Key Exercise Physiology Formulas and Conversions

Posted on Feb 25, 2025 in Physical Education

Exercise Physiology: Key Formulas and Conversions

Conversions

  • 1 kg = 2.2 lb
  • 1 inch = 2.54 cm
  • 1 mph = 26.8 m/min
  • 1 L of O2 = 5 kcal
  • 1 lb of fat gain/loss = 3500 kcal
  • 1 inch = 0.0254 m

Cardiac Output (Q) and Stroke Volume (SV)

Oxygen Consumption (VO2) – Fick Equation

VO2 (ml/min) = Cardiac Output (Q) x a-v O2 difference (ml/100ml)

Myocardial Oxygen Demand (MVO2) – Double Product or Rate-Pressure Product

MVO2 (mmHg/min) = [HR (bpm) x Systolic BP (mmHg)] / 100

Oxygen Pulse (O2 Pulse)

O2 pulse (ml O2/beat) = VO2 (ml O2/min) / HR (bpm)

Pulse Pressure

Pulse pressure (mmHg) = Systolic BP (mmHg) – Diastolic BP (mmHg)

Mean Arterial Pressure (MAP)

MAP (mmHg) = [(Systolic BP – Diastolic BP) / 3] + Diastolic BP

Maximum Heart Rate and Target Exercise Heart Rate

Maximal Heart Rate (HR max)

Predicted HRmax (bpm) = 220 – age in years (yields a low estimate)

Predicted Tanaka-HRmax (bpm) = 208 – (0.7 x age in years)

Target Exercise Heart Rate (THR)

Karvonen method (also referred to as heart rate reserve: HRR)

THR (bpm) = [% exercise intensity x HRR] + HR rest, where HRR = HR max – HR rest

%Predicted HRmax method

THR (bpm) = [% exercise intensity x HR max]

Weight Loss and Target Body Weight

Target Body Weight

  1. Calculate fat-free mass: FFM (lb) = BM (lb) x present %FFM
  2. Target BM (lb) = FFM (lb) / %FFM goal

Weight Loss

  1. BM loss (lb) = present BM (lb) – target BM (lb)
  2. Caloric deficit (1 lb fat loss = 3,500 kcal): BM loss (lb) x 3,500 (kcal/lb) = total kcal deficit needed

Metabolic Calculation (ACSM equations)

Walking (1.9 to 3.7 mph)

Gross VO2 (ml/kg/min) = [S x 0.1] + [S x G x 1.8] + 3.5

Running (>5.0 MPH)

Gross VO2 (ml/kg/min) = [S x 0.2] + [S x G x 0.9] + 3.5

Leg Ergometry (300 to 1,200 kgm/min)

Predicted VO2 (ml/kg/min) = [Watts / M x 10.8] + 3.5 + 3.5

Gross VO2 (ml/kg/min) = [W / M x 10.8] + 3.5 + 3.5

Arm Ergometry (150 to 750 kgm/min)

Gross VO2 (ml/kg/min) = [W / M x 10.8] + 3.5

Stepping (300 to 1,200 kgm/min; Includes stepping up & down)

Gross VO2 (ml/kg/min) = [F x 0.2] + [F x ht x 1.8 x 1.33] + 3.5

Key

  • S = speed of treadmill in m/min; 1 mph = 26.8 m/min
  • G = grade (%incline) of treadmill in decimal form (e.g. 10% = 0.10)
  • W = work rate in kgm/min
  • M = body mass in kg; 1kg = 2.2 lb
  • F = frequency of stepping in steps/min
  • ht = bench in height in meters; 1 in. = 0.0254 m

Lab 1: Body Composition

Evans et al. (1987) equation: BF% = 8.997 + 0.2468(Σ3SKF) – 6.343(S) – 1.998(E)

Where S = sex (1=male, 0= female) and E = ethnicity (1= African American and 0= Caucasian).

Jackson and Pollock (1980) for males (chest, abdomen, and thigh): Db = 1.109380 – 0.0008267(Σ3SKF) + 0.0000016(Σ3SKF)2 – 0.0002574(age)

Jackson and Pollock (1978) for females (Suprailiac crest, Triceps and thigh): Db = 1.0994921 – 0.0009929 (Σ3SKF) + 0.0000023(Σ3SKF)2 – 0.0001392(age)

Siri (1961) equation: %BF = [(4.95 / Db) – 4.50] x 100

Lab 2: ECG Interpretation

HR: Bradycardia (<60bpm) Normal sinus rhythm (60-100BPM) tachycardia (>100bpm)

PR Interval: normal (<0.20s) prolonged (>0.20s) 0.20s = 5 small squares

QRS Interval: normal (<0.12 s) prolonged (>0.12s) 0.12s = 3 small squares

Lab 3: VO2max Prediction

Note: Predicted VO2max based on performance in the Bruce Protocol can be calculated from the following gender-specific equations: where, time is expressed in fractions of a minute e.g. 10 minutes 15 seconds = 10.25 minutes.

Females: Predicted VO2 max (mL/kg/min) = 14.76 – 1.379 (time) + 0.451 (time2) – 0.012(time3)

Males: Predicted VO2 max (mL/kg/min) = 4.38 (time) – 3.90

VO2max Calculation Example

Therefore, if the participant runs 0.78 miles in 5 minutes, then we can determine their VO2max as follows:

First, solve for vVO2max: 0.78 miles / 5 minutes = 0.156 mi/min, convert to km/min by multiplying mi/min by 1.6 = 0.250 km/min, convert to m/min by multiplying km/min by 1000 = 250 m/min

Next, solve for VO2max by entering the known values: 0.210 mL/kg/min and 250 m/min = 0.210 mL/kg/min x 250 m/min = 52.5 mL/kg/min

The relationship is as follows: For running (>5.0 mph): gross VO2 (ml/kg/min) = [S x 0.2] + [S x G x 0.9] + 3.5

Where, S = speed of treadmill In m/min; 1 mph = 26.8 m/min G = grade (% incline) of treadmill in decimal form (e.g., 10% = 0.10)

Therefore, for the same participant as exampled above: = [250 m/min x 0.2] + [250 m/min x 0 x 0.9] + 3.5 = [50] + [0] + 3.5 = 53.5 mL/kg/min

Non-Exercise VO2max Estimation

Estimated VO2max (mL/kg/min) = 65 + 1.8 (frequency) – 10 (sex, M=0 and Females= 1) – 0.3 (age) – 0.6 (BMI= kg/m2)

Estimated VO2max (mL/kg/min) + 3.5 (mL/kg/min) = METS Note: 1 MET = 3.5 (mL/kg/min)

Non-Exercise Determination of VO2max Based on ratio between Maximum and Resting Heart Rates

Uth, Niels; Henrik Sørensen; Kristian Overgaard; Preben K. Pedersen (2004). Estimation of VO2max from the ratio between HRmax and HRrest – the Heart Rate Ratio Method. Eur J Appl Physiol. 91 (1): 111-5.

Estimated VO2max (mL/kg/min) = 15.3 x [estimated Maximum Heart Rate (bpm) / Resting Heart Rate (bpm)] = 15.3 x (MHR / RHR)

Where, MHR = Maximum heart rate (beats/minute) 208 – (0.7 x Age) RHR = Radial Pulse resting heart rate (beats/20 seconds) = 20 second heart rate x 3 = bpm