg Ergometry: VO2 = (10.8 x W x M-1
) + 7
Use (mathematically equivalent); VO2 = 1.8 (work rate)/body mass + 7
1.8 ml x kg-1
x min-1
= cost of cycling against external load
3.5 ml x kg-1
x min-1
= cost of unloaded cycling above and
beyond resting metabolism, so “7” is 3.5 + 3.5.
W = watts, M = mass in Kgs

3. 3
Arm Ergometry
Arm Ergometry: VO2 = V (resistive) + R
Arm Ergometry: VO2 = (18 x W x M-1
) + 3.5
Use (mathematically equivalent); VO2 = 3 (work rate)/body mass + 3.5
Note: 1. There is no horizontal component in leg ergometry
2. The vertical component is actually a resistive component.
3. In arm ergometry, arm muscle mass is so small that there is
no term for unloaded cyling. Hence, no “7” is seen.
Also needed for arm and leg ergometry:
Power (Kg x m x min-1
) = (Kg setting)(D)(pedaling cadence in rpm)
D = 6 meters for Monark
= 3 meters for Tunturi
= 2.4 for Monark arm ergometer
Stepwise Approach to Metabolic Calculation
1. Conversion to appropriate units and knowledge of common
equivalents.
A. Convert all weights from pounds (lbs) to kilgrams.
* Pounds/2.2 = kilograms
B. Convert speed from miles per hour (m/hr) to meters per minute
(m/min).
* miles/hr x 26.8 = meters/minute
* (also useful; 60/(min/mile) = miles per hour
C. Common equivalents
* (Caloric expenditure in kcals x min-1
)/5 = VO2 in L x min-1
* Liters O2 x 5 kcals/liter O2 = kcals
* 1 pound of fat = 3,500 kcals
* METs x 3.5 m x kg-1
x min-1
= VO2 in ml x kg-1
x min-1
* Gross VO2 in ml x kg-1
x min-1
/ 3.5 = METs
* Power in watts x 6 = workload in kg x m x min-1
* (kgm/min)/6 = watts

4. 4
2. Transform VO2 into the most appropriate units.
A. If weight bearing; walking, running, stepping, use ml x kg-1
x min-1
B. If cycling or arm, use ml/min
C. If caloric expenditure needed, convert from ml x kg-1
x min-1
to
liters/minute
3. Choose the proper equation for gross VO2:
Walking: VO2 = 0.1(speed) + 1.8 (speed) (fractional grade) + 3.5
Running: VO2 = 0.2 (speed) + 0.9 (speed)(fractional grade) + 3.5
Stepping: VO2 = 0.2 (step rate) +1.33 x 1.8 (step height)(step rate) +3.5
(step height in meters, where 1 inch =.0254 m)
Leg Ergometry: VO2 = 1.8 (work rate)/body mass + 7
Arm Ergometry VO2 = 3 (work rate)/body mass + 3.5
Power (Kg x m x min-1
) = (Kg setting)(D)(pedaling cadence in rpm)
Example from ACSM Guidelines
1. 30 year old man: He wants to walk at 3.5 mph
* 180 lbs
* RHR of 60
* MHR of 190
* VO2 max 48 ml/kg/min.. You want him at 70 % of his VO2 R
A. What is his minimum training heart rate by the Karvonen method?
THR = (.70)(190 - 60) + 60
THR = 91 + 60 = 151 beats/min
B. What is his target VO2?
VO2R = 48 ml/kg/min – 3.5 ml/kg/min = 44.5 = net VO2
= .70 x 44.5 = 31.2 ml/kg/min

5. 5
C. How steep should the treadmill be if he is walking at his preferred
3.5 mph?
VO2 = 0.1 (speed) + 1.8 (speed)(fractional grade) + 3.5 ml/kg/min
31.2 = 0.1 (93.8) + 1.8 (93.8) (frac grade) + 3.5 ml/kg/min
27.7 = 0.1 (93.8) + 1.8 (93.8)(frac grade)
27.7 = 9.38 + 168.8 (frac grade)
18.3 = 168.8 (frac grade)
fractional grade = 10.8 %
D. What is his target work rate on the Monark bike?
His body mass = 180 lbs/2.2 = 81.8 kg
VO2 = 7.0 +1.8 (work rate)/body mass
VO2 = 7.0 +1.8 (work rate)/81.8
31.2 = 7.0 + 1.8 (work rate)/81.8
24.2 = 1.8 (work rate)/81.8
1980 = 1.8 (work rate)
work rate = 1100 kg x m-1
x min-1
E. If he wants to pedal at 60 rpm on a Monark cycle, what resistance
setting should be used.
Power (Kg x m x min-1
) = (Kg setting)(D)(pedaling cadence in rpm)
Work rate = (resistance setting)(D)(pedal cadence)
1100 = (resistance setting)(6)(60)
1100 = (resistance setting)360
Resistance setting = 3.05 kg
F. What is the caloric expenditure during 30 minutes of exercise?
Net VO2 = 31.2 ml/kg/min
(VO2 in ml/kg/min)(body mass)/1000 = VO2 L/min
(31.2)(81.8)/1000 = 2.55 L/min
2.55 L/min x 5 = 12.8 kcal/min
12.8 kcal/min x 30 = 383 kcals

6. 6
Text examples, page 311, Guidelines
HPRED 1410, Feb 23, 2004
1. A man weighing 176 lbs runs a pace of 9 minutes per mile outdoors, on
level ground. What is his estimated gross VO2 ?
Conversion to appropriate units and knowledge of common
equivalents.
S = 9 minutes/mile, to convert to m x min-1
,
1. mph = 60  min/mile = mph
= 60/9 = 6.66
2. m x min-1 = 6.66 x 26.8 = 178.5
Choose the proper equation for gross VO2: Running:
VO2 = 0.2 (speed) + 0.9 (speed)(fractional grade) + 3.5
VO2 = (0.2 x 178.5 m x min-1
) + 0 + 3.5
VO2 = 35.7 + 0 + 3.5 = 39.2 ml x kg-1
x min -1
2. To match this exercise intensity (from above) on a Tunturi cycle
ergometer, what setting would you use at a pedal rate of 60 rpm?
Conversion to appropriate units and knowledge of common
equivalents.
176lbs/2.2 = 80 kgs
Choose the proper equation for gross VO2: Leg Ergometry:
VO2 = 1.8 (work rate)/mass + 7
39.2 ml x kg-1
x min -1
= (1.8 x W)/80 + 7
32.2 = 1.8W/80
1431 kg m min = work rate

7. 7
Power (Kg x m x min-1
) = (Kg setting)(D)(pedaling cadence in rpm)
1431 = Kg (3)(60)
Kg = 7.95
3. If this same man exercised at this intensity 5 times a week for 30
minutes each session, how long would it take him to lose 12 pounds?
(20) p. 311 top
Net VO2 = 39.2 -3.5 = 35.7
Liter of oxygen used =
35.7 ml x kg-1
x min -1
x 80 kg/1000 = 2.856 L/min O2
Kcals used per minute =
2.856 L/min x 5 kcals/Liter O2 = 14.28 kcals
Kcals per session = 14.28 kcals/min x 30 minutes = 428.4 kcals
Kcals/week = 5 times/wk x 428.4 = 2142 kcals/wk
Total Kcals to lose = 12 lbs x 3500 kcals/lb = 42000 kcals
Weeks to lose it = 42000kcals/2142 kcals/week = 19.6 weeks
4. For a desired training intensity of 75 % of the VO2res, at what heart rate
should a 45 year old woman exercise ? Her resting heart rate is 70 beats
a minute.
MHR = 220 - 45 = 175
HRR = 175- 70 = 105
.75 x 105 = 78.75
78.75 + 70 = 149
5. A 198 pound cardiac patient wishes to use an arm ergometer for part of
his rehabilitation program. He works at a power output of 300
kgxmxmin for 15 minutes and then at 450 kgxmxmin for 15 minutes.
What is his average net VO2 (in ml x kg-1
x min -1
) over this session?
198/2.2 = 90 kgs

8. 8
Arm Ergometry VO2 = 3 (work rate)/body mass + 3.5
First 15 minutes; VO2 = 3 (300)/90 + 3.5
Gross VO2 = 900/90 +3.5 = 13.5 ml x kg-1
x min -1
Net VO2 = 13.5 –3.5 = 10 ml x kg-1
x min -1
15 minutes x 10.0 = 150.0 ml x kg-1
x min -1
Second 15 minutes: VO2 = 3 (work rate)/body mass + 3.5
Gross VO2 = 3(450)/90 + 3.5 = 18.5 ml x kg-1
x min -1
Net VO2 = 18.5 – 3.5 = 15 ml x kg-1
x min -1
15 minutes x 15.0 = 225.0 ml x kg-1
x min -1
Average net= (150 + 225)/30 = 12.5 ml x kg-1
x min -1
6. If an individual reduces his or her dietary intake by 1750 kcal per week,
how much weight (in lbs) would he or she lose in 6 months (26 weeks)?
Weight lost per week = 1750/3500 = .5 pounds
26 x .5 = 13 pounds
7. If an 18 year old girl steps up and down on a 12 inch step at a rate of 20
steps (complete up and down cycles) per minute, what would her gross
VO2 be (in ml x kg-1
x min -1
) ?
Stepping:
Gross VO2 = 0.2 (step rate) +1.33 x 1.8 (step height)(step rate) +3.5
= 0.2(20) + 1.33 x 1.8 (12)(20) + 3.5
1 inch = 0.0254 meters
step height in meters = 12 x .0254 = .3048

9. 9
VO2 = 0.2(20) + 1.33 x 1.8 (.3048)(20) + 3.5
= 4 + 14.59 + 3.5 = 22.09 ml x kg-1
x min -1
8. A 71-year-old man weighing 180 pounds walks on a motor-driven
treadmill at 3.5 mph and a 15 % grade. What is his gross MET level?
Walking: VO2 = 0.1(speed) + 1.8 (speed) (fractional grade) + 3.5
3.5 mph x 26.8 = 93.8 m/min
VO2 = 0.1(speed) + 1.8 (speed) (fractional grade) + 3.5
= 0.1(93.8) + 1.8(93.8)(.15) + 3.5
= 9.38 + 25.33 + 3.5 = 38.2 ml x kg-1
x min -1
Gross MET level = 38.2/3.5 = 10.9 METs

10. 10
Case Studies for HPRED 1410
Case Study 1:
70 kg man uses 2 liters of oxygen in one minute.
A. How many calories did he burn?
B. What was his exercise in METs?
Case Study 2: A man with the following information will burn how many
kcals each exercise session while running?
Treadmill at 1 % grade
Speed = 6.5 mph
Time = 30 minutes
5 times a week
Body weight = 175 pounds
= 79.5 kg
Case Study 3: If the same man walks for 30 minutes per session, how many
calories per session will he burn?
Treadmill at 4 % grade
Speed = 4.4 mph
Time = 30 minutes
5 times a week
Body weight = 175 pounds
Case Study 4: 38 year old male, resting heart rate = 60, body weight of 170
pounds, percent body fat = 18%
1. Calculate his training heart rate range from 60 to 75 % of the heart rate
reserve.
2. How many weeks would it take him to reduce his body weight to 12 %
body fat if he adhered to a proper program?

11. 11
Case Study 5: A 25 year old woman who weighs 130 pounds has a
predicted VO2 max of 40 ml x kg-1
x min -1
. You decide that you want her to
exercise (run) at 60 % of her VO2 R.
1. How fast should you set the treadmill speed in miles per hour assuming
zero percent grade?
2. If she runs for 40 minutes, 4 days per week, how many calories wills she
burn?
3. At this rate, many weeks would it take her to burn 10 pounds through
this exercise?
Case Study 6: A 24 year old male client tells you that during his last
treadmill run, he measured his heart rate at 145 beats per minute. He tells
you that his resting heart rate is 60. He wants to know “how intense” you, as
an exercise physiologist, think this is.
What percentage of the heart rate reserve (% VO2R ) was he running at?
Case Study 7: You measure a 48 year old man’s VO2 max to be 30 ml x kg-
1
x min –1
. He tells you that he wants to begin shoveling snow from his
driveway from now on for exercise, instead of hiring a local kid. According
to the ACSM RM, heavy shoveling is about 9 MET exertion. What would
you advise him?
Your advice:

12. 12
Case Study Solutions for ACSM Guidelines Problems
Case Study 1:
70 kg man uses 2 liters of oxygen in one minute.
A. How many calories did he burn?
2 liters x 5 kcals/liter = 10 kcals
B. What was his exercise in METs?
1. 2 liters of oxygen = 2000 millilters of oxygen
2. 2000/70 kg = 28.6 ml/Kg oxygen in one minute
3. MET level = 28.6 ml x kg-1
x min-1
/ 3.5 ml/kg/min= 8 METs
4. This is a light jog pace.
Case Study 2: A man with the following information will burn how many
kcals each exercise session while running?
Treadmill at 1 % grade
Speed = 6.5 mph
Time = 30 minutes
5 times a week
Body weight = 175 pounds
= 79.5 kg
Running: Gross VO2 = 0.2 (speed) + 0.9 (speed)(fractional grade) + 3.5
First you need speed in m/min: 6.5 mph x 26.8 = 174.2 m/min
Gross VO2 = 0.2 (174.2) + 0.9 (174.2)(.01) + 3.5
= 34.84 + 1.57 + 3.5 = 39.9 ml x kg-1
x min -1
Net VO2 = 39.9 –3.5 = 36.4 ml x kg-1
x min -1
Liters/minute = (36.4 x 79.5)/1000 = 2.895 Liters/min
2.895 x 5 kcals/liter = 14.5 kcals/minute

13. 13
30 x 14.5 = 434.3 kcals
Case Study 3: If the same man walks for 30 minutes per session, how many
calories per session will he burn?
Treadmill at 4 % grade
Speed = 4.4 mph
Time = 30 minutes
5 times a week
Body weight = 175 pounds
Walking: Gross VO2 = 0.1(speed) + 1.8(speed)(fractional grade) + 3.5
4.4 mph x 26.8 = 117.92 m/min
Gross VO2 = 0.1(117.92) + 1.8(117.92)(.04) + 3.5
11.79 + 8.49 + 3.5 = 23.7 ml x kg-1
x min –1
Net VO2 = 23.7 –3.5 = 20.2 ml x kg-1
x min -1
Liters/minute = (20.2 x 79.5)/1000 = 1.6 Liters/min
1.6 x 5 = 8 kcals/minute, 30 x 8 = 240 kcals
Case Study 4: 38 year old male, resting heart rate = 60, body weight of 170
pounds, percent body fat = 18%
1. Calculate his training heart rate range from 60 to 75 % of the heart rate
reserve.
Minimum THR = (182 - 60) x .60 + 60 = 133.2
Maximum THR = (182 - 60) x .75 + 60 = 151.5
2. How many weeks would it take him to reduce his body weight to 12 %
body fat if he adhered to a proper program?

14. 14
Case Study 5: A 25 year old woman who weighs 130 pounds has a
predicted VO2 max of 40 ml x kg-1
x min -1
. You decide that you want her to
exercise (run) at 60 % of her VO2 R.
1. How fast should you set the treadmill speed in miles per hour assuming
zero percent grade?
VO2 R: 40 ml/kg/min – 3.5 ml/kg/min = 36.5 ml/kg/min
Running: VO2 = 0.2 (speed) + 0.9 (speed)(fractional grade) + 3.5
Target VO2 = .60 x 36.5 ml x kg-1
x min –1
= 24 ml x kg-1
x min –1
.
21.9 = 0.2 (speed) + 0.9 (speed)(0) + 3.5
21.9 = 0.2 (speed) + 3.5
18.4 = 0.2 (speed)
Speed = 92 meters/min
miles/hr x 26.8 = meters/minute
miles/hr x 26.8 = 92 meters/minute
Speed in mph for the treadmill = 92/26.8 = 3.4 mph
(Note: You might find that this client will prefer to walk and need to
recalculate.)
2. If she runs for 40 minutes, 4 days per week, how many calories wills she
burn?
Weight in Kgs = 130/2.2 = 59.1 kgs
Net VO2 = 24 -3.5 = 20.5 ml x kg-1
x min –1
(20.5 ml x kg-1
x min –1
x 59.1)/1000 = 1.211 Liters/O2 per minute
Kcals burned per minute = 1.211 x 5 kcals/liter O2 = 6.06 kcals
Kcals burned per session = 6.06 x 40 minutes = 242.31 kcals
Kcals burned per wk = 242.31 kcals x 4 days/week = 969.2 kcals/week

15. 15
3. At this rate, many weeks would it take her to burn 10 pounds through
this exercise?
10 pounds x 3,500 kcals/pound = 35,000 kcals
35,000/969.2 = 36.1 weeks
Case Study 6: A 24 year old male client tells you that during his last
treadmill run, he measured his heart rate at 145 beats per minute. He tells
you that his resting heart rate is 60. He wants to know “how intense” you, as
an exercise physiologist, thinks this is.
What percentage of the heart rate reserve (% VO2R ) was he running at?
% VO2R = (Exercise HR - Resting HR)/(Max HR - Resting HR)
% HRR = (145 – 60)/(196-60)
= 85/136 = 62.5 % HRR
Case Study 7: You measure a 48 year old man’s VO2 max to be 30 ml x kg-
1
x min –1
. He tells you that he wants to begin shoveling snow from his
driveway from now on for exercise, instead of hiring a local kid. According
to the ACSM RM, heavy shoveling is about 9 MET exertion. What would
you advise him?
Functional Capacity = 30/3.5 = 8.57 METs
Your advice:
This would often require supramaximal (above his VO2 max) exertion and he
is 48 years old, at least “moderate risk”. Keep hiring the kid and begin a
light supervised exercise program.