Three fitness numbers people track as percentages — body fat, macro splits, and weight lost. Here's the actual math behind each, including the US Navy circumference equation in full.
The US Navy body-fat circumference formula step by step, how to turn a calorie goal into macro grams (40/30/30), and how percentage of body weight lost is actually calculated.
See also: Percentage calculator · Formula cheat sheet
Trackers for medical programs and weight-class sports report loss as a percentage of starting weight, not just raw pounds — because losing 20 lb means something very different at 150 lb than at 300 lb:
Weight loss % = (Start − Current) ÷ Start × 100
From 200 lb down to 180 lb: (200 − 180) ÷ 200 = 10% of body weight lost. This normalizes progress across people of different sizes.
The Navy method estimates body fat from tape measurements (in inches) using a logarithmic formula. The measurements differ by sex:
Men — measure waist (at the navel), neck, and height:
%BF = 495 ÷ (1.0324 − 0.19077 × log₁₀(waist − neck) + 0.15456 × log₁₀(height)) − 450
Women — measure waist, hip, neck, and height:
%BF = 495 ÷ (1.29579 − 0.35004 × log₁₀(waist + hip − neck) + 0.22100 × log₁₀(height)) − 450
Worked example (male): waist 34″, neck 16″, height 70″. Then waist − neck = 18, log₁₀(18) = 1.2553, log₁₀(70) = 1.8451. Denominator = 1.0324 − 0.19077(1.2553) + 0.15456(1.8451) = 1.0781. So %BF = 495 ÷ 1.0781 − 450 = 9.1%. (A female example with waist 34″, hip 44″, neck 13″, height 65″ works out to about 16.2%.)
The method is an estimate — it tends to read a little low for very lean builds — but it's free, repeatable, and needs only a tape measure.
Macros are usually set as percentages of total calories, then converted to grams using each nutrient's energy density: carbohydrate 4 kcal/g, protein 4 kcal/g, fat 9 kcal/g. For a 2,000-calorie day on a 40/30/30 split:
| Macro | % of calories | Calories | Grams |
|---|---|---|---|
| Carbohydrate | 40% | 800 kcal | ÷ 4 = 200 g |
| Protein | 30% | 600 kcal | ÷ 4 = 150 g |
| Fat | 30% | 600 kcal | ÷ 9 = 66.7 g |
The two-step recipe: (1) multiply total calories by each percentage to get calories per macro, then (2) divide by that macro's kcal-per-gram to get grams. Fat looks like a small gram number because it packs more than twice the calories per gram.
Note: 40/30/30 is a popular illustrative split (the “Zone” ratio), not an official target. The government’s Acceptable Macronutrient Distribution Ranges (AMDR) are 45–65% carbohydrate, 10–35% protein, and 20–35% fat.
Percentage allocation — whether it's a diet, a household budget, or a project's time — is always category amount ÷ total × 100, and a valid set of allocations sums to exactly 100%. If your macro or budget percentages don't add to 100, something is double-counted or missing.
Use the US Navy circumference formula. For men: 495 / (1.0324 - 0.19077 x log10(waist - neck) + 0.15456 x log10(height)) - 450, with measurements in inches. Women add the hip measurement. It's an estimate but needs only a tape measure.
Multiply total calories by each macro's percentage, then divide by its energy density: 4 kcal/g for carbs and protein, 9 kcal/g for fat. On 2,000 kcal at 40/30/30, that's 200 g carbs, 150 g protein, and 66.7 g fat.
Divide the pounds lost by your starting weight, then multiply by 100: (Start - Current) / Start x 100. Losing 20 lb from 200 lb is a 10% loss. This normalizes progress across different body sizes.
Fat contains 9 calories per gram versus 4 for carbs and protein. So an equal share of calories converts to fewer than half as many grams of fat.
Links point to primary sources and standards bodies. Tax rates and official formulas change over time — verify against the source for current figures.