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Health & Fitness

Body metrics, nutrition, exercise and wellness formulae

Body Mass Index (BMI)

Basic
BMI=mh2BMI = \frac{m}{h^2}

Weight-to-height ratio used to classify body weight.

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BMI (Imperial)

Basic
BMI=703×mh2BMI = 703 \times \frac{m}{h^2}

BMI using pounds and inches.

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BMR (Mifflin, Men)

Intermediate
BMR=10m+6.25h5a+5BMR = 10m + 6.25h - 5a + 5

Basal metabolic rate — daily calories at rest for men.

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BMR (Mifflin, Women)

Intermediate
BMR=10m+6.25h5a161BMR = 10m + 6.25h - 5a - 161

Basal metabolic rate for women.

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Total Daily Energy (TDEE)

Intermediate
TDEE=BMR×activity factorTDEE = BMR \times \text{activity factor}

Daily calories burned including activity.

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Max Heart Rate

Basic
HRmax=220aHR_{max} = 220 - a

Estimated maximum heart rate by age.

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Target Heart Rate (Karvonen)

Advanced
HRtarget=(HRmaxHRrest)I+HRrestHR_{target} = (HR_{max} - HR_{rest})\,I + HR_{rest}

Training heart rate at intensity I.

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Body Fat % (Navy, Men)

Advanced
BF=4951.03240.19077log10(wn)+0.15456log10h450BF = \frac{495}{1.0324 - 0.19077\log_{10}(w-n) + 0.15456\log_{10}h} - 450

US Navy body-fat estimate for men from tape measurements.

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Waist-to-Hip Ratio

Basic
WHR=waisthipWHR = \frac{\text{waist}}{\text{hip}}

Fat-distribution health indicator.

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Ideal Body Weight (Devine)

Intermediate
IBW=50+2.3(h60)IBW = 50 + 2.3(h - 60)

Devine formula for men (kg), height in inches; women use base 45.5.

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Calories Burned (MET)

Intermediate
C=MET×m×tC = MET \times m \times t

Energy used during exercise.

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One-Rep Max (Epley)

Intermediate
1RM=w(1+r30)1RM = w\left(1 + \frac{r}{30}\right)

Estimated maximum single-lift weight.

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VO₂ Max (Cooper)

Advanced
VO2=d504.944.73VO_2 = \frac{d - 504.9}{44.73}

Aerobic fitness from a 12-minute run distance (metres).

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Daily Water Intake

Basic
W=0.033×mW = 0.033 \times m

Rough daily water need in litres.

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Lean Body Mass (Boer, Men)

Intermediate
LBM=0.407m+0.267h19.2LBM = 0.407m + 0.267h - 19.2

Body mass excluding fat for men.

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Protein from Calories

Basic
g=0.30×C4g = \frac{0.30 \times C}{4}

Grams of protein for a 30% protein diet (4 kcal/g).

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Running Pace

Basic
pace=td\text{pace} = \frac{t}{d}

Time taken to cover one unit of distance.

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Step Length from Height

Basic
L0.415×hL \approx 0.415 \times h

Estimated walking step length from height.

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Fat-Free Mass Index

Advanced
FFMI=LBMh2FFMI = \frac{LBM}{h^2}

Muscularity index normalised for height.

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Corrected QT (Bazett)

Advanced
QTc=QTRRQTc = \frac{QT}{\sqrt{RR}}

Heart-rate-corrected QT interval from an ECG.

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Mean Arterial Pressure

Intermediate
MAP=DBP+13(SBPDBP)MAP = DBP + \tfrac{1}{3}(SBP - DBP)

Average blood pressure during a cardiac cycle.

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Creatinine Clearance (Cockcroft-Gault)

Advanced
CrCl=(140a)m72×ScrCrCl = \frac{(140 - a)\,m}{72 \times S_{cr}}

Kidney function estimate (men; ×0.85 for women).

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Due Date (Naegele)

Basic
EDD=LMP+280 days\text{EDD} = LMP + 280\ \text{days}

Estimated delivery date from last menstrual period.

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BMR (Katch-McArdle)

Intermediate
BMR=370+21.6LBMBMR = 370 + 21.6\,LBM

Resting calories from lean body mass.

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RMR (Cunningham)

Intermediate
RMR=500+22LBMRMR = 500 + 22\,LBM

Resting metabolic rate favoured for athletes.

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Body Surface Area (Mosteller)

Intermediate
BSA=h×m3600BSA = \sqrt{\frac{h \times m}{3600}}

Total skin surface area of the body.

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Waist-to-Height Ratio

Basic
WHtR=waistheightWHtR = \frac{\text{waist}}{\text{height}}

Central-fat health indicator.

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BMI Prime

Basic
BMI prime=BMI25BMI\ prime = \frac{BMI}{25}

Your BMI relative to the upper healthy limit.

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Ponderal Index

Intermediate
PI=mh3PI = \frac{m}{h^3}

A leanness index that scales better for extreme heights.

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One-Rep Max (Brzycki)

Intermediate
1RM=w×3637r1RM = w \times \frac{36}{37 - r}

Estimated one-rep max, an alternative to Epley.

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Max Heart Rate (Tanaka)

Basic
HRmax=2080.7aHR_{max} = 208 - 0.7\,a

A more accurate maximum heart rate estimate.

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Heart Rate Reserve

Intermediate
HRR=HRmaxHRrestHRR = HR_{max} - HR_{rest}

The usable range between rest and maximum heart rate.

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Fat Mass

Basic
FM=m×BF%100FM = m \times \frac{BF\%}{100}

Total mass of body fat.

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MET to Oxygen Uptake

Intermediate
VO2=3.5×METVO_2 = 3.5 \times MET

Oxygen consumption from a MET activity level.

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Fat Loss from Deficit

Intermediate
Δm=deficit7700\Delta m = \frac{\text{deficit}}{7700}

Body-fat lost from a total calorie deficit.

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Daily Protein Target

Basic
P=1.6×mP = 1.6 \times m

Grams of protein per day to build muscle.

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Speed from Pace

Basic
v=60pacev = \frac{60}{\text{pace}}

Running speed in km/h from pace in min/km.

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Corrected QT (Fridericia)

Advanced
QTc=QTRR3QTc = \frac{QT}{\sqrt[3]{RR}}

Heart-rate-corrected QT interval using a cube root.

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Blood Glucose Conversion

Basic
mmol/L=mg/dL18\text{mmol/L} = \frac{\text{mg/dL}}{18}

Converts blood-sugar units between countries.

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