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Calorie Calculator Formulas: BMR and TDEE

Review Mifflin-St Jeor, revised Harris-Benedict, Katch-McArdle, TDEE, calorie-target, unit-conversion, and weekly-energy formulas.

How do the Calorie Calculator formulas work?

This formula page defines the variables used by the Calorie 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 first estimates basal metabolic rate with one of three equations. It then multiplies the selected BMR by the activity factor to estimate TDEE and maintenance calories. The entered deficit and surplus create comparison targets.

Variable Definitions

SymbolMeaningUnit or code
WBody weightKilograms
HHeightCentimeters
AAgeCompleted years
FBody-fat percentagePercent in the form; decimal in lean-mass calculation
LBMEstimated lean body massKilograms
AFActivity factorMultiplier
DUser-entered daily deficitCalories/day
SUser-entered daily surplusCalories/day

Unit Conversions

The production engine converts U.S. customary measurements before applying the BMR equations.

Wkg=Wlb×0.45359237W_{kg}=W_{lb}\times0.45359237
Hcm=[12(feet)+inches]×2.54H_{cm}=[12(feet)+inches]\times2.54
kilojoules=Calories×4.184kilojoules=Calories\times4.184

The pound-to-kilogram and inch-to-centimeter factors are exact conversion relationships used by the engine.

Mifflin-St Jeor Equations

The calculator uses the simplified sex-specific equations published with the 1990 study.

Male Equation

BMR=10W+6.25H−5A+5BMR=10W+6.25H-5A+5

Female Equation

BMR=10W+6.25H−5A−161BMR=10W+6.25H-5A-161

The research paper derived the equation from measured resting energy expenditure in 498 healthy adults aged 19-78 years. A prediction for one person can still differ from indirect calorimetry.

Revised Harris-Benedict Equations

Male Equation

BMR=88.362+13.397W+4.799H−5.677ABMR=88.362+13.397W+4.799H-5.677A

Female Equation

BMR=447.593+9.247W+3.098H−4.330ABMR=447.593+9.247W+3.098H-4.330A

These coefficients come from the Roza and Shizgal reevaluation of the Harris-Benedict data. Different coefficients explain why this result does not exactly match Mifflin-St Jeor.

Katch-McArdle Equation

LBM=W(1−F100)LBM=W\left(1-\frac{F}{100}\right)
BMR=370+21.6(LBM)BMR=370+21.6(LBM)

Katch-McArdle does not use age or height directly. It depends on estimated lean body mass, so body-fat error flows directly into the BMR estimate.

TDEE and Maintenance Calories

TDEE=BMR×AFTDEE=BMR\times AF
Maintenance=TDEEMaintenance=TDEE

In this calculator, estimated TDEE and maintenance calories are the same number. The activity factor is visible and editable in Calculation settings.

Calorie Deficit and Surplus Targets

Loss target=TDEE−DLoss\ target=TDEE-D
Gain target=TDEE+SGain\ target=TDEE+S
Target percent=TargetTDEE×100Target\ percent=\frac{Target}{TDEE}\times100

The calculator rejects a deficit that is equal to or greater than estimated maintenance. The targets are arithmetic comparisons and do not predict a guaranteed rate of weight change.

Weekly Energy and BMI

Weekly maintenance=7(TDEE)Weekly\ maintenance=7(TDEE)
BMI=W(H/100)2BMI=\frac{W}{(H/100)^2}

BMI is displayed as a screening metric. It does not change the calorie estimate unless height and weight also affect the selected BMR equation.

Worked Mifflin-St Jeor Calculation

For age 30, male, height 177.8 cm, weight 79.3787 kg, and activity factor 1.55:

BMR=10(79.3787)+6.25(177.8)−5(30)+5≈1760.04BMR=10(79.3787)+6.25(177.8)-5(30)+5\approx1760.04
TDEE=1760.04×1.55≈2728.06TDEE=1760.04\times1.55\approx2728.06
Selected BMR1760.04 Calories/day
Maintenance calories2728.06 Calories/day
Deficit scenario2228.06 Calories/day
Surplus scenario3028.06 Calories/day
Weekly maintenance19096.40 Calories/week

Precision, Validation, and Limitations

  • The engine keeps full JavaScript numeric precision through intermediate calculations.
  • Results are rounded for display and reports.
  • Age is limited to adults 18-100.
  • Height, weight, activity factor, body fat, deficit, and surplus must fall within configured validation ranges.
  • The published equations use binary sex terms exactly as defined by their coefficients.
  • The calculator does not model dynamic metabolic adaptation or guarantee body-weight change.
  • Indirect calorimetry is a direct measurement approach for resting energy; these equations are estimates.

See the worked calorie examples for three reproducible scenarios.

References

Use the Calorie Calculator