Understanding body-fat estimation
A tape measure, three circumferences, one percentage.
The US Navy formula behind most body-fat tools, the four real measurement methods ranked by accuracy, and the percentages that mean what.
The US Navy formula.
Developed by the US Navy in the 1980s for fitness assessments without equipment. For men: %BF = 86.010 · log10(waist − neck) − 70.041 · log10(height) + 36.76 (inches). For women: includes hip circumference too. Empirical fit to population data; accurate to ±3-4 percentage points compared to DEXA gold standard. Free, requires only a measuring tape, takes 30 seconds.
What the four methods get you.
Bio-impedance scale (consumer): ±5 percentage points, varies with hydration. Skinfold calipers (good operator): ±3 points, requires practice. US Navy tape: ±3-4 points, easy to do. DEXA scan (clinic): ±1 point, ~£100 per session. The expensive option is much more accurate; the free option is good enough for tracking trends. For "did I lose body fat this month", the tape beats the scale because hydration noise is smaller.
What the percentages mean.
Men: 3-5 % is essential (organs, marrow, nervous system — below this medically dangerous); 6-13 % is athlete; 14-17 % is fit; 18-24 % is average; 25 %+ is obese. Women have higher essential fat (sex-specific reproductive tissue): 10-13 % essential, 14-20 % athlete, 21-24 % fit, 25-31 % average, 32 %+ obese. These bands come from American Council on Exercise and ACSM. Bodies vary; treat them as ranges, not strict cutoffs.
A worked measurement.
A 30-year-old man, 70 inches tall, waist 34", neck 15". %BF = 86.010 × log10(34 − 15) − 70.041 × log10(70) + 36.76. log10(19) ≈ 1.279; log10(70) ≈ 1.845. 86.010 × 1.279 − 70.041 × 1.845 + 36.76 ≈ 110.0 − 129.2 + 36.76 ≈ 17.6 %. Lower bound of "fit" range. The DEXA might say 16 %; the tape's ±3 % uncertainty includes that range.
Male tape measurement
waist 34", neck 15", height 70"
Plug into log10-based formula.
86.010·log10(19) − 70.041·log10(70) + 36.76
= ≈ 17.6 %
Why BMI is worse for this.
BMI doesn't distinguish lean from fat. A 100 kg muscular athlete and a 100 kg sedentary adult of the same height both score BMI 30 — "obese" by BMI's bands. Body-fat percentage immediately differentiates them. For fitness tracking, body fat is the more useful number. The trade: easier to measure consistently (BMI needs only weight and height; body-fat needs circumferences or equipment), but BMI is a much worse proxy for what you actually want to know.
Tracking over time matters more than absolute number.
Whether a single measurement says 17 % or 19 % matters less than whether the trend over four months is down or up. Measure the same way (same tape, same time of day, same hydration state, same position), record monthly, watch the trajectory. The Navy formula's ±3 % noise is fine for trends because the noise is roughly symmetric; the absolute value isn't, but the direction is. That's the right use of the tool.