BMI Machine: Five Tests for the One You Already Own
A BMI machine measures exactly one physical quantity: your weight. It divides that by a height you typed in once, and everything else on the display is computed from the same two numbers. So there are only two ways it can be wrong about your weight — a gain error, which multiplies with how heavy you are, and an offset error, which is the same for everybody — and a home test can see the first one only with difficulty and the second one not at all. Below are five tests you can run in ten minutes, with the pass and fail thresholds computed rather than guessed. Every number on this page is arithmetic performed here; no device was measured and no product is named, ranked or reviewed.
The two reference masses give a slope of 1.0200 and an intercept of 0.05 kg. At your weight that splits into 1.56 kg of gain error — a 2.00% slope error that scales with how heavy you are — and 0.05 kg of offset, which is the same for every person who steps on it. Your BMI 25.5 (Overweight) is really 24.94–25.47 once the machine error is taken out.
The nearest category line is BMI 25, which sits 1.44 kg away. Machine error plus placement spread is 2.41 kg, so your category is at risk — the error is wide enough to flip which category you land in.
Can the test see that? The add-mass test says 2.00% gain, or 1.56 kg at your weight, but its own noise is ±1.87 kg. The error is smaller than the test's own noise, so you cannot conclude anything from it — use a heavier reference mass or average more readings. At 3 readings per weigh-in the smallest gain error this test can detect is 2.40%. Remember that the add-mass test is blind to the offset: a machine that reads half a kilogram high on everything passes it perfectly.
Placement. A 0.80 kg corner-to-corner spread is 0.261 BMI points, or 5.2% of the whole overweight band (15.31 kg wide at your height). Repeatability. At ±0.3 kg and 3 readings, the smallest change you can call real is 0.48 kg (0.157 BMI points); at half a kilogram a week that takes 6.7 days of real loss before the machine can see it. You would need 3 readings to resolve 0.5 kg and 18 to resolve 0.2 kg.
Drift. At 0.20 kg over 180 days the sensor is moving 0.00111 kg/day, which is one BMI point every 7.6 years and would take 3.5 years to carry you across the nearest category line on its own.
One sensor, two numbers. Every kg of weight error moves BMI by 0.327 and the body fat reading by 1.00 points; every cm of height error moves BMI by 0.291 and body fat by 0.89 points. The two displayed numbers are not independent checks on each other — they share the same measurement, so they fail together.
ΔBMI = ΔW ÷ H² and ΔBMI = 2·BMI·(ΔH ÷ H)
ΔBF (points) = 100·(1 − BF)·(relative error in fat-free mass)The first line is the whole machine: a straight line with a slope and an intercept. A slope error is a percentage, so it grows with the person standing on it; an intercept error is a constant, so a big and a small person pay the same. The second line is exact calculus on the BMI definition — weight error divides by height squared, height error is doubled because height is squared and sits in the denominator. The third line is the structural fact behind every body fat number the display prints: fat-free mass is a measured quantity divided by an assumed constant, so a relative error anywhere in that chain moves the reported body fat in proportion to your remaining lean fraction. Every table below is this page evaluating those identities. None of it is copied from anywhere, and none of it involves measuring a device.
The short answer
You cannot calibrate a bathroom machine against a laboratory standard at home, and this page will not pretend otherwise. What you can do is find out whether yours behaves like a straight line, whether that line has the right slope, where in the room it agrees with itself, how much it disagrees with itself from minute to minute, and whether it is slowly moving. Those five answers decide what the display is worth.
- There are only two ways the weight can be wrong. A gain error is a percentage and scales with you — a 2 percent slope error is 1.56 kg at 78 kg and 0.98 kg at 49 kg. An offset is fixed — 0.05 kg is 0.05 kg whether you weigh 45 or 120 kg.
- The easy home test is blind to half the problem. Stepping on holding a known weight measures the slope only. A machine that reads two kilograms high on everything passes it perfectly, which is why the two-mass test exists.
- The test is noisier than the error it is looking for. With a 20 kg reference mass, 0.3 kg of reading scatter and three weigh-ins averaged into each reading, the smallest gain error you can detect is 2.4 percent — nearly five times the 0.5 percent error that already costs 0.39 kg at 78 kg.
- Where the machine stands matters more than people think. At 1.70 m the overweight band is 14.45 kg wide, so a 2 kg corner-to-corner spread eats 13.8 percent of an entire category.
- Drift is slow, and that is good news. Even a sensor creeping 0.5 kg a year needs 5.8 years at 1.70 m to move your BMI by one point. Re-test once a year, not once a month.
If you only run one test, run the corner test. It takes ninety seconds, it needs no reference mass, and a spread above half a kilogram means every other number on this page is being measured on a moving target.
What the machine measures and what it merely computes
The table below maps each field a typical body composition scale can display to the inputs it actually depends on. Only the first row is measured. Everything below it is arithmetic performed on that one measurement plus whatever you typed in at setup. This matters because the errors inherit: a fault in row one appears in every row beneath it, and no amount of extra decimal places further down can remove it.
The practical consequence: if the weight is wrong, every other row is wrong, and they are wrong in a correlated way. Two numbers that agree with each other on the same machine is not evidence that either is right.
Test 1 — the add-mass test, which sees the slope
Weigh yourself, then weigh yourself holding something whose mass you know: a dumbbell, a case of water, a bag of flour with the weight printed on it. The reading should rise by exactly that mass. The ratio of what the machine saw to what you added is the slope, k = (reading with the mass − reading without) ÷ mass, and a slope of 1.0200 means the machine over-reads by 2 percent.
Because a percentage of a bigger number is a bigger number, the same slope error costs a heavy person more kilograms than a light one. The table below is (k − 1) × weight, computed at five body weights and five slope errors.
Divide by height squared to get the same error in the units the machine reports. At 1.70 m, where one BMI point is 2.89 kg, the identical table reads:
Note what is not in this test: any constant. If the machine reads 1.5 kg high on everything, the difference between two readings is still exactly right, and the test reports a perfect slope of 1.0000. That is the blind spot this test has, and it is why it cannot stand alone.
Test 2 — two known masses, which sees the slope and the offset
Put one known mass on the machine and read it, then a second, larger one. Two points fix a straight line completely: the slope comes from the difference of the two readings, and the intercept — the amount the machine reports when nothing is on it — falls out of either point. Once you have both, you can predict the machine's error at any body weight as (k − 1) × W + b.
The offset is the more interesting of the two, because it does not scale with the person. It is the same number of kilograms for a 45 kg teenager and a 120 kg adult, which means it is worth more BMI points to the shorter and lighter one. The table is b ÷ height², in BMI points.
The conversion factor behind that table is worth memorising, because it turns every kilogram on this page into something you can compare against a category boundary.
A worked example, the one the calculator is loaded with: the machine reads 5.15 kg for a 5 kg mass and 20.45 kg for a 20 kg mass. The slope is 15.30 ÷ 15 = 1.0200 and the intercept is 5.15 − 1.0200 × 5 = 0.05 kg. At 78 kg that is 1.56 kg of gain error plus 0.05 kg of offset, so 1.61 kg — 0.53 BMI points at 1.75 m, against a 1.44 kg gap to the BMI 25 line. The gain error alone is already enough to move the category.
Computed: how big an error your test can actually see
This is the part that decides whether the tests above are worth doing, and the answer is less encouraging than the tests themselves. Both tests work out a slope from the differenceof two readings, and each reading carries the machine's own scatter. The difference of two readings has that scatter multiplied by the square root of two, and dividing by the reference mass turns it into a slope.
So there is a floor: a gain error smaller than 1.96 × √2 × (scatter ÷ √readings) ÷ mass is invisible. The table below is that floor in percent, computed for a single reading at each point and five reference masses.
Read that against the first table. A 0.5 percent slope error costs a 78 kg person 0.39 kg, which is the kind of error that matters at the edge of a category. With a 20 kg dumbbell and 0.1 kg of scatter, the smallest error you can detect is 1.39 percent — nearly three times too coarse. The error you care about and the error you can see are different sizes, and the fix is a heavier reference mass, not a better scale.
The second consequence is that the test's own uncertainty is amplified by how far your body weight sits from the reference mass. The inferred error is (k − 1) × your weight, so the noise in k gets multiplied by your weight and divided by the mass. The table is the resulting uncertainty in kilograms, per 0.1 kg of reading scatter, at one reading each.
A third problem appears if you run the two-mass test with small weights and then apply the resulting line at body weight. That is an extrapolation, and extrapolation amplifies noise. With the line built from 5 kg and 5 + s kg, the reading noise at the two calibration points is re-combined with weights (1 − t) and t, where t = (your weight − 5) ÷ s. The amplification factor is the square root of the sum of those squared weights:
Calibrating with a 5 kg and a 10 kg weight and then applying the line at 80 kg multiplies the reading noise by 20.5. That is not a test, it is an amplifier. The add-mass test avoids this entirely, because it measures the slope right where you stand — which is the strongest argument for owning one heavy reference mass rather than a set of light ones.
Test 3 — placement: move the machine, not yourself
Four load cells share your weight, and how they share it depends on where your feet are and what is under the device. Put the machine on a hard, level floor, weigh yourself four times in the same spot, then move it to a different spot and repeat. The corner-to-corner spread is the placement error, and unlike the reading scatter it does not shrink when you average, because it is a fixed property of that spot.
To judge a spread, compare it with the width of a category. The overweight band, BMI 25 to 30, is five BMI points wide, which is 5 × height² kilograms. The table is the spread as a percentage of that band.
A working rule that follows from the table: a spread above half a kilogram is worth chasing, because at 1.70 m it is 3.5 percent of a whole category and it will not average away. Carpet, tiles with a grout line under one foot, and a machine stored leaning against a wall are the usual causes. Fix the spot once and leave the machine there.
Test 4 — repeatability: how much of a change is real
Step off, step on, repeat. The scatter you get is the machine's short-term noise, and it sets the smallest change you are allowed to believe. Comparing two weigh-ins means comparing two noisy numbers, so the threshold is 1.96 × √2 × (scatter ÷ √readings) — the √2 because there are two readings in the comparison, and the √readings because averaging shrinks random scatter.
Turned into time: if you are genuinely losing half a kilogram a week, how long until the loss is bigger than what the machine can resolve?
With typical scatter and a single reading, you need roughly eleven days of real progress before the machine is entitled to say anything. Three readings a day cuts that to about a week. This is the whole argument for averaging: not that it makes the number more accurate, but that it lets you hear a real signal sooner.
Test 5 — drift: is the machine slowly moving
Keep one known mass and weigh it every few months, writing the reading down. A change in that reading is the sensor moving, not you. Drift is expressed in kilograms per year and converted into the units that matter by dividing it into the kilograms that make one BMI point.
Two conclusions. First, drift is slow relative to everything else on this page: even a full kilogram a year takes nearly three years at 1.70 m to move your BMI by a single point, so an annual check is plenty. Second, the units matter — the same drift rate is worth 60 percent more time to a tall person, because a BMI point is more kilograms for them.
One sensor, two numbers: why BMI and body fat fail together
The most common way people use a body composition scale is as a cross-check: if the BMI and the body fat roughly agree, the reading must be right. They cannot disagree in the way you would hope, because both are computed from the same weight.
Differentiate both. BMI = W ÷ H², so a weight error of one kilogram moves BMI by 1 ÷ H². Body fat = 1 − fat-free mass ÷ W, and the fat-free mass comes from impedance, not from the scale — so if the weight is wrong and the impedance estimate is held fixed, the reported body fat moves by 100 × (1 − BF) ÷ W points per kilogram. The ratio of the two is 100 × (1 − BF) ÷ BMI, which depends only on how big and how lean you are:
Those are body fat points per BMI point, and they are all positive: the two numbers move in the same direction, always. At the calculator's default body — BMI 25.47, 22 percent — one BMI point is worth 3.06 body fat points, and a single kilogram of weight error moves BMI by 0.33 and body fat by 1.00 point.
The height you typed in behaves the same way, only harder. It enters BMI squared, so ΔBMI = 2 × BMI × (ΔH ÷ H). It also enters the impedance chain, because the device estimates body water as proportional to height squared — so the same one centimetre error hits the body fat number through the fat-free mass as well:
The ratio is constant at 3.06 because it is the same 100 × (1 − BF) ÷ BMI as before — the height error is simply routed through both chains at once. One centimetre of wrong height costs a 175 cm person 0.29 BMI points and 0.89 body fat points, and no amount of averaging will fix either, because it is the same wrong number every morning.
The five tests, in order
Run them in this sequence, because each one decides whether the next is worth doing.
- 1. Placement (2 minutes, no equipment). Weigh yourself four times in one spot, move the machine, repeat. Keep the spread under 0.5 kg. If it is over, fix the floor before anything else — every later test inherits this.
- 2. Repeatability (2 minutes, no equipment). Ten step-off, step-on cycles. Note the scatter and use the table to set your own threshold for what counts as a change.
- 3. Add-mass (1 minute, one heavy object). Slope only. Use the heaviest single mass you can hold safely — the detection floor falls in direct proportion to it.
- 4. Two masses (2 minutes, two known masses). Slope and offset. Keep the two masses as far apart as your objects allow, and remember that applying the result at your body weight is an extrapolation if both are small.
- 5. Drift (ongoing). Weigh one reference mass once a year and write the number down. Anything under about half a kilogram a year is slower than the other errors on this page.
What none of these tests can do is tell you whether the body fat number is right. That number depends on impedance, on electrode contact, on your hydration, and on constants the manufacturer chose, and there is no household object that checks any of it. Treat it as a trend with a noise band, never as a measurement of your tissues.
Frequently asked questions
Is a BMI machine accurate?
For weight and BMI, usually yes within the limits above: the largest error is typically the height you typed in, and one centimetre of it is worth 0.29 BMI points at 175 cm. For body fat, the machine is not measuring fat at all — it is measuring how your tissues conduct a small current and converting that through assumed constants. This page deliberately gives no accuracy figure for that conversion, because it has not measured any device against a reference method and a number quoted without a measurement would be invented.
What should I use as a known mass?
Anything with the mass printed on it and no ambiguity about the unit: a dumbbell, a kettlebell, a case of bottled water, a bag of rice or flour. Heavier is better — the smallest slope error your test can detect is inversely proportional to the mass, so a 20 kg object sees four times further than a 5 kg one. Avoid anything whose printed figure is a volume, and check whether the package is quoting net or gross.
My two tests disagree. Which one is right?
Probably neither, and that is informative. The add-mass test measures the slope where you actually stand, with its noise amplified by your weight divided by the mass. The two-mass test measures the slope between 5 and 20 kg and then extrapolates, which amplifies the noise further the smaller those masses are. If the difference between the two slopes is larger than the uncertainties in the tables above, the most likely explanation is that the machine is not a straight line across its range — which is itself a reason not to trust a single correction factor.
Does it matter where I put the scale?
Yes, and it is the cheapest error to fix. Four load cells share your weight, and a soft or uneven surface changes how they share it. A 2 kg corner-to-corner spread is 13.8 percent of the entire overweight band at 1.70 m, and unlike scatter it does not shrink when you average, because it is fixed to that spot. Hard, level floor, same spot every time.
Why does my body fat jump around when my weight barely moves?
Because the two numbers come from different places. BMI is arithmetic on the weight and your stored height, so it is as stable as the load cells. Body fat comes from impedance, which moves with hydration, skin temperature, foot contact and time of day. Our smart scale page prices the hydration part directly, and the repeatability tables on this page tell you how much of any jump is noise.
Can a BMI machine measure visceral fat?
No. Visceral fat sits inside the abdominal cavity and a current passed through your feet cannot separate it from the fat under your skin. Any visceral rating on the display is the estimated body fat number with more assumptions stacked on top. A tape measure at your waist is more honest, and our visceral fat page computes exactly what a waist measurement can and cannot support.
Should I replace my scale if the tests fail?
Only after the cheap fixes. Most failures on this page are placement, a height typed in from memory, or a reference mass that is too light to see anything — none of which need a new device. If the corner spread stays above half a kilogram on a hard floor and the slope is still off with a heavy reference mass, the sensor is the problem. What buying a more expensive one does to the body fat number is a separate question, priced on our best BMI scale page.
Where this page's arithmetic stops being true
- No device was measured. Every number here is this page evaluating the identities at the top on values you supply. Nothing is a test result, no product is named, ranked or reviewed, and no comparison against DEXA, underwater weighing or any other reference method is quoted, because quoting one without measuring it would be fabrication.
- The straight-line model is an assumption. Real load cells are not perfectly linear and can be non-linear near zero or near their maximum. The two-mass test assumes one line describes the whole range; if it does not, no single correction factor exists.
- The scatter figures are placeholders until you measure your own. The repeatability, detection and drift tables are all computed from a scatter value. Until you run test 2 and write down your actual number, the output describes a hypothetical machine.
- Independence is assumed in the error arithmetic. The corner spread, the slope error and the reading scatter are treated as separate and combined by simple addition or quadrature. If they share a cause — a sensor that is both non-linear and drifting — the totals here understate the real error.
- The body fat sensitivities come from one model of the impedance chain.The height term, the hydration constant and the shared-sensor ratios follow from the assumption that fat-free mass is estimated as body water divided by a constant. A manufacturer's actual firmware is not published and is almost certainly not this simple.
- The sensitivities are local. Every per-kilogram and per-centimetre figure is a derivative evaluated at your current numbers. Move a long way from there and they change.
- WHO categories are screening bands, not diagnoses. Being near a boundary is an arithmetic statement about where the number sits, not a statement about your health.
Related tools
BMI calculator · what a smart scale actually measures · what a spec sheet is really worth · body fat calculator · how small a change your tape can see · picking the method you can repeat · fat percentage across three methods · how to measure body fat at home · body fat percentage chart
Not medical advice.Every figure on this page is arithmetic performed here on the BMI definition and on a stated model of how a body composition scale works. No device was measured, no product is ranked, and nothing here is a claim about any manufacturer's accuracy. See our disclaimer.