The Shape Test

A number that goes up is either compounding or just adding the same amount, and those futures are nothing alike. You cannot tell which by looking — watch the verdict arrive, later than you expect.

Nothing you type leaves this page. No upload, no account, and no code in here that could send anything. Our host counts the visit like any web page; what you enter it never sees.

Every number below is computed in your browser, from your numbers, as you move.

01The instrument your data, the two paths competing to explain it, and the dials that move them

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Not yet knowable

Both shapes still fit inside the margin you set.

← straightthe threshold bandcompounding →

points seen: —
grown by: —
fit as straight: —
fit as compounding: —
gap vs threshold: —
doubling: —

Fits are R², scored 0 to 1, least-squares on the points — not on the two drawn paths. The verdict reads only the gap between them.

When you would have known

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How much have you seen? the one control that matters

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paths scale

Both paths run through your first and latest point. Turn both off and judge the bare points yourself.

The series · build one or bring your own

Source

A curve whose true shape you chose, with noise you control — any failure to read it is the test's, never the data's.

The shape it builds

You know which one you built. It does not.

Growth per period 3%

Faster growth brings the date forward. It barely moves how far the curve must grow before the answer arrives — until the eight-point minimum binds at fast rates.

Measurement noise 8%

Real numbers are never clean. Noise settles the verdict later, and early calls can wobble — trust the settled one.

The test

Separation you demand 0.020 · ordinary

The gap the test demands before it commits. Raise it: right more often, silent for longer.

02The price of confidence why the answer lands where it does

How far a clean, noiseless curve must grow before the statistic commits. Read across a row: the multiple barely moves, whatever the growth rate. Read down a column: what certainty costs, paid in growth you have to sit through. The spread column is each row's lowest to highest. One honest footnote: from about 19% a period the tool's own eight-point minimum binds before the statistic does, so there it cannot speak this early.
margin	1%	2%	5%	10%	20%	30%	spread

A candidate reading, not a verdict on your business. What it actually separates is a constant-rate exponential path from a linear one: "compounding" here names the shape, never the machinery, and a real compounding engine whose rate shifts month to month is not a constant-rate exponential at all. A curve that is flattening off is a third shape it will call straight, correctly for now and misleadingly later. A steadily shrinking series reads as compounding too — the test detects multiplication, not direction. It needs eight points before it will say anything at all, and it never accepts a zero or a negative value, because a zero has no ratio and a negative value no logarithm.

The threshold labels are measured, not assumed. Across 7,200 simulated noisy series, scored at all three thresholds, the ordinary and strict settings never once ended at the wrong shape; every wrong final call in the grid came from loose, on slow, noisy straight lines. Stricter settings pay in silence instead, and that is the whole trade. Ended is the load-bearing word. Score the same runs on the first shape they were willing to name and seven per cent name the wrong one, rising to forty-six in the worst cell. The settled verdict is the reliable one; the early verdict is the one you are reading here.

Built for The Durability Curve · Fitted 2026·07·31. The full argument, and the three mistakes this tool nearly shipped with, are in the essay this came from.

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