The scale · Decision 12 of 12

Why the weight chart draws a line you did not measure

The heavy line on the weight chart is not your weighings. It is a weighted average of them, where recent days count for more. The kilos-per-week figure beside it is read off that line, not off the scale.

Written and maintained by Mattias Geniar. Last updated 10 September 2026.

What the app does: Moves the line a tenth of the way towards each new reading, and shows a rate measured over whichever range you are looking at. The dots stay on the chart.
How sure we are Fair , Real, but small, indirect, or thinly measured.: The noise figure comes from two small studies measuring different kinds of variation. The smoothing itself is an engineering choice, not a research finding, and it runs about nine days behind.

The evidence for it

Two studies describe daily variation using different metrics. Reading the rate off the range you selected is our engineering choice, not a validated precision guarantee.

0.54% of body weight: mean coefficient of variation around fitted trends, not a personal error bound Khosla & Billewicz (1964) · 19 people, daily, range 0.39–0.78%

0.53% standard deviation of day-to-day weight differences in ONE man over 9,521 days Schneditz et al. (2023) · rising to 0.69% across a week

7, 30 or 90 days the rate is read off the range you have selected; not an uncertainty interval Product setting; a shorter range is a noisier answer, and real uncertainty depends on sampling and biological variation

We are showing you a calculated figure in the place where a measurement would go, so here is the case for it.

Twelve weeks of a person losing 0.63 kg a week Simulated: the app's own smoothing, on a scale a little noisier than the studies below report, with one morning in five missed.

What the scale said, 67 mornings What the app draws The true weight, which nobody can see

The dashed line is the true weight the simulation was given, which nobody in real life gets to see. The dots are what the scale said. The heavy line is what the app draws, and it is the argument: it reduces short-term scatter while lagging behind the simulated change. The lag varies during this run; the plotted line uses the production filter, including missed-day handling. Run with a fixed seed, so this is the same picture every time the page loads. It is a simulation of our own smoothing, not a finding about people.

Why a single weighing tells you little

Khosla & Billewicz (1964) weighed nineteen people daily under standard conditions for several weeks and measured how far each morning was from that person's own trend. The day-to-day variation ranged from 0.39% to 0.78% of body weight, with a mean of 0.54%. They concluded that day-to-day changes rarely go above 1.5% of body weight. Schneditz et al. (2023) studied one man over 9,521 days of standardised measurements. The standard deviation was 0.53% between one day and the next, rising to 0.69% across a week. Unlike the older study’s residual variation around a fitted trend, this measures differences between two readings. The similar percentages are not interchangeable measurements.

The noise is six times the size of a day's progress At 82 kg, losing 0.5 kg a week. Both bars are kilograms.

Illustrative SD around a fitted trend ≈0.4 kg

0.54% × 82 kg = 0.44 kg, rounded; not a bound for an individual

What losing 0.5 kg a week is, per day 0.07 kg

The thing you are trying to measure, underneath the bar above

0 0.5 kg

Taking the last weighing of a month minus the first is subtracting two numbers that each carry five days' worth of real progress as error. So it can show weight going up through two weeks of real loss. That is the obvious way to do it, and it is why the app does not.

Khosla & Billewicz did more than describe the noise. They set out the arithmetic for estimating a change from several readings at each end rather than one. They also noted that readings on nearby days tend to be off in the same direction. So readings spread further apart tell you more than readings bunched together. Averaging the ends is exactly what a smoothed line does, continuously.

The numbers behind our two settings

The smoothing moves the line a tenth of the way towards each new day's reading, which means a change takes about a week to show half of itself. The weekly rate is measured over the range the chart is showing, so the 7, 30 and 90 day views answer with three different numbers: the short one is about this week and is the noisiest, the long one is about the whole stretch. After a gap of d days, the next reading gets weight 1 − 0.9ᵈ, so a long gap is not treated like a single day. The chart above calls the same WeightTrend calculation as the app. Its noise is independent Gaussian variation with SD 0.6% of simulated weight, and each day has a 20% chance of being missed. These are illustrative assumptions.

How quickly the filter responds to a lasting change Calculated response with a reading every day: 1 − 0.9ᵈ. No biological noise in this illustration.

After 1 day 10%

After 7 days 52%

After 14 days 77%

After 28 days 95%

0 100% of a lasting change

After seven daily readings, about half a permanent step change has reached the line. These percentages describe the filter, not its accuracy. We removed the previous ±0.10 kg/week precision claim because the published illustration did not reproduce that uncertainty analysis.

The evidence against

Both studies are small. Khosla & Billewicz is nineteen people in 1964, including two babies and pregnant participants, weighed on household scales. Schneditz et al. is a single man, and its purpose was setting target weights for dialysis, not dieting. They measure different quantities and cannot establish a universal noise allowance.

The smoothing itself is not a research finding. A weighted average that takes about a week to show half of a change is an engineering choice with a long history in weight tracking. A Kalman filter could produce a model-based band, but its validity would depend on assumptions and calibration. We chose the simpler one because you can check it by hand and because we cannot yet show a band we would trust.

A smoothed line runs behind reality by design. For a constant linear change and daily readings, the steady-state lag is about nine days. Gaps and changing trends alter that behavior. If you change something today, the line will not agree with you for a week or two, and during that time it is wrong in a direction we can predict. That is the cost of a line that does not react to water weight.

None of this makes the scale a measure of fat. Everything above is about separating a trend from noise in body weight. Glycogen, salt, the menstrual cycle and creatine all change weight without changing fat, and the 30 day range is uncomfortably close to the length of a cycle. The dots stay on the chart on purpose, so you can see the scatter the line is drawn through, rather than being handed a confident line and asked to trust it.