1. Metabolic Equations
ACSM Formulas

2. Conversion Factors used in Metabolic Calculations
1 KG= 2.2 lb
160 lb/2.2=72.7 kg kgX 2.2=132 lb
1 inch= 2.54 cm
12 in. x 2.54= 30.5 cm
1 m= 100cm
30.5 cm/100= m
1 mph= 26.8 meters per minute
6.0 mph x 26.8 = m.min

3. Conversions, cont. Min/mile pace= 60 min/mph 1 L = 1000 ml
60 min/7mph= 8.6 min/mile or 8:36 min:sec/mile
60 sec x 0.6 min= 36 sec
1 L = 1000 ml
1 L of O2= 5 kcal
1 MET = 3.5 ml . Kg . Min
1 MET = 1 kcal . Kg . Hr
1 Watt= 6 kgm.min
540 kgm/6 = 90 Watts
kgm.min= kg x 6 x rpm (monark cycle)

4. Metabolic terms: Absolute VO2= rate of O2 uptake in Liters/min.
Relative VO2= rate of O2 uptake in ml/kg/min. Used to compare VO2 between individuals of different body size.
Gross VO2= total consumption of O2 under any circumstances
Net VO2= O2 consumption rate above resting O2 consumption rate.
Used to describe the caloric cost of exercise

5. ACSM Leg Ergometry Equation:
For power outputs between kgm/min, or watts
VO2= (1.8 x kgm/min)/ M (wt. in kg) +(7) Or
VO2= (10.8 x watts) / M (wt. in kg) + (7)

6. ACSM Leg Ergometry Equation
To calculate the energy expenditure of a 62 kg woman cycling at a work rate of 450 kgm.min:
VO2= (1.8 x 450)/
VO2= 810/62 + 7
VO2=
VO2= 20 ml/kg/min

7. ACSM Walking Equation
For speeds of m/min. ( mph)
VO2= Resting Component + Horizonal Component + Vertical Component
R= 3.5 ml. kg. min.
H=speed (m/min) X 0.1
V=grade (decimal) X m/min X 1.8
VO2= (0.1 x S) + (1.8 x S x G) + 3.5
(H) (V) (R)

8. ACSM Walking Equation
Calculate VO2 for a 70 kg subject who is walking on the treadmill at a speed of 3.5 mph and a grade of 10%:
1. Convert speed in mph to m.min (3.5 x 26.8= 93.8)
2. Calculate horizontal component. H = speed (m.min) x 0.1 (93.9 x 0.1 = 9.38 ml.kg.min)
3. Calculate vertical component: V= grade (decimal) x speed x 1.8 (.10 x 93.8 x 1.8= ml.kg.min
4. Calculate total VO2 by adding H, V, and R (resting) components: VO2= H + V + R ( )= ml.kg.min
Convert VO2 to METS by dividing by 3.5: (29.76/3.5 = 8.5 METS

9. ACSM Running/Jogging Formula
For speeds > 134 m/min (>5.0 mph), (or for speeds as low as 3mph if jogging)
VO2= Resting Component + Horizontal Component + Vertical Component
R= 3.5 ml.kg.min
H= speed (m/min) X 0.2
V= grade (decimal) X m/min X 0.9
VO2= (0.2 x S) + (0.9 x S x G) + 3.5
(H) (V) (R)

10. ACSM Jogging/running Formula
Calculate VO2 for someone running a 7.5 mph. (200 meters/min) With a 5% grade?
VO2= 3.5+ (m/min X 0.2)
43.5= (200 x 0.2)
For uphill running, add:
grade (decimal) x m/min x 0.9
VO2= (200 x 0.2) + (.05 x 200 x 0.9)
VO2= 52.5

11. Arm Ergometer Equation
For power outputs between kgm.min or watts:
VO2= (3 x kgm) / kg + 3.5 Or
VO2= (18 x watts) / kg + 3.5

12. ACSM Arm Egometer Equation
Calculate VO2 for a 50 kg. Individual cycling at 600 kgm:
VO2= 3 x 600/
VO2= 1800/
VO2=
VO2= 39.5 ml.kg.min

13. ACSM Stepping Equation
Convert stepping height in inches to meters
Stepping rate is steps per minute
VO2=
(0.2 x stepping rate) +
(1.33 x 1.8 x step height in meters x rate) +
3.5

14. ACSM Stepping Equation:
To calculate VO2 for bench stepping using a 16 inch step height at a cadence of 24 steps/min.
16 inches = meters
(0.2 x 24) + (1.33 x 1.8 x x 24) + 3.5
VO2=
VO2= 38.8 ml/kg/min

15. Estimating VO2 from Maximal Bruce Protocol
Male:
VO2 max = (1.379 x time) + (0.451 x time2) - (0.012 x time3)
Female:
VO2 max= (4.38 x time) – 3.90

16. Estimating VO2 Max from Balke Protocol (max)
Male:
VO2 max= x time
Female:
VO2 max= 1.38 x time

17. Estimating VO2 max from Submax Treadmill Protocol (multistage)
Use HR and WL data from two or more submaximal stages of treadmill test.
Client must reach steady-state HR between
Determine slope: (b)= (SM2-SM1)/(HR2-HR1)
SM1 and SM2 are expressed as VO2
VO2= SM2 + b (Hr max- HR2)

18. Estimating VO2 from Submaximal Treadmill Test (single-stage)
Use one submaximal HR and one workload
Steady-state HR should reach between bpm
Calculate SM VO2 and METS using ACSM equation (remember…1MET= 3.5 ml/kg/min)
VO2 (male)= SM VO2 (expressed as METs) x (Hrmax-61)/ (HRsm- 61)
VO2 (female)= SM VO2 (expressed at METs) x (Hrmax-72)/ HRsm –72)