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 inch= 2.54 cm– 12 in. x 2.54= 30.5 cm

• 1 m= 100cm– 30.5 cm/100= 0.305 m

• 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

• 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:

• 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%:• 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

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?

• 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

Arm Ergometer Equation

• For power outputs between 150-750 kgm.min or 25-125 watts:

• VO2= (3 x kgm) / kg + 3.5

• Or

• VO2= (18 x watts) / kg + 3.5

ACSM Arm Egometer Equation

• Calculate VO2 for a 50 kg. Individual cycling at 600 kgm:

• VO2= 3 x 600/50 +3.5

• VO2= 1800/50 + 3.5

• VO2= 36 + 3.5

• VO2= 39.5 ml.kg.min

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

ACSM Stepping Equation:

• To calculate VO2 for bench stepping using a 16 inch step height at a cadence of 24 steps/min.

• 16 inches = .4064 meters

• (0.2 x 24) + (1.33 x 1.8 x .4064 x 24) + 3.5

• VO2= 4.8 + 30.5 + 3.5

• VO2= 38.8 ml/kg/min

Estimating VO2 from Maximal Bruce Protocol

• Male:

• VO2 max = 14.76 - (1.379 x time) + (0.451 x time2) - (0.012 x time3)

• Female:

• VO2 max= (4.38 x time) – 3.90

Estimating VO2 Max from Balke Protocol (max)

• Male:

• VO2 max= 1.444 x time + 14.99

• Female:

• VO2 max= 1.38 x time + 5.22

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 115-150

• Determine slope: (b)= (SM2-SM1)/(HR2-HR1)– SM1 and SM2 are expressed as VO2

• VO2= SM2 + b (Hr max- HR2)

Estimating VO2 from Submaximal Treadmill Test

(single-stage)

• Use one submaximal HR and one workload• Steady-state HR should reach between 130-150 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)