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Metabolic Equations ACSM Formulas

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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

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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)

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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

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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)

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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

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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)

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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

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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)

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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

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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

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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

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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

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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

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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

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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

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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)

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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)

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