Metabolic Equations
ACSM Formulas
Conversion Factors
used in Metabolic Calculations
• 1 KG= 2.2 lb
– 160 lb/2.2=72.7 kg
60 kgX 2.2=132 lb
• 1 mph= 26.8 meters per minute
– 6.0 mph x 26.8 = 160.8 m.min
Conversions, cont.
• Min/mile pace= 60 min/mph
– 60 min/7mph= 8.6 min/mile or 8:36 min:sec/mile
– 60 sec x 0.6 min= 36 sec
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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)
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
ACSM Leg Ergometry Equation:
• For power outputs between 300-1200
kgm/min, or 50-200 watts
– VO2= (1.8 x kgm/min)/ M (wt. in kg) + (7)
– Or
– VO2= (10.8 x watts) / M (wt. in kg) + (7)
ACSM Leg Ergometry Equation
• To calculate the energy expenditure of a 62
kg woman cycling at a work rate of 450
kgm.min:
To calculate the energy expenditure
of a 62 kg woman cycling at a work
rate of 450 kgm.min:
VO2= (1.8 x 450)/ 62 + 7
VO2= 810/62 + 7
VO2= 13 + 7
VO2= 20 ml/kg/min
ACSM Walking Equation
• For speeds of 50-100 m/min. (1.9-3.7 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)
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%:
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= 16.88 ml.kg.min
4. Calculate total VO2 by adding H, V, and R (resting)
components: VO2= H + V + R (9.38 + 16.88 + 3.5)= 29.76
ml.kg.min
Convert VO2 to METS by dividing by 3.5: (29.76/3.5 = 8.5 METS
How many kcals burned in 20 minutes?
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)
ACSM Jogging/Running
Formula
• Calculate VO2 for someone running a 7.5
mph. (200 meters/min) With a 5% grade?
Calculate VO2 for someone running at
7.5 mph. (200 meters/min)
With a 5% grade?
VO2= 3.5+ (m/min X 0.2)
43.5= 3.5 + (200 x 0.2)
For uphill running, add:
grade (decimal) x m/min x 0.9
VO2= 3.5 + (200 x 0.2) + (.05 x 200 x 0.9)
VO2= 52.5
What is the total amount of work on a cycle ergometer
Kpm/min
Joules
With 2-kg resistance, 6 m•rev–1, 60 rev•min–1 for 5 min
With 2-kg resistance, 6 m•rev–1, 60
rev•min–1 for 5 min
2 kg needs to go to N - 2 X 9.79 = 19.58
19.58 x 6m/rev x 60 revs/min x 5 min
35244 Joules
For kpm/min – use 2 kg and do not convert to N
3600 kpm/min
Calculate the avg. power output during 10 min of cycle ergometer
Exercise in which a total of 10,000 kpm of work was performed
Answer in kpm/min and Watts
Calculate the avg. power output during 10 min of cycle ergometer
exercise in which a total of 10,000 kpm of work was performed.
Answer in kpm/min and Watts
Work = Force X Distance
Power = Force X Distance divided by time
10,000 kpm of work
Divide by 10 min
1,000 kpm/min
1,000/6 = 166.7 Watts
1 Watt = 6 kgm/min
Calculate the work during 2-min
of treadmill exercise by a 60-kg
person running at 200
meters/min up a 10 % grade.
Calculate the work during 2-min of
treadmill exercise by a 60-kg person
running at 200 meters/min up a 10 %
grade.
Vertical displacement = % grade x distance
0.1 x (200 m•min–1 x 2 min) = 40 m
Work = body weight x total vertical distance
60 kg x 9.79 = 587.4 N
587.4 N x 40 m = 23496 J
Power = work ÷ time
23496 J ÷ 120 s = 195.8 W