Health & Fitness

Body metrics, nutrition, exercise and wellness formulae

The Health & Fitness category brings together practical formulas for measuring the body, planning nutrition, and tracking exercise and wellness goals. From BMI and BMR to heart rate, body fat, and calories burned, these equations help students, exam learners, and professionals in fitness, healthcare, and sports use numbers to make informed, real-world decisions about health.

Body Mass Index (BMI)

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

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

BMI (Imperial)

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

BMI using pounds and inches.

BMR (Mifflin, Men)

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

Basal metabolic rate — daily calories at rest for men.

BMR (Mifflin, Women)

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

Basal metabolic rate for women.

Total Daily Energy (TDEE)

TDEE = BMR \times \text{activity factor}

Daily calories burned including activity.

Max Heart Rate

HR_{max} = 220 - a

Estimated maximum heart rate by age.

Target Heart Rate (Karvonen)

HR_{target} = (HR_{max} - HR_{rest})\,I + HR_{rest}

Training heart rate at intensity I.

Body Fat % (Navy, Men)

BF = \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.

Waist-to-Hip Ratio

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

Fat-distribution health indicator.

Ideal Body Weight (Devine)

IBW = 50 + 2.3(h - 60)

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

Calories Burned (MET)

C = MET \times m \times t

Energy used during exercise.

One-Rep Max (Epley)

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

Estimated maximum single-lift weight.

VO₂ Max (Cooper)

VO_2 = \frac{d - 504.9}{44.73}

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

Daily Water Intake

W = 0.033 \times m

Rough daily water need in litres.

Lean Body Mass (Boer, Men)

LBM = 0.407m + 0.267h - 19.2

Body mass excluding fat for men.

Protein from Calories

g = \frac{0.30 \times C}{4}

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

Running Pace

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

Time taken to cover one unit of distance.

Step Length from Height

L \approx 0.415 \times h

Estimated walking step length from height.

Fat-Free Mass Index

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

Muscularity index normalised for height.

Corrected QT (Bazett)

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

Heart-rate-corrected QT interval from an ECG.

Mean Arterial Pressure

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

Average blood pressure during a cardiac cycle.

Creatinine Clearance (Cockcroft-Gault)

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

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

Due Date (Naegele)

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

Estimated delivery date from last menstrual period.

Waist-to-Hip Ratio

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

Body-shape ratio linked to health risk.

Ideal Body Weight (Devine)

IBW = 50 + 2.3(h - 60)

Estimated ideal weight in kg for men (h in inches).

Daily Water Intake

W = m \times 0.033

Approximate daily water need in liters.

Daily Protein Need

P = m \times 0.8

Baseline daily protein in grams per kg.

Target Heart Rate (Karvonen)

THR = (HR_{max} - HR_{rest})\times I + HR_{rest}

Training heart rate at a given intensity.

Running Pace

pace = \frac{time}{distance}

Time per unit distance.

Lean Body Mass

LBM = m(1 - BF\%)

Body mass excluding fat.

Calories Burned (MET)

C = MET \times m \times t

Energy expenditure from activity intensity.

BMR (Katch-McArdle)

BMR = 370 + 21.6\,LBM

Resting calories from lean body mass.

RMR (Cunningham)

RMR = 500 + 22\,LBM

Resting metabolic rate favoured for athletes.

Body Surface Area (Mosteller)

BSA = \sqrt{\frac{h \times m}{3600}}

Total skin surface area of the body.

Waist-to-Height Ratio

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

Central-fat health indicator.

BMI Prime

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

Your BMI relative to the upper healthy limit.

Ponderal Index

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

A leanness index that scales better for extreme heights.

One-Rep Max (Brzycki)

1RM = w \times \frac{36}{37 - r}

Estimated one-rep max, an alternative to Epley.

Max Heart Rate (Tanaka)

HR_{max} = 208 - 0.7\,a

A more accurate maximum heart rate estimate.

Heart Rate Reserve

HRR = HR_{max} - HR_{rest}

The usable range between rest and maximum heart rate.

Fat Mass

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

Total mass of body fat.

MET to Oxygen Uptake

VO_2 = 3.5 \times MET

Oxygen consumption from a MET activity level.

Fat Loss from Deficit

\Delta m = \frac{\text{deficit}}{7700}

Body-fat lost from a total calorie deficit.

Daily Protein Target

P = 1.6 \times m

Grams of protein per day to build muscle.

Speed from Pace

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

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

Corrected QT (Fridericia)

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

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

Blood Glucose Conversion

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

Converts blood-sugar units between countries.