kcalcraft Nutrition calculators that show the equation behind every number

Four TDEE Formulas, One Honest Comparison

Every TDEE calculator quietly picks an equation for you and prints the answer to the nearest calorie. Here are the four equations this site uses, what each one assumes, who it was validated on, and where each one drifts, so you can see exactly what the number on your screen is made of.

Written by Nan Liang · Sources: peer-reviewed equations, see references per tool

Why four different equations exist

A TDEE estimate is built in two steps: predict resting energy expenditure from body size, then scale it by an activity factor. The first step is where the equations differ. Each equation was created by measuring resting expenditure with calorimetry in a specific group of people, then fitting a line through weight, height, age, and sex (or fat-free mass). Because the groups differed, the fitted lines differ. None of them is "the truth" — each is a population average that you borrow for an individual, and the borrowing error is invisible unless you know which average you borrowed.

This page compares the four equations used across KcalCraft: Mifflin-St Jeor, the revised Harris-Benedict, the equation commonly called Katch-McArdle, and the 2023 NASEM Estimated Energy Requirement equations. Our TDEE calculator shows Mifflin alongside a NASEM second reading precisely so you can watch two honest estimates disagree — that disagreement is real information about your uncertainty.

The four equations, side by side

Mifflin-St Jeor (1990, PMID 2305711) uses weight, height, age, and sex: for men 10 x weight(kg) + 6.25 x height(cm) - 5 x age + 5; for women the constant is -161 instead of +5. The revised Harris-Benedict (Roza & Shizgal 1984) uses the same inputs with different coefficients: for men 88.362 + 13.397 x weight + 4.799 x height - 5.677 x age; for women 447.593 + 9.247 x weight + 3.098 x height - 4.330 x age. It is a re-derivation of Harris and Benedict's 1919 data with modern statistics, not a new measurement campaign.

The third family keys on fat-free mass rather than total weight: commonly called Katch-McArdle, with the same form published by Cunningham 1991 (PMID 1957828) as 370 + 21.6 x FFM, building on Cunningham 1980 (500 + 22 x FFM). Because muscle burns more than fat per kilogram, an FFM-based equation should, in principle, beat weight-based ones when body composition is genuinely known. The catch is that "genuinely known" is doing a lot of work: consumer body-fat estimates from bioimpedance scales or circumference equations carry errors of several percentage points, and the equation multiplies that error by 21.6 kcal per point of fat-free mass.

The fourth option is not a single line but a family: the Estimated Energy Requirement equations from the 2023 National Academies report (DOI 10.17226/26818), the current basis for US and Canadian dietary reference intakes. NASEM models energy needs with explicit terms for sex, age, body size, BMI category, and physical activity level, instead of bolting a generic multiplier onto a resting prediction. By design it does not cover BMI below 18.5, and its activity term inherits every weakness of self-reported activity — which brings us to the multiplier problem.

What the validation evidence actually says

The most cited head-to-head comparison is Frankenfield 2005, a systematic review of resting metabolic rate prediction in healthy nonobese and obese adults. Its conclusion is the reason Mifflin is our default: Mifflin-St Jeor performed best overall across the studied populations, while Harris-Benedict variants tended to overestimate expenditure, with the bias growing in obesity. "Best overall" still means an average — individual prediction errors of several hundred kilocalories per day are common in every equation tested.

Athletes are a different story. A 2023 systematic review with meta-analysis of RMR equations in athletic populations (Sports Medicine, DOI 10.1007/s40279-023-01896-z) found large heterogeneity across studies for nearly every equation: depending on the cohort, the same equation could overestimate Olympians and underestimate ultra-endurance athletes. The practical reading is not that one equation secretly wins, but that general-population equations transfer poorly to training extremes, and even sport-specific equations were rarely validated in independent samples.

Older adults are systematically underrepresented. The classic equations were built and validated mostly on younger and middle-aged cohorts, and prediction error tends to grow with age as body composition changes in ways weight and height no longer capture. If you are over 65, treat any equation output as a starting hypothesis to be calibrated, not a measurement — the calibration guide exists for exactly this.

The activity multiplier is the weakest link

Every weight-based TDEE estimate then applies an activity multiplier: sedentary 1.2, lightly active 1.375, moderately active 1.55, very active 1.725, extremely active 1.9. An honest declaration, as required by our methodology: this mapping from a self-chosen label to a single number is a rough mapping, not systematically validated for individuals. The labels are subjective, most people pick the tier they aspire to rather than the one they live, and the difference between adjacent tiers is roughly 150-250 kcal — larger than the difference between most prediction equations.

The multiplier is also where site-to-site differences get loudest: two calculators with identical BMR math will still disagree by 300 kcal if they label the same lifestyle differently. This is why every TDEE result here is shown with a range spanning half an activity tier in each direction, and why the number that should ultimately govern your intake is not any equation but your own four-week weight trend.

Why you can't just add your workout calories

The intuitive model — resting metabolism plus each workout's measured burn, added up like a ledger — runs into a hard empirical problem. Pontzer 2016 measured daily energy expenditure in Hadza hunter-gatherers, whose physical activity dwarfs that of industrialized populations, and found their total daily burn comparable to sedentary Westerners. The pattern, called constrained total energy expenditure, shows up across species: beyond a moderate activity level, the body increasingly compensates for exercise by economizing elsewhere — less spontaneous movement, lower background metabolic spending, subtle behavioral changes.

The practical consequence for calculators: logging a 500 kcal run does not raise your TDEE by 500 kcal. If your activity already sits in the moderate-to-high range, a large share of workout energy is offset by compensation, which is exactly what the multiplier tiers encode in compressed form. Treat exercise as nudging you up an activity tier, not as an exact line item to add on top — and treat "I exercised, so I earned back every calorie" as the most common arithmetic mistake in weight management.

Which equation should you actually use?

For most people, Mifflin-St Jeor is the sensible default: the best-supported single equation in the general adult population. If you have a trustworthy body-fat estimate — from a consistent measurement method, not a guess — the fat-free-mass form adds useful information, and our body-fat calculator exists to produce that input. The NASEM equations are worth reading as a second opinion, and where they land far from Mifflin, that spread is your honest uncertainty band, not an error to be resolved by picking the number you prefer.

Whatever you choose, the sequence is the same everywhere on this site: equation first, calibration second, your own trend last and highest authority. The formulas decide where you start; four weeks of logged intake and weight decide where you actually are.

The four equation families compared (W = weight in kg, H = height in cm, A = age in years, FFM = fat-free mass in kg)
EquationInputsFormula (men / women)Built and validated onKnown bias
Mifflin-St Jeor (1990)Weight, height, age, sex10W + 6.25H - 5A + 5 / same with -161Several hundred healthy adults spanning normal weight and obesityBest overall in Frankenfield 2005; individual errors still large
Revised Harris-Benedict (Roza & Shizgal 1984)Weight, height, age, sex88.362 + 13.397W + 4.799H - 5.677A / 447.593 + 9.247W + 3.098H - 4.330ARe-derivation of the 1919 Harris & Benedict datasetTends to overestimate, bias grows with obesity
Katch-McArdle / Cunningham form (1991)Fat-free mass370 + 21.6 x FFM (Cunningham 1980: 500 + 22 x FFM)FFM-driven; same form as Cunningham 1991Very sensitive to body-fat measurement error
NASEM 2023 EERSex, age, body size, PAL classLinear coefficients per sex x PAL class (officially no BMI split; category testing was not significant at p=.05)2023 National Academies update behind current US/Canada DRI energy intakesAdults 19+ only; inherits self-reported PAL weakness

Frequently asked questions

Which TDEE formula is most accurate?

On average, for healthy nonobese and obese adults, Mifflin-St Jeor performed best in the Frankenfield 2005 systematic review. That is an average over study populations, not a promise for any individual: personal prediction errors of a few hundred kilocalories per day are normal for every equation. Four weeks of your own intake and weight trend beats any formula for accuracy about you.

Why does the calculator show two different TDEE numbers?

Because two honest equations genuinely disagree. We show Mifflin alongside the NASEM 2023 EER as a second reading. Treat the spread between them as your uncertainty band rather than assuming one must be wrong.

Is Katch-McArdle better if I know my body fat?

Potentially, because fat-free mass drives metabolism more directly than total weight. But the equation multiplies any body-fat measurement error by about 21.6 kcal per point of fat-free mass, so a rough guess can make it worse than Mifflin. Use a consistent measurement method and treat the result as a range.

Do the activity multipliers account for my workouts?

Partially, and coarsely. The five tiers are a rough mapping from a self-reported label to a number, not a validated model of your training. Deliberate training usually justifies at most one tier bump, and high-volume athletes should read the athlete evidence section above before trusting any multiplier.

Why doesn't my 500-calorie run raise my TDEE by 500 calories?

Because total daily expenditure is constrained, not freely additive. Work by Pontzer and colleagues found that bodies compensate for added exercise by economizing elsewhere — spontaneous movement, background metabolism — so beyond a moderate activity level, extra workouts raise daily burn far less than their measured cost. The compensation is why exercise alone is a weaker weight-loss lever than arithmetic suggests.

References & sources

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