Measure Body Fat Percentage
Two home methods, run at once — the Navy tape method and the Jackson–Pollock 3-site skinfold method. This page also answers the question most calculators skip: how small a change can the instrument in your hand actually see? Enter your measurements and the tape's graduation, and you get your percentage, the range that your tape is really capable of reporting, and what one mark on it is worth in kilograms of fat. Everything runs in your browser; nothing is uploaded.
Your tape can only report it to the nearest mark, so the honest answer is a band: 20.3–21.7% is everything a 1 cm tape can say about the body you measured. The band is 1.41 points wide, and it is not caused by you measuring badly — it is the instrument.
Resolution floor: 0.70 points. That is the smallest change your tape can register at this waist — one mark. At 80 kg it corresponds to 0.71 kg of fat, so any real change smaller than that is invisible to this tape no matter how carefully you pull it.
Rounding noise alone is ±0.29 points (one standard deviation), ±0.56 at 95%. To push that under 0.5 points you need 1 readings; under 0.25 points, 2.
Skinfold method on the same body: 18.5%, consistent band 18.1–18.9% with a 1 mm caliper. Its floor is 0.28 points (0.27 kg of fat).
Jackson–Pollock 3-site: density = 1.10938 − 0.0008267·Σ + 0.0000016·Σ² − 0.0002574·age (men) — then BF% = 495 ÷ density − 450Circumferences and height in inches, skinfolds in millimetres, Σ is the sum of three sites. Both are published prediction equations, not inventions of this page. Every table below is arithmetic this page performs on them: derivatives taken analytically for the tape equation and numerically for the skinfold equation, rounding treated as a uniform error of half a mark per reading. None of it is copied from anywhere, and none of it is a claim about how accurate these equations are — only about how much precision the instrument destroys before the equation ever sees your numbers.
The protocol this page assumes
Before any of the arithmetic matters, the numbers have to be taken the same way every time. This is the protocol the calculator above is built around — the same landmarks this site uses on its Navy and fat-calculator pages.
The full landmark list and the ten common mistakes, with what each one costs in points, are on our fat calculator page. This page picks up where that one stops: even with perfect technique, the instrument itself throws precision away, and that loss is the subject of every table below.
Your tape has a resolution floor
The Navy equation is logarithmic in the waist–neck difference, so its sensitivity has a closed form: 37.35 divided by that difference in centimetres gives the percentage points you move per centimetre of waist, for men; the constant is 70.89 for women, whose argument also carries the hip. Multiply by the size of one mark on your tape and you have the floor — the smallest change your instrument can register.
Read the male table at the reference body used throughout this page — 178 cm, 80 kg, 30 years, 92 cm waist, 39 cm neck, so a = 53 cm. With a tape marked in whole centimetres, one mark is worth 0.705 points. Switching to a 1 mm digital tape drops the floor to 0.070 points, a factor of ten. Switching to an inch-marked tape raises it to 1.790 points, which is more than two and a half times worse than the centimetre tape — not because inches are worse units, but because the marks are further apart.
The same computation for women, whose argument is waist + hip − neck:
Two structural facts fall out of these grids. First, the floor gets lower as the argument gets bigger: the same tape resolves a 170 cm female argument nearly twice as finely as a 100 cm one. A tape resolves lean bodies worse than it resolves larger ones, which is the opposite of what most people expect. Second, the floor is a property of the tape, not of the body — which is why the fix is to buy a better tape, not to measure more often.
The bracket your instrument can actually report
A tape reading is not a number, it is a rounding. What you write down as 92 cm means the true circumference is somewhere within half a mark of 92. The male Navy argument is a difference of two such roundings, so its error can reach a full mark in either direction; the female argument adds hip as a third reading, so it can reach a mark and a half. Propagating that through the derivative gives the band of percentages consistent with what you measured.
Men are evaluated at a = 53 cm and women at S = 144 cm — the reference bodies. The worst-case column is the honest bracket; the 1.96 SD column is what you would quote if you assumed each reading's rounding error is uniform over half a mark and independent, which is the standard textbook assumption for rounded data. Both columns are computed here, neither is copied.
Applied to the two reference bodies, the brackets are:
The last column is the one worth sitting with. A centimetre tape on a 178 cm man cannot distinguish 21.0% from 21.6%, and the difference between those two numbers is real fat. If your tracking plan calls for detecting changes smaller than the bracket, the plan is asking more of a tape than a tape can give, and the failure will look like a plateau rather than like a rounding error.
How many different numbers can your tape produce
Another way to see the same thing: count the outputs. Sweep the waist across a realistic range in steps of one graduation and count how many distinct body fat percentages the equation can return. Everything between two adjacent values is unreachable — the tape has no way to say it.
The span is identical in all three rows of each block — the equation covers the same range no matter how finely you measure — but the number of reachable values differs by a factor of ten. Note the direction of the step size inside each row: the step is largest at the small end of the waist range and smallest at the large end. A tape resolves better on a large waist than on a small one, so the leaner you get, the coarser your instrument becomes.
Skinfolds behave the same way, and worse, because the caliper is the cruder instrument:
A caliper read to the nearest 5 mm can only produce fifteen different answers across the whole plausible skinfold range, at a mean step of 1.37 points for men. That is the instrument, not the technician: no amount of care turns a 5 mm scale into a 1 mm one.
What one mark is worth in fat
Points are abstract, so convert them. If fat leaves the body and lean mass stays, weight falls with the fat, and the exact relationship is Δ = dF·(1 − BF%) ÷ (W − dF), which inverts to dF = Δ·W ÷ (1 − BF% + Δ) with Δ in fractions. That gives the kilograms of fat corresponding to one mark on your tape.
Kilograms of fat at 20% body fat. On the reference man — 80 kg, 1 cm tape — one mark is 0.70 kg of fat. On a woman at 65 kg and 30%, whose sensitivity is 0.492 points per centimetre, one mark is 0.45 kg. If instead you hold weight constant and imagine recomposition, the constant-weight conversion dF = W·Δ/100 gives 0.42 kg at 60 kg and 0.70 kg at 100 kg for the same 0.705-point mark; the two versions differ because one lets the scale move and the other does not.
That is the practical meaning of the resolution floor. A tape marked in whole centimetres cannot see a fat loss smaller than about two thirds of a kilogram on an 80 kg man. Sub-kilogram changes are real, they are just below the instrument.
Switching landmarks is not free
Protocols disagree about where the waist is: at the navel, at the narrowest point of the torso, or midway between the lowest rib and the top of the hip bone. This page takes no position on which definition is correct. It prices the difference. Whatever the true displacement d is between the landmark you used last month and the one you use today, the reading moves by d multiplied by the sensitivity — and that movement will be read as progress or as a stall.
Points of body fat for men; the last column converts the a = 53 cm case into kilograms of fat at 80 kg and the 21.0% that body's own tape returns. For women at S = 144 cm the same displacements are worth 0.49, 0.98, 1.48, 1.97 and 2.46 points, or 0.46, 0.91, 1.36, 1.80 and 2.23 kg of fat at 65 kg and 30.7%.
The severity is worth stating plainly. A two-centimetre difference in where you put the tape — entirely plausible between the navel and the narrowest point of a torso — is worth 1.41 points on the reference man, which is twice the resolution floor of the tape itself. In other words, the landmark choice is a bigger source of error than the instrument, and unlike the instrument it is free to fix: write down where you measured, and go back to the same place.
Calipers: the same problem in millimetres
The skinfold equations take the sumof three sites, so the caliper's graduation enters three times — and the rounding errors of three independent readings have a standard deviation of half a graduation on the total. Sensitivity is also much flatter here than in the tape equation: the derivative barely moves across the plausible skinfold range, so the floor is set almost entirely by the instrument.
Points per mark for men at 30 years old. For women the same grid reads:
And the bracket that follows from it, for a man at 30 years old with a 62 mm three-site sum:
A caliper you read to the nearest 5 mm carries a 4.18-point band on that body — nearly three times the band of a 1 cm tape, and worth 3.90 kg of fat at 80 kg. The same body, the same technician, the same morning; only the scale on the tool differs. For a woman with the same 62 mm sum the 5 mm band runs 22.31 – 27.15%, a width of 4.83 points.
What averaging readings actually buys
Averaging n independent readings cuts the standard deviation by √n, so the number of readings needed to bring rounding noise under a target is (SD ÷ target)². Using the reference male tape (a = 53 cm) and a male caliper at Σ = 45 mm:
Two things follow. Repeating a measurement helps only until the rounding noise falls below the other errors in the chain — the slip of the tape, the landmark, the equation itself — and past that point it buys nothing. And when the instrument is coarse, averaging is a poor substitute for a finer scale: reaching ±0.10 points with an inch-marked tape would take 54 readings of the same morning, which is absurd, while a 1 mm tape needs one.
The unit trap
The single most common way to get a wildly wrong number at home is to put inches into a centimetre field. The equations are not dimensionally guarded — they take logarithms of whatever they are given — so a unit mistake produces a plausible-looking percentage instead of an error message. Here is what the Navy equation returns for the reference man and woman under each mismatch, computed by feeding it the wrong units on purpose:
The dangerous row is the fourth. Mixing units can produce a number that looks entirely reasonable — 14.4% instead of 21.0% — and nothing in the output flags it. The defence is a sanity check against something independent: if the tape says 14% and your waist-to-height ratio says otherwise, one of them is in the wrong unit.
How to write your number down
Recording 21.3% when your tape resolves 0.7 points is writing down digits you did not earn. The reporting precision follows directly from the floor: round to the nearest step that your instrument can actually distinguish.
Evaluated on the reference man; recompute for your own body with the calculator at the top. Better still, record the band rather than the point — 20.3 to 21.7% — because that is what the measurement actually established.
Where this page's arithmetic stops being true
Every number above is this page's own arithmetic on two published equations, and each step rests on assumptions worth naming:
- The resolution floor is a floor, not an error bar. It is the precision lost in the instrument. The equations themselves carry their own error, which is larger and which this page does not attempt to quantify — no home method can tell you how far a given equation sits from the truth for you.
- Rounding is modelled as uniform over half a mark, independently per reading. Real reading habits are not uniform: people favour round numbers, and a reader who likes 92 will not produce the error distribution assumed here. The SD columns are therefore optimistic.
- Landmark displacement is treated as a pure shift in centimetres. Moving the tape from the navel to the narrowest point changes the circumference, but it may also change which tissue the tape encircles; the tables price the shift and nothing else.
- The fat-mass conversions assume all change is fat. The inversion dF = Δ·W ÷ (1 − BF% + Δ) holds lean mass fixed. During recomposition, or during anything that moves water, neither version of the conversion describes what happened.
- Sensitivity is local. Every points-per-mark figure is a derivative evaluated at one argument. Move far enough and it changes — the direction is shown in the grids, but a single number from the calculator applies only to the body entered.
- None of this is a claim about the equations themselves. Both are population prediction equations fitted on specific groups. This page describes how much precision the tape or the caliper destroys before the equation sees the numbers; it says nothing about whether the equation was the right one to use.
Frequently asked questions
How do I measure my body fat percentage at home?
Two practical routes are the Navy tape method — waist, neck and, for women, hip, plus height — and the Jackson–Pollock 3-site skinfold method with a caliper. This page runs both, and adds the part most guides leave out: the band of values your instrument can actually distinguish, which for a tape marked in whole centimetres is about 1.4 points wide on a typical male body.
Is a tape or a caliper more precise?
On the reference bodies computed here, a 1 cm tape has a floor of 0.705 points for men and 0.492 for women; a 1 mm caliper has a floor of about 0.28 points for men. A caliper read only to the nearest 5 mm is far worse than either, at 1.48 points per mark. The instrument's smallest mark decides the answer, not the method.
Why does my number jump around when I have not changed?
Partly rounding — one mark on a centimetre tape is 0.705 points on the reference man — and partly landmarks. A two-centimetre change in where you place the tape is worth 1.41 points, twice the instrument's own floor. Fix the landmark first; the tape is the smaller problem.
Should I buy a digital tape?
If you track month to month, yes, and it is the cheapest precision available. Going from 1 cm marks to 1 mm cuts the floor tenfold, from 0.705 to 0.070 points, and it removes the averaging chore entirely: one reading with a 1 mm tape beats nine readings with a 1 cm one.
How many decimal places should I record?
As many as your instrument supports and no more. A 1 cm tape resolves 0.7 points, so write 21% or the band 20.3–21.7%. A 1 mm tape resolves 0.07 points and can carry one decimal honestly.
Does averaging three readings help?
It helps exactly as far as the arithmetic says: with a 1 cm tape on the reference man, one reading has a rounding SD of 0.288 points, two bring it under 0.25, and nine are needed to reach 0.10. Past the point where rounding falls below your landmark and technique error, averaging buys nothing.
My result is negative or absurd. What happened?
Almost always a unit mismatch. Entering 36.2 and 15.4 — inches — into centimetre waist and neck fields returns −14.0% for the reference man, because the waist–neck difference collapses. The quieter failure is the all-inches case, which returns a believable 14.4% against a true 21.0%.
Where exactly should the waist tape go?
This page follows the convention used across this site: at the navel for men, at the narrowest point of the torso for women, with the neck just below the larynx and the hip at its fullest. Other protocols define the waist differently. Whichever you choose, choose it once — a 2 cm difference between visits is worth 1.41 points. The full landmark list is on our fat calculator page.
Is a smart scale better than this?
It is a third method with a different failure mode: bioelectrical impedance infers composition from an electrical signal that moves with hydration, so its error is not reduced by measuring more carefully. Our BMI and smart scale page covers what those devices actually measure.
Related tools
body fat calculator · fat calculator with error budget · how to measure body fat at home · Navy body fat calculator · fat percentage across three methods · measure body fat by age and sex · body fat percentage chart
Not medical advice. Every figure on this page is arithmetic this page performs on two published prediction equations. It describes precision lost in the instrument and in the protocol; it says nothing about how close either equation is to the truth for you. See our disclaimer.