What Is the Katch–McArdle Equation?
The Katch–McArdle Equation is an evidence-informed metabolic formula that estimates an individual's Resting Energy Expenditure (REE) or Basal Metabolic Rate (BMR) directly from their Fat-Free Mass (FFM) / Lean Body Mass.
Unlike standard predictive formulas—such as the Mifflin–St Jeor Calculator or the Harris–Benedict Calculator—which estimate metabolic rate using four demographic variables (body weight, stature, age, and biological sex), the Katch–McArdle formula relies strictly on body composition:
Assumes average, population-standard proportions of lean tissue and body fat for a given height and weight.
Eliminates height, age, and sex assumptions by directly calculating the metabolic output of your actual lean tissue mass.
Body composition as a determinant of energy expenditure: a synthetic review and a proposed general prediction equation
John J. Cunningham (1991) · Department of Nutrition, University of Massachusetts
Why Is This Formula Named Katch–McArdle vs. Cunningham?
In online fitness discussions, software calculators, and sports nutrition communities, the formula 370 + (21.6 × FFM) is almost universally referred to as the Katch–McArdle Equation. This naming arose from exercise physiologists William D. McArdle, Frank I. Katch, and Victor L. Katch, who popularized body composition-based BMR calculations in their landmark textbook, Exercise Physiology: Nutrition, Energy, and Human Performance.
However, in peer-reviewed clinical nutrition literature, this exact mathematical relationship was synthesized and published by John J. Cunningham in 1991 in The American Journal of Clinical Nutrition as a generalized prediction equation for resting energy expenditure.
On TDEE.page, we treat Katch–McArdle and Cunningham (1991) as the same mathematical model. We do not count them as two independent equations in comparison charts, as doing so would artificially exaggerate scientific consensus.
The Lean-Mass Energy Architecture: From Composition to REE & TDEE
How your body weight and body-fat percentage decompose into fat-free mass and 24-hour calorie output
The Katch–McArdle Formula (Cunningham 1991)
Linear regression model estimating resting energy expenditure strictly from Fat-Free Mass
FFM = Total Body Weight × (1 − Body Fat % / 100)The mathematical regression baseline constant derived in Cunningham's 1991 synthetic review across 223 adult subjects.
The regression slope coefficient applied to each kilogram of fat-free mass (representing lean body tissue).
Total body weight minus estimated fat mass. Measured in kilograms before formula substitution.
What Exactly Is Fat-Free Mass (FFM)?
A common misconception in commercial fitness media is equating Fat-Free Mass directly with “muscle mass.” Fat-free mass (also called lean body mass) encompasses all non-fat tissue components in the human body:
Accounts for ~40–50% of total lean mass. Has a modest resting burn (~13 kcal/kg/day) that surges exponentially during exercise.
Liver, brain, heart, and kidneys constitute only ~5–6% of body mass but consume over 60% of total resting energy (200–440 kcal/kg/day).
The structural skeletal frame contributes ~3–4 kg of dense mineral mass with minimal resting oxygen consumption.
Intracellular and extracellular fluids make up ~72–74% of healthy lean tissue mass by weight.
Tissue-Level Metabolic Architecture: Why Fat-Free Mass Matters
Specific metabolic rates of individual human tissues (for a reference 75 kg adult with 60 kg FFM)
High-metabolic organs (liver, brain, heart, kidneys) comprise less than 6% of total body weight but generate over 54% of resting daily calorie burn. Skeletal muscle contributes another 23% at rest. The coefficient 21.6 × FFM mathematically synthesizes these diverse organ and muscle burn rates into a single, unified regression equation.
Worked Manual Example: How to Calculate Step-by-Step
To understand how the arithmetic works under the hood, consider an individual weighing 75 kg (165.3 lbs) with a measured body fat percentage of 20%:
Fat Mass = Total Weight × (Body Fat % ÷ 100) = 75 kg × 0.20 = 15.0 kg
FFM = Total Weight − Fat Mass = 75 kg − 15.0 kg = 60.0 kg (or 132.3 lbs)
REE = 370 + (21.6 × 60.0 kg FFM) = 370 + 1,296 = 1,666 kcal/day
1,666 kcal × 4.184 = 6,971 kJ/day (6.971 MJ/day)
How Body-Fat Measurement Accuracy Impacts Your Result
Because the Katch–McArdle equation derives your fat-free mass directly from your body fat percentage, the accuracy of your resting energy estimate is directly constrained by the accuracy of your body-composition measurement.
| Measurement Modality | Typical Error Margin | Primary Confounding Variables | Practical Utility |
|---|---|---|---|
| DEXA (Dual-Energy X-Ray) | ±1.5% to ±3% | Hydration status, recent meal timing, glycogen depletion | Clinical benchmark; 3-compartment body composition |
| Skinfold Calipers | ±3% to ±5% | Technician experience, caliper pressure, site location | Inexpensive and reliable for longitudinal tracking with same tester |
| Smart Scale / BIA | ±4% to ±8% | Electrolyte balance, skin temperature, bladder fullness | Convenient daily baseline; track rolling averages rather than daily spikes |
| Navy Circumference Tape | ±3% to ±6% | Tape tension, post-meal bloating, neck/waist structure | No equipment required; good general population approximation |
Scientific Rigor: Explained Variation (R²) vs. Prediction Accuracy
In Cunningham's 1991 meta-analysis, the author observed that fat-free mass accounted for 65% to 90% of the statistical variance (R² = 0.65–0.90) in resting energy expenditure across clinical trials.
Explaining 80% of population variance ($R^2 = 0.80$) does not mean the equation is “80% accurate” for every single person. In human energetics, two individuals with identical measured FFM (e.g. 60 kg) can still exhibit different resting metabolic rates due to differences in individual organ mass ratios (such as liver and brain size), thyroid hormone receptor sensitivity, mitochondrial efficiency, and autonomic nervous system tone.
REE vs. BMR vs. TDEE: Understanding Physiological Boundaries
In fitness media and nutrition forums, REE, BMR, and TDEE are frequently used interchangeably. However, each term represents a specific physiological testing condition:
| Quantity | Full Term | Clinical Testing Protocol | Share of Daily Energy Output |
|---|---|---|---|
| REE (Katch–McArdle) | Resting Energy Expenditure | Resting in a comfortable chair or bed in a quiet, thermo-neutral room ~4 hours post-meal. Typically 3–8% higher than strict BMR. | ~60–75% of TDEE |
| BMR (Harris–Benedict) | Basal Metabolic Rate | Measured immediately upon waking after a strict 12-hour overnight fast in total thermal neutrality without physical exertion. | ~60–70% of TDEE |
| TDEE | Total Daily Energy Expenditure | Full 24-hour calorie output: Resting Energy (REE) + Exercise + Non-Exercise Activity (NEAT) + Thermic Effect of Food (TEF). | 100% of Daily Output |
Frequently Asked Questions About the Katch–McArdle Equation
What is the Katch–McArdle equation?▼
The Katch–McArdle equation is a body-composition-based formula that calculates resting energy expenditure (REE) using fat-free mass (FFM). Its formula is REE = 370 + (21.6 × FFM in kg).
Why doesn't the Katch–McArdle formula require age, height, or sex?▼
In traditional formulas, age, sex, and height serve as mathematical proxies to estimate how much lean tissue you have. When you directly measure and input fat-free mass, those demographic proxies become redundant because metabolically active lean mass is already accounted for.
Is Katch–McArdle the same as Cunningham (1991)?▼
Yes. The mathematical relationship 370 + 21.6 × FFM was published by John J. Cunningham in 1991 in The American Journal of Clinical Nutrition. In commercial fitness literature, this exact formula was popularized under the name Katch–McArdle.
What is Fat-Free Mass (FFM)?▼
Fat-free mass represents total body weight minus all adipose fat tissue. It includes skeletal muscle, internal organs (liver, kidneys, heart, brain), bones, connective tissue, and cellular water.
Is Katch–McArdle more accurate than Mifflin–St Jeor?▼
Neither equation is universally “more accurate.” Katch–McArdle is advantageous for highly muscular athletes or individuals with known body-fat measurements because it does not assume standard body composition. However, if your body-fat estimate is inaccurate, Mifflin–St Jeor often provides a more reliable baseline.
How do I calculate lean body mass in pounds?▼
Multiply your weight in pounds by (1 − Body Fat % ÷ 100). For example, at 165 lbs with 20% body fat: 165 × (1 − 0.20) = 132 lbs FFM. Our calculator automatically converts pounds to kilograms before applying the formula.
What if I already know my Fat-Free Mass from a DEXA scan?▼
Simply toggle to the “Enter Known Fat-Free Mass” mode at the top of our calculator. You can enter your DEXA lean mass directly without needing to estimate body fat percentage.
Is lean mass the same as skeletal muscle mass?▼
No. Skeletal muscle accounts for approximately 40% to 50% of total fat-free mass. The remaining 50% consists of vital organs (which burn the majority of baseline calories), skeletal bones, and body water.
Does 1 kg of muscle really burn 21.6 calories per day?▼
No. In resting human physiology, isolated skeletal muscle burns approximately 13 kcal/kg/day, while high-metabolic organs burn 200–440 kcal/kg/day. The factor 21.6 is an aggregate regression slope across all lean tissues combined.
How does body fat measurement error change my results?▼
Each 1% error in body fat shifts calculated resting energy expenditure by approximately 15 to 20 kcal/day for an average adult. A 3% scan variance corresponds to roughly ~50 kcal/day.
Why is Katch–McArdle popular among bodybuilders and athletes?▼
Standard formulas assume average body fat and may underestimate energy needs for muscular individuals with low body fat. Katch–McArdle rewards muscular development by scaling resting energy expenditure directly with lean tissue mass.
Is my Katch–McArdle result my total daily calorie burn?▼
No. Katch–McArdle estimates resting energy expenditure (REE). To determine your total daily burn (TDEE), your REE must be multiplied by a Physical Activity Level (PAL) factor between 1.2 and 1.9.
Can I use imperial pounds instead of metric kilograms?▼
Yes. You can switch between Imperial (lbs) and Metric (kg) at any time. Our calculator automatically normalizes values to kilograms internally using the exact standard conversion 1 lb = 0.45359237 kg.
What is the best way to estimate my body fat percentage?▼
DEXA scans and multi-frequency bioimpedance offer good clinic-grade estimates. For home tracking, consistent caliper measurements or calibrated smart scale rolling averages provide valuable relative trends.
Why does Katch–McArdle predict different calories than Schofield?▼
The Schofield equation is a global FAO/WHO weight-and-age formula developed from historical metabolic data, whereas Katch–McArdle isolates fat-free mass. Differences reflect demographic versus body-composition modeling.
Should I eat below my Katch–McArdle BMR for weight loss?▼
Calorie deficits for fat loss should be calculated from your Total Daily Energy Expenditure (TDEE), not your resting baseline. Aggressive deficits far below resting energy expenditure may compromise recovery, muscle retention, and daily vitality.
Informational & Personal Awareness Notice:
This calculator provides a population-based mathematical estimate of resting energy expenditure for nutritional awareness, fitness planning, and journaling purposes. It is not a clinical metabolic test or individualized medical advice. For specialized dietary or metabolic planning, consult an appropriately qualified nutrition professional.