Decision 8 of 10

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 a fixed four weeks. The dots stay on the chart.
How much we believe it: The noise figure comes from two small studies that agree closely. The smoothing itself is an engineering choice, not a research finding, and it runs about nine days behind.

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 falls at the right rate, while the dots tell you nothing on any single morning. It also runs about 0.8 kg above the truth throughout, which is the nine-day lag the section below admits to. Run from App\Domain\TrendSimulation 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) found the same size of effect in a much longer series of 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.

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.

How far a typical morning is from the truth ≈0.4 kg

0.54% of 82 kg. A bad morning is over a kilo

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 number this app used to show.

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 a fixed four weeks, whatever range the chart is showing. We picked that by simulating this smoothing against a known true rate of 0.63 kg/week, with noise a little larger than the papers above report and one day in five missed. That is the same run drawn at the top of this page.

How much the quoted rate wobbles, depending on how long it is measured over Width of the 95% interval around the reported rate. The true rate is 0.63 kg/week throughout.

Measured over 10 days ±0.24 kg/week

Nearly 40% of the rate being reported

Measured over 14 days ±0.19 kg/week

A third of the answer

Measured over 21 days ±0.13 kg/week

Measured over 28 days, which is what the app uses ±0.10 kg/week

The first window where the first decimal place is stable

0 ±0.30 kg/week

The average error is nil everywhere, which is what we wanted to check: +0.005, +0.005, +0.005 and +0.004 kg/week respectively. What changes is the spread. ±0.19 on a rate of 0.63 is a third of the answer, a number that visibly moves every morning without you having changed anything. Four weeks is the first window where a tenth of a kilo means something, which is also why the rate is printed to one decimal and not two.

The evidence against

Both studies are small. Khosla & Billewicz is nineteen people in 1964, two of them babies and one pregnant, weighed on household scales. Schneditz et al. is a single man, and its purpose was setting target weights for dialysis, not dieting. They agree with each other closely, which is reassuring, but two small studies agreeing is not the same as one large one.

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 is the more rigorous version and would also give a proper uncertainty band, which ours does not. 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. Ours is about nine days behind the truth. 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 price of not reacting to water.

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 a four-week window 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.