Fat Calculator
Enter the measurements you can actually take at home — three tape circumferences, or three skinfolds with a caliper — and get a body fat percentage plus the number most calculators leave out: how much of that answer is measurement error. Everything runs in your browser; nothing is uploaded.
At 1 cm of slip per site, the measurement error alone is ±0.58 percentage points across 2 measurement with 3 readings averaged at each. That is the error bar on this number, not a prediction about your health.
Fat mass 16.8 kg, lean mass 63.2 kg. Body fat percentage is a ratio, so the same measurement slip moves the percentage more when you are light and less when you are heavy.
The waist carries 0.70 points per centimetre, and the neck moves the result 0.70 points in the opposite direction. One full percentage point is 1.42 cm of waist at your current measurements. A height entry 2 cm off shifts the answer 0.34 points.
Comparing two sessions taken this way, a change has to exceed 1.60 points before it is larger than the noise. Smaller movements are real or not — this method cannot tell you which.
Navy (women): BF% = 163.205·log₁₀(waist + hip − neck) − 97.684·log₁₀(height) − 78.387
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 the three skinfolds. These are published prediction equations, not inventions of this page — but every sensitivity figure, error budget and mistake table below is arithmetic this page performs on them, and none of it is copied from anywhere. The ± band the calculator prints covers measurement error only. It does not include the equations' own error against a laboratory reference method, which is a separate and usually larger problem.
What a fat calculator is actually doing
A fat calculator takes two or three numbers off your body and runs them through a prediction equation fitted long ago on a specific group of people. It does not measure your fat. It predicts it, and the prediction carries two separate kinds of error that almost every calculator hides: the error of the equation itself, and the error of the numbers you typed into it.
This page deals honestly with the second kind and is explicit that it cannot fix the first. The equation error is a property of the equation and the population it was fitted on; no amount of careful measuring removes it. The measurement error is entirely yours, it is often larger than people assume, and unlike the equation error it is something you can shrink this afternoon. Everything below is about shrinking it and knowing when you have.
There is also a structural point worth making before any table: both equations here are built on differences and ratios of circumferences, not on the circumferences themselves. A waist that reads 2 cm large does not add a fixed amount of body fat — it adds an amount that depends on how big the waist−neck difference already is. That single fact is why the sensitivity tables below exist, and why a one-centimetre slip is worth almost three times as much to a lean person as to a heavy one.
Tape protocol: where exactly to put it
These are the landmark definitions the circumference equations were developed with. The equations were fitted on measurements taken this way, so departing from it does not just add noise — it adds a bias that never averages out.
Two habits change the result more than any landmark debate. First, read at the end of a normal exhale every single time — holding a breath or sucking in changes the circumference by more than the landmark argument is worth. Second, measure on bare skin. A t-shirt hem adds more than a centimetre and it adds it non-uniformly, which is the worst kind of error because it does not cancel between sessions.
Caliper protocol: the pinch is the measurement
With skinfolds, the caliper is the easy part. The pinch is the measurement, and the pinch is where self-measurement goes wrong. The rule is that you are lifting a fold of skin plus the fat directly under it, and nothing else. If you feel the muscle underneath, you have grabbed the wrong tissue and the reading is meaningless at that site.
Take all measurements on the same side of the body — conventionally the right — and rotate through the sites rather than measuring one site three times in a row. A repeated pinch on the same spot compresses the tissue and reads progressively lower, which is a real effect that will make consecutive readings look like they are converging when they are actually just draining.
Computed: what one centimetre is worth
Differentiate the circumference equation with respect to each measurement and you get the exact sensitivity at your own numbers. Below are two worked profiles — a 178 cm, 80 kg, 30-year-old man with a 92 cm waist and 39 cm neck, and a 165 cm, 65 kg, 30-year-old woman with a 78 cm waist, 98 cm hip and 32 cm neck. Every figure is the derivative above evaluated at those measurements.
The woman's profile has three measurement sites to the man's two, yet each one is worth less in absolute terms, because her waist + hip − neck difference is 144 cm against his 53 cm waist − neck. Sensitivity falls as the circumference difference grows. She is not measuring more carefully; her arithmetic is simply less twitchy.
The height row deserves a comment because it surprises people. Height enters the equation as a divisor, so entering a height 2 cm too short adds about 0.34 points to the man's result and 0.51 to the woman's. That is not a measurement you repeat every session — you type it once and forget it — which makes it the classic source of a constant offset between two calculators that otherwise agree.
Computed: the same sensitivity across body sizes
Because the derivative depends on the circumference difference, the cost of a slip is not a constant. Here it is evaluated across the range real bodies occupy. Find your own difference — waist minus neck for men, waist plus hip minus neck for women — and read the cost of a centimetre.
The spread is close to threefold at the extremes. A lean man with a 25 cm waist-to-neck difference pays 1.49 points for a single sloppy centimetre; a man with a 60 cm difference pays 0.62. The practical consequence is that body fat estimates from circumferences get noisier as you get leaner, exactly when you care most about the number. That is not a flaw you can fix by buying a better tape — it is in the equation.
Computed: what one millimetre is worth
The skinfold equation behaves differently. Its derivative with respect to the sum falls as the sum grows, so a millimetre is worth most when you are leanest — the same direction as the tape method, but reached through a different route.
At the two worked profiles — the man at a 62 mm sum and the woman at 70 mm — a millimetre is worth 0.279 and 0.309 points respectively. Note what that means in practice: a skinfold measurement is recorded to the nearest millimetre, and the rounding alone is worth about a third of a percentage point per site. Rounding error on three sites is not negligible next to the changes people try to detect month to month.
Age enters the skinfold equation and not the circumference one. For these profiles it contributes 0.114 points per year for men and 0.064 for women, so a birthday moves the estimate by about a tenth of a point. Small, but it is a systematic nudge that runs the same direction every year and will quietly flatten or steepen a long trend if you never account for it.
Computed: the total error budget
Assume the slip at each site is independent and roughly the same size. Then the errors do not add — they combine as the square root of the sum of squares, because a slip in one direction at one site partly offsets a slip in the other. These totals use the two worked profiles above.
Read the 1 cm tape row against the 2 mm caliper row, because those are the two honest descriptions of a first attempt by an untrained person: both land near one percentage point. The caliper is not inherently more precise at home. It is more precise only in trained hands, and the gap between those two rows — 0.24 against 2.41 points — is the entire skill of skinfold measurement expressed as a number.
Computed: what the common mistakes are worth
The slip sizes in the first column are illustrative — how big yours actually is depends on you. The shift columns are not illustrative: they are exact arithmetic on the sensitivities above, for the same two profiles. Use this table to decide which mistake is worth fixing, because they are nowhere near equal.
The bias-versus-noise column is the one that should change how you behave. A bias shifts every measurement the same direction by the same amount, which means it ruins comparisons against a chart or another person's number while leaving month-to-month tracking perfectly intact. Noise does the opposite. If your goal is to watch your own trend, the male belt-line mistake — worth 2.11 points — costs you nothing at all as long as you make it identically every month. If your goal is to know whether you are at 15 percent or 18 percent, it costs you everything.
Computed: how small a change you can actually detect
Two sessions each carry their own error, so the difference between them carries √2 times a single session's error. At 95 percent confidence, a change has to be at least 1.96 × √2 × σ before you can call it real. Averaging n readings at each site divides σ by √n. Both rules applied to the worked profiles:
This is the table that should set your re-measurement schedule. With a tape, one reading per site, a change smaller than roughly 2.4 to 2.8 points is indistinguishable from measurement noise — and a genuine month of fat loss is often under one point. Taking three readings per site and averaging them cuts that to about 1.4 to 1.6 points, which is still larger than a month of progress for most people. The honest conclusion is that a tape measurement cannot resolve one month of change at all; it resolves about a quarter's worth.
The caliper rows are better but not transformative: at a realistic 2 mm per site with three readings averaged, you can resolve about 0.8 points, which is roughly two to three months of progress. Anyone reporting skinfold-derived body fat changes week to week is reporting noise, whatever the caliper cost.
Notice also that averaging has sharply diminishing returns. Going from one reading to three buys a 42 percent reduction in the error bar; going from three to five buys only another 22 percent. Three readings per site is where the effort stops paying.
Tape and caliper on the same person
Run both methods on the same two profiles and they do not agree. The man comes out at 21.0 percent by tape and 18.5 percent by the caliper equation on a 62 mm sum — a 2.5 point gap. The woman comes out at 30.7 percent and 27.3 percent — 3.4 points. Neither is wrong in any simple sense; they are different prediction equations fitted on different populations, and they answer slightly different questions about where the fat is.
The diminishing per-centimetre return in the last column is the derivative shrinking as the waist grows, exactly as the sensitivity table predicted. It also means the tape method is at its most informative in the middle of the range, and least informative at both ends — for the very lean and for the very heavy, a centimetre of waist tells you less.
The single rule that follows from all of this: pick one method and never switch. A trend built from tape measurements is comparable to other tape measurements and to nothing else. The moment you compare a tape number to a caliper number — or either to a smart scale — you are reading the difference between equations, not a change in your body. Our body fat percentage calculator with an error bar runs the cross-method comparison explicitly if you want to see the spread on your own numbers.
How to run this at home
- Choose the method you can repeat, not the one that sounds most accurate. Per the error budget, a careful tape measurement beats a sloppy caliper measurement every time.
- Measure at the same time of day, in the same state. Morning, after the bathroom, before food and training is the standard for a reason: it removes the largest single source of within-person variation.
- Take three readings per site and average them. That is where averaging stops paying, and it cuts the error bar by more than 40 percent for about two extra minutes.
- Write down the raw measurements, not just the percentage. When a number looks wrong six weeks later, the raw waist reading is what tells you whether you measured badly or changed.
- Re-measure monthly, not weekly. The detectable-change table says a single month of real progress is smaller than the noise of any home method. Quarterly is honest; weekly is theatre.
- Track the raw circumference as well. Waist in centimetres needs no equation, carries no prediction error, and moves in the direction you care about. It is often the better number to watch.
- Cross-check against something independent occasionally. A photo-based estimate or a reference chart will not settle the truth, but a method that disagrees with everything else is a method you are using wrong.
Where this is weak
- The error bar covers measurement error only. It does not include how far the equation itself sits from a laboratory reference method for your body. That second error is usually larger, and this page does not compute it because it cannot be computed from your inputs.
- Prediction equations are population-specific. Both equations here were fitted on particular samples decades ago. They are known to behave differently outside those groups, and no arithmetic on this page repairs that.
- The slip sizes are yours to supply.Every error budget figure is conditional on the slip you selected. The calculator's default of 1 cm or 2 mm is a guess about a typical self-measurement, not a measurement of yours.
- Independence between sites is assumed, not proven. If you measure badly you often measure badly at every site in the same direction, which makes the true error larger than the root-sum-square figure here.
- Women's body fat varies across the menstrual cycle. Water shifts change circumferences and skinfolds alike; this page has no way to model it, so compare like phase to like phase.
- Nothing here is a health assessment. A body fat percentage is one number with a wide error band. It is not a diagnosis and not a target by itself.
Frequently asked questions
What is a fat calculator?
A tool that predicts your body fat percentage from a few body measurements rather than measuring it directly. This one runs two published equations — the Navy circumference method and the Jackson–Pollock 3-site skinfold method — and then computes how much of the answer is measurement error.
How accurate is a body fat calculator?
The measurement part is computable and the tables above give it: around ±1 percentage point for a careful tape measurement, ±0.5 to ±1 for careful skinfolds, and ±2 to ±3 for a rushed job either way. The larger and uncomputable part is the equation's own error against a laboratory reference, which this page does not claim to know.
Tape or caliper — which should I use?
Whichever you can repeat identically. At realistic self-measured slip sizes both land near one percentage point of error. The caliper only wins clearly in trained hands, where its error budget drops to about a quarter of a point.
Why do I get a different number from every calculator?
Because they use different equations, and sometimes different landmark definitions for the same equation. A 2 cm difference in where you place the waist tape moves the Navy result by 1.4 points on the male profile above, which is more than the gap between most calculators.
How much does 1 cm of waist change my body fat percentage?
It depends on your waist-to-neck difference: 1.49 points per centimetre at a 25 cm difference, 0.70 at 53 cm, and 0.62 at 60 cm. For the worked male profile, one full percentage point is 1.42 cm of waist.
Can I track progress weekly with this?
No. The detectable-change table puts the smallest trustworthy difference at roughly 1.4 to 2.8 points depending on method and care, while a month of genuine fat loss is usually under one point. Measure monthly at best, quarterly if you want to be certain.
Does taking more readings help?
Yes, with diminishing returns. Averaging three readings instead of one cuts the error bar by about 42 percent; going to five cuts it by a further 22 percent. Three is the practical stopping point.
Why does my neck measurement matter?
The Navy equations use the difference between waist (and hip, for women) and neck, so a larger neck lowers the estimate. It is not a decoration — on the male profile it is worth −0.70 points per centimetre, exactly as much as the waist is worth positively.
Is a smart scale better than this?
Different failure mode, not a better one. Bioelectrical impedance infers body composition from an electrical signal that moves with hydration, so its error is dominated by something you cannot control by measuring more carefully. Our BMI scale page goes into what those devices actually measure.
Do I need someone else to measure me?
For skinfolds, it helps a lot — several of the sites are hard to pinch correctly on yourself, and the error budget table shows the difference between a 0.5 mm and a 3 mm slip is 0.24 versus 1.45 points. For tape measurements, self-measurement is fine if you can keep the tape parallel all the way round.
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Not medical advice. Every error figure on this page is conditional on the slip size you selected and covers measurement error only, not the prediction error of the underlying equations. See our disclaimer.