The US Navy method uses neck, waist, and (for women) hip circumference plus height — no scale needed, just a flexible measuring tape.
Typically within about 3-4% of more precise clinical methods like DEXA scans or hydrostatic (underwater) weighing. That's more than accurate enough for tracking trends over time using nothing but a flexible tape measure, though it's not a substitute for a proper medical-grade body composition test if precision matters for your situation.
Measure your neck just below the larynx (Adam's apple), your waist level with the navel, and — for women — hips at their widest point. Use a flexible cloth or vinyl tape, keep it snug against the skin without pulling tight or compressing it, and measure standing normally rather than flexing muscles or sucking in your stomach, since either will throw the result off.
Body fat distribution patterns differ meaningfully by sex — men tend to store more visceral fat around the abdomen, while women store proportionally more around the hips and thighs. The US Navy method accounts for this by using a waist-minus-neck relationship for men and a waist-plus-hip-minus-neck relationship for women, each with its own set of fitted constants, rather than applying one formula to both.
BMI is calculated from height and weight alone, so it can't tell muscle from fat — a heavily muscled person can register as "overweight" on BMI despite having very low body fat. Body fat percentage estimates the fat portion directly from body measurements, making it a more informative number for body composition specifically. See the BMI Calculator for that quicker screening number, or the Ideal Weight Calculator for a target weight range by height.
For men: roughly 2-5% is classed as essential fat, 6-13% is typical of athletes, 14-17% a general fitness range, 18-24% average, and 25%+ falls into the obese category. For women: 10-13% is essential fat, 14-20% athletes, 21-24% fitness, 25-31% average, and 32%+ obese. Essential fat is the minimum your body needs for normal hormonal and organ function — going below it isn't a fitness goal, it's a health risk.
Worked example: a man 70 inches tall with a 15-inch neck and a 34-inch waist: bodyFat% = 86.010 × log10(34−15) − 70.041 × log10(70) + 36.76 = 86.010 × 1.2788 − 70.041 × 1.8451 + 36.76 ≈ 17.51% — squarely in the "Fitness" category.