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BMR Formulas and Calculation Steps

Compare Mifflin-St Jeor, revised Harris-Benedict, and Katch-McArdle BMR formulas with variables, unit conversions, and a worked calculation.

How do the BMR Calculator formulas work?

This formula page defines the variables used by the BMR Calculator, shows how those values are combined, and explains the order of operations behind the result. Use the worked steps to verify an estimate, compare scenarios, and understand which assumptions or rounding rules can affect the displayed answer.

Formula Overview

The calculator runs three published prediction equations from one normalized input set. Mifflin-St Jeor and revised Harris-Benedict use weight, height, age, and a sex-specific term. Katch-McArdle uses estimated lean body mass.

Every equation returns dietary Calories per day. The selected formula becomes the headline result, while the other estimates remain visible for comparison.

Variable Definitions

SymbolMeaningUnit
WCurrent body weightkilograms
HHeightcentimeters
AAgecompleted years
PBody-fat percentagepercent
FBody-fat fraction, P divided by 100decimal
LBMEstimated lean body masskilograms
BMREstimated basal metabolic rateCalories per day

Unit Conversions

All formulas require kilograms and centimeters. U.S. measurements are normalized before calculation.

Wkg=Wlb×0.45359237W_{kg}=W_{lb}\times0.45359237
Hcm=(12×feet+inches)×2.54H_{cm}=(12\times feet+inches)\times2.54

For example, 175 pounds becomes 79.379 kg and 5 feet 10 inches becomes 177.80 cm.

Mifflin-St Jeor Equation

BMRmale=10W+6.25H−5A+5BMR_{male}=10W+6.25H-5A+5
BMRfemale=10W+6.25H−5A−161BMR_{female}=10W+6.25H-5A-161

The two equations use identical weight, height, and age coefficients but different constants. The calculator uses Mifflin-St Jeor as its default general-adult estimate.

Revised Harris-Benedict Equation

BMRmale=88.362+13.397W+4.799H−5.677ABMR_{male}=88.362+13.397W+4.799H-5.677A
BMRfemale=447.593+9.247W+3.098H−4.330ABMR_{female}=447.593+9.247W+3.098H-4.330A

These are the revised coefficients published by Roza and Shizgal, not the original early twentieth-century coefficients. A result can differ from Mifflin-St Jeor because every coefficient is different.

Katch-McArdle Equation

F=P100LBM=W(1−F)F=\frac{P}{100}\qquad LBM=W(1-F)
BMR=370+21.6(LBM)BMR=370+21.6(LBM)

Age, height, and the sex term are not used in this equation. The body-fat estimate determines lean mass, so measurement error flows directly into Katch-McArdle.

Derived Energy Rates

After the selected daily BMR is calculated, the engine derives equivalent time and energy units.

BMRkJ/day=BMRCal/day×4.184BMR_{kJ/day}=BMR_{Cal/day}\times4.184
BMRCal/hour=BMRCal/day24BMR_{Cal/hour}=\frac{BMR_{Cal/day}}{24}
BMRCal/week=7×BMRCal/dayBMR_{Cal/week}=7\times BMR_{Cal/day}

These are conversions of one estimate. They do not add activity or create separate metabolic measurements.

Formula Comparison and Spread

Spread=max⁡(BMR1,BMR2,BMR3)−min⁡(BMR1,BMR2,BMR3)Spread=\max(BMR_1,BMR_2,BMR_3)-\min(BMR_1,BMR_2,BMR_3)

The spread shows equation disagreement in Calories per day. It is not an error margin, probability, confidence interval, or measured distance from a person's true metabolism.

Worked BMR Calculation

For a 30-year-old man who is 5 feet 10 inches tall and weighs 175 pounds, the normalized measurements are 177.80 cm and 79.379 kg.

10(79.37866)+6.25(177.80)−5(30)+5=1760.03710(79.37866)+6.25(177.80)-5(30)+5=1760.037
OutputEngine result
Mifflin-St Jeor1760.037 Calories/day
Revised Harris-Benedict1834.750 Calories/day
Katch-McArdle at 20% body fat1741.663 Calories/day
Selected BMR in kilojoules7363.993 kJ/day
Formula spread93.087 Calories/day

The live calculator generally rounds headline energy values for readability while retaining precision for dependent calculations.

Precision, Assumptions, and Limits

  • Calculations use normalized metric inputs without intermediate display rounding.
  • Displayed precision does not imply measurement accuracy.
  • Mifflin-St Jeor and revised Harris-Benedict use published binary sex-specific terms.
  • Katch-McArdle assumes the entered body-fat percentage is meaningful.
  • None of the equations include ordinary activity or planned exercise.
  • The result is a population-based adult estimate, not indirect calorimetry.

BMR Formula FAQ

Which BMR formula is most accurate?

No prediction equation is guaranteed to be most accurate for an individual. Mifflin-St Jeor is a useful general-adult starting point, while measured resting energy may differ. Use realistic inputs and review the BMR Calculator formula assumptions before relying on this result for decisions.

Why do the formulas give different answers?

They use different datasets, coefficients, and predictors. Katch-McArdle also depends on body-fat percentage rather than age and height. For a useful BMR Calculator formula result, use realistic inputs, compare relevant scenarios, and review the stated assumptions before making a decision.

Can I multiply BMR by an activity factor?

That is a common way to estimate TDEE, but the multiplier adds another assumption. Use the TDEE Calculator to keep that step explicit. Use realistic inputs and review the BMR Calculator formula assumptions before relying on this result for decisions.

References

Return to the BMR Calculator or compare the three worked BMR examples.

Use the BMR Calculator