Opening the index
A number that goes up can be compounding (multiplying each period), straight (adding the same amount each period) or flattening, and those futures are nothing alike.
A built curve, not your numbers: its shape is known, so any misreading is the test's own.
Not yet knowable
Paste at least eight values and the chart draws here.
Retype the misread value above and the chart draws here.
Both paths are the best fits to the points you have seen. Turn both off and judge the bare points yourself.
Both shapes still fit inside the margin you set.
How sure the test must be before it names a shape. Raise it: right more often, silent for longer.
Your numbers at each margin
Ordinary is the default for a decision. Loose calls sooner, but on the test curves 49% of its first calls (the first shape it named on each curve) were wrong; strict waits longer, and 21% were (ordinary: 40%).
Every series is the running total of its own additions, monthly revenue included, so the kind of number does not settle it. Test the additions when the totals read Compounding: additions that rise by a steady amount also make totals curve upward, and the additions can tell the two apart. Additions that hold steady read Not yet knowable, since there is no growth in them to name; they make a straight total. Additions are noisier than totals, so they take more points to read, and one period that added nothing or fell stops the test, which is common in a noisy series.
One value per line, or separated by commas, spaces or tabs. On a line with dates, labels or several columns, the last number is the one used. 1,234 and £1,234 read as 1234; k, M and B multiply; (500) is minus 500. A paste written the European way (1.234,5 or 1 234,50) is read that way. Check the values read back below the box. The unit only dates the next check when the answer is not yet knowable.
Press watch to bring the points in; pause or drag any time, and call the shape when you are sure.
02 · How it decides
Seven checks · the first to fire decides
Seven checks, in this order. The first one that fires gives the verdict.
Gap how much better the compounding path fits than the straight one: its R² minus the straight path's, worked out on the values and again on their logs.
Margin the separation you demand, set on the test dial.
| Order | Check | If yes, the verdict | Why |
|---|---|---|---|
| 01 | Fewer than eight points? | Not enough yet | Eight points is our own unsourced minimum before any verdict is worth printing. |
| 02 | Any value at zero or below? | Cannot be read | A zero has no ratio, and a negative value has no logarithm. |
| 03 | Turned down inside your data? | Turned down | The values rise and then turn down inside your data, so none of the three shapes describes them. |
| 04 | Multiplying wins on both scales? | Compounding | Both gaps clear your margin towards the multiplying path, on the values and on their logs. If the straight fit dips to zero or below inside your data, the log gap has no score: it shows n/a and counts for compounding, because a line that goes below zero cannot describe numbers that never do. A shrinking series reads Compounding decline. |
| 05 | 12 or more points, rising, with a downward bend? | Flattening | On a rising series, a curve that bends downwards beats the straight path by more than your margin and explains at least half of what the straight path misses. |
| 06 | Adding wins on both scales? | Straight | Both gaps clear your margin towards the adding path. |
| 07 | None of the above? | Not yet knowable | Neither shape wins on both scales by more than your margin. More points may move it. |
Each gap is the compounding fit's R² minus the straight fit's R², worked out once on the values and once on their logs, so both shapes are always scored on the same scale. The test names Compounding or Straight only when both gaps clear your margin in the same direction (Flattening has its own rule, below); the needle shows the smaller of the two. If the straight fit dips to zero or below inside your data, it has no log score: that gap shows n/a and counts for compounding, because a line that goes below zero cannot describe values that are all above zero.
Flattening: with 12 or more points (our own unsourced minimum) on a rising series, if a curve that bends downwards (the least-squares fit of a + b·t + c·t², with c below zero) raises R² on the values by more than your margin and explains at least half of what the straight fit leaves unexplained, the verdict is Flattening, unless the series has turned down.
Turned down, checked before any shape is named: the values climb to a peak and then fall, with the points before the peak trending up and the points after it trending down, each by more than three times the slope's standard error, the fall after the peak larger than twice the scatter around it and at least a tenth of the rise before it, with at least 4 points on each side; or, after a climb of at least 4 points that trends up by more than three times its slope's standard error, the last two values both sit more than half that climb, and more than five times its scatter, below where the climb's own line stands at the peak (so a single outlying point cannot trigger it). Then the verdict is Turned down. A steady decline has no earlier rise, so it is not turned down.
The straight path on the chart is the least-squares line through the values; the compounding path is the least-squares line through their logs, drawn back on the values.
Every threshold on this page is our own unsourced choice: the eight- and 12-point minimums, the margins, the at-least-half rule and the turned-down tests. The calibration below measures how often they lead to a wrong call.
03 · Confidence
Clean curves, no noise
How far a clean, noiseless curve must grow before the statistic commits.
Across growth rates the multiple barely moves, whatever the growth rate.
Across margins what certainty costs, paid in growth you have to sit through.
| Margin | 1% | 2% | 5% | 10% | 20% | 30% | Spread |
|---|
Spread is each margin's lowest to highest.
From about 12% a period at the loose margin and about 18% at the ordinary one, the tool's own eight-point minimum binds before the statistic does, so in the marked cells it cannot speak this early.
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04 · Limits
Eight, and what each assumes
Where it stops, and what it assumes.
You cannot tell which shape by looking: at the ordinary margin, even a clean compounding or straight curve has to roughly triple before the test can say; noise can bring an earlier call, and an early call can be wrong.
05 · Calibration
270,000 series · measured 27 Oct 2026
Measured on 27 October 2026 against this page's rules, on 270,000 series whose true shape was known: 90,000 each of straight, compounding and flattening curves, generated with noise added, each 64 points long, and not real businesses. A wrong call names a shape the series was not built as.
| The call | At 12 points | At 24 points | After all 64 |
|---|---|---|---|
| Compounding | 8.2%3,760 of 46,074 | 1.2%722 of 60,040 | 0.03%21 of 78,496 |
| Straight | 56%34,385 of 61,641 | 42%31,758 of 75,556 | 24%20,093 of 84,940 |
| Flattening | 16%675 of 4,091 | 0.03%6 of 21,684 | 0none of 41,062 |
A levelling curve looks straight until it bends. Of the flattening curves the test named, it called 86% Straight first, and of those it named at point 64 a third were still Straight (20,080 of 61,142). Almost every wrong Straight call was one of them (98% at 24 points). Compounding and Flattening calls were rarely wrong once 24 points were in.
| Margin | Wrong at the end | No verdict | First call wrong |
|---|---|---|---|
| Loose 0.010 | 13%28,848 of 225,672 | 16% | 49% |
| Ordinary 0.020 | 9.8%20,114 of 204,498 | 24% | 40% |
| Strict 0.050 | 0.50%795 of 158,372 | 41% | 21% |
“Wrong at the end” (after all 64 points) is a share of the series given a verdict. “First call wrong” is a share of the series that named a shape (219,636 at ordinary). Almost all of the wrong calls at the end are flattening curves read as Straight. On the straight and compounding curves alone (the 180,000 of 9 October), wrong at the end is 0.45%, 0.02% and none, and first calls are wrong 26%, 15.5% and 1.7%.
Best case Real series can be noisier or differently shaped than these, so treat the figures as the best case.
Settles (in the reading above) means the verdict is unchanged through the data you have; one more point can still move it.
| Shapes | straight 1000 × (1 + r·t), compounding 1000 × (1 + r)t, or flattening 1000 × (1 + 16r(1 − e−t/16)), for t = 0 to 63 |
|---|---|
| Growth r | 1, 2, 3, 5, 8, 10, 15, 20, 30 or 40% a period |
| Noise | 5, 10, 15, 20 or 25% |
| Noise kind | proportional: each value times 1 + u, with u drawn evenly between minus and plus the noise level · fixed: a normal draw added, with standard deviation equal to the noise level times 1,000, the starting value |
| Floor | values below 1 were set to 1 |
| Volume | 300 series per combination make 90,000; three runs make 270,000 |
| Seeds | 1, 2 and 3; each run draws from one mulberry32 stream |
| Draw order | shape (straight, compounding, then flattening, so the first two are the draws of 9 October), growth rate, noise level, noise kind (proportional, then fixed), 300 series, 64 points |
| Proportional | one draw per point: u = (2d − 1) × noise |
| Fixed | all 300 × 64 first draws of its combination, then all 300 × 64 second draws, each pair turned into a normal value with Box–Muller, √(−2 ln d₁) · cos 2πd₂ |
Built for The Durability Curve · live since 31 July 2026. There is no companion essay: the method, its calibration and its limits are all on this page.