SizingKitMachining · ISO 286
Tolerance calculator for limits and stack-up
Enter a basic size and a designation and this returns the two limits of the hole and the two of the shaft, in millimeters and inches, from the ISO 286-1 standard tolerance table and the ISO 286-2 fundamental deviations. A second panel stacks a chain of features and resolves it twice — worst case and root-sum-square — so the disagreement between the two methods is visible rather than buried in whichever one the calculator picked. Free, no signup, grades IT5 to IT16 up to 500 mm.
- 100% free
- No signup
- ISO 286-1 and 286-2
- IT5 to IT16
- Worst case and RSS
Limits from a designation
The letter places the zone and the number sets its width. Pick both halves and the four numbers a gauge is set to fall out of the two ISO 286 tables.
The nominal on the drawing, before any deviation. Inch sizes are converted to millimeters first, because the table is metric and there is no inch original.
H only — EI is zero.
g h k p s
HOLE
25.000 / 25.021
0.98425 / 0.98508 in
SHAFT
24.980 / 24.993
0.98346 / 0.98398 in
| Feature | Lower limit | Upper limit | Deviations |
|---|---|---|---|
| 25.000 H7 | 25.000 mm 0.98425 in | 25.021 mm 0.98508 in | 0 / +21 µm zone 21 µm |
| 25.000 g6 | 24.980 mm 0.98346 in | 24.993 mm 0.98398 in | -20 / -7 µm zone 13 µm |
- TIGHTEST
- +7 µm
- 0.00028 in
- LOOSEST
- +41 µm
- 0.00161 in
- SPREAD
- 34 µm
- 0.00134 in
Clearance throughout — the shaft is smaller than the hole at every combination of limits.
The spread between tightest and loosest is the two zone widths added: H7 supplies 62% of it. Moving g6 one grade finer changes the fit less than moving H7 does, and on a hole that difference is a reamer rather than a tool offset.
Nominal size range over 18 up to 30 mm, standard tolerance factor i = 1.3074 µm, taken over the geometric mean of that range’s bounds. ISO 286-1, Geometrical product specifications (GPS) — ISO code system for tolerances on linear sizes: standard tolerances IT5 to IT16 for nominal sizes up to 500 mm, in micrometers. The tolerance unit column is the standard tolerance factor i = 0.45 ∛D + 0.001 D of the same standard, with D the geometric mean of each range.
ISO 286-2, Geometrical product specifications (GPS) — tables of standard tolerance classes and limit deviations for holes and shafts: fundamental deviations for shaft positions g, h, k, p and s, in micrometers. h is zero by definition. The tabulated values follow the rules ISO 286-1 states for each position — es(g) = −2.5 D^0.34, ei(k) = +0.6 ∛D for grades IT4 to IT7, ei(s) = IT7 + 0.4 D above 50 mm — with D the geometric mean of the size range; the values up to 3 mm are the printed ones, which those rules do not reproduce.
Stack a chain of tolerances
Every feature that lies along the axis of the gap you care about, with the sign that says whether it opens the gap or closes it. The answer comes back twice.
A unit written into a field beats this one, so a chain that mixes a bought-in metric bearing with an inch housing needs no conversion first.
| Feature | Sign | Nominal | ± tolerance | Remove |
|---|---|---|---|---|
WORST CASE
0.200 ± 0.250
-0.050 to 0.450 mm
-0.00197 to 0.01772 in
ROOT-SUM-SQUARE
0.200 ± 0.139
0.061 to 0.339 mm
0.00240 to 0.01334 in
The two methods disagree about whether these parts assemble at all: worst case closes the gap to -0.050 mm and root-sum-square leaves 0.061 mm. That gap is the decision, and it is a production question rather than a geometry one — how many are being built, whether they are inspected, and what it costs when one will not go together.
Both columns describe this same chain and neither is a prediction. The left one is what a single assembly has to survive; the right one is where a long run settles. Which of them applies is a question about the shop rather than about the geometry — how many are being built, in how many setups, and on tooling that drifts one way as it wears — and the section below sets out where the statistical column stops being safe.
How to read a designation and stack a chain
Two panels, two different questions a drawing raises.
Enter the basic size, not one of the limits
The basic size is the round number the drawing is dimensioned to — 25, not 25.021. Both zones are measured from it, so putting a limit in instead shifts the whole answer by one tolerance. Inch drawings are welcome in the same box: 1 1/2" and 0.9843 in are read as written and converted to millimeters, because ISO 286 is a metric table with no inch original to read from.
Set the letter and the number as two separate decisions
The letter says where the zone sits relative to the basic size and the number says how wide it is. Move the letter from g to p and the shaft goes from always-smaller to always-larger without its width changing at all; move the number from IT6 to IT8 and the width quadruples while the zone stays put. The panel prints both deviations in micrometers beside the limits so the two effects stay visible separately.
List the features that lie along the gap you care about
In the second panel, one row per feature, with a plus sign for anything that opens the gap and a minus for anything that closes it — a housing depth against a bearing, a spacer and a shim. The nominal column gives the gap and the tolerance column gives the band around it, twice: once by adding the tolerances and once in quadrature.
Technical specifications
| Standard tolerance table | ISO 286-1, grades IT5 through IT16 across 13 nominal size ranges from over 0 up to 500 mm |
|---|---|
| Tolerance positions | Hole H (lower deviation zero); shafts g, h, k, p and s from ISO 286-2. The remaining letters and the shaft-basis holes G7, K7 and P7 are not reproduced |
| Finest and coarsest available | IT5 up to 3 mm is 4 µm (0.00016 in); IT16 over 400 up to 500 mm is 4,000 µm (0.157 in) — a factor of a thousand across one table |
| Worked example | 25H7 is 25.000 / 25.021 mm; 25g6 is 24.980 / 24.993 mm; the pair runs 7 to 41 µm of clearance across a 34 µm spread |
| Where the table stops | 500 mm nominal, and 200 mm for the s position — ISO 286-2 subdivides s into finer bands above 50 mm and this site carries them only that far |
| Tolerance unit shown | i = 0.45 ∛D + 0.001 D with D the geometric mean of the size range, printed for the range in use alongside the published grade values |
| Stack-up methods | Worst case Σ|t| and root-sum-square √(Σt²) on the same chain, with signed nominals summed so the result is a gap rather than a bare ± band |
| Units in and out | Millimeters or inches typed into any field, fractions included; limits printed to 0.001 mm and 0.00001 in, deviations in micrometers |
Frequently asked questions
Why does a 30 mm feature use the 18–30 mm row and not the 30–50 one?
Because the ranges read "over 18 up to and including 30", so 30.000 mm is the last size in the lower row rather than the first size in the upper one. It matters: IT7 is 21 µm in the 18–30 row and 25 µm in the 30–50 row, and reading one row too far turns a 30H7 bore from 30.000/30.021 into 30.000/30.025. This is the single most common mistake in reading the standard tolerance table, and it happens precisely at the round numbers a designer is most likely to have picked.
Is IT7 the same width on a hole as it is on a shaft?
Yes — the grade sets the width and nothing else. At 25 mm, IT7 is 21 µm whether the feature is a bore, a spindle, an H7 hole or a p7 shaft. What changes between them is where those 21 µm sit: H puts the bottom of the zone exactly on the basic size, h puts the top of it there, g hangs it a few micrometers below and p stands it above. That separation is the whole reason the designation is a letter and a number rather than a two-column lookup.
When is root-sum-square the wrong answer?
On a short chain, on features made in one setup, and on any process that is not centered. Quadrature earns its smaller number from many independent departures partly canceling, so with three contributors there is nothing to average and the reduction is arithmetic without a population behind it. Features cut in a single setup share a fixturing error rather than varying independently, a tool wearing through a run puts every part on the same side of nominal, and a supplier who sorts parts to ship the ones nearest a limit hands you a distribution with a hole in the middle of it.
Why does the published IT value differ from the formula on small sizes?
Because ISO 286-1 rounds the computed figure up to a preferred number in the smallest ranges, and the published table is what governs. The tolerance unit i = 0.45 ∛D + 0.001 D reproduces the printed table exactly from 18 mm upward, but below that it disagrees: IT7 up to 3 mm computes to 8.7 µm and is published as 10, and IT7 over 6 up to 10 computes to 14.4 and is published as 15. A 3 mm H7 hole is therefore 3.000/3.010 and not 3.000/3.009, so this page carries the table and shows the formula rather than the other way round.
Which hole and shaft positions does this page cover?
Hole H, and shafts g, h, k, p and s — the positions the five preferred hole-basis fits are built from. ISO 286-2 defines roughly two dozen more shaft letters and the corresponding hole positions, and the whole shaft-basis system (an h6 shaft running in G7, K7 or P7 holes) that gets used where the shaft is bought as ground stock rather than turned. H11/c11 loose running, H9/d9, H8/f7 running and H7/n6 are all real and none of them are here; take those deviations from ISO 286-2 directly.
How do I turn a ±0.005 in drawing tolerance into an IT grade?
Double it and convert: ±0.005 in is a 0.010 in band, which is 254 µm. On a 50 mm feature that is a hair over IT12's 250 µm and well inside IT13's 390, so the drawing is asking for IT12 at best. The comparison has to be made at the actual size: the same 254 µm band is IT14 on a 6 mm feature and IT11 on a 400 mm one, so a blanket ± figure in a title block means three or four different grades across one part.
Does a stack-up need the nominal dimensions as well as the tolerances?
It needs them if you want to know whether the parts go together. Tolerances alone give the width of the band; the signed nominals give where that band sits, and a chain can have a comfortable ±0.14 mm and still close to a negative gap because the nominals never left room for one. That is why the second panel asks for both and prints the resulting gap rather than only the ± figure.
About ISO 286 limits and tolerance chains
An ISO 286 designation is two independent halves and reading it as one lookup is what makes it feel arbitrary. The letter is a position: H starts a hole exactly at the basic size and goes up, h ends a shaft exactly at it and goes down, g hangs a few micrometers below and p and s stand well above. The number is a width, the standard tolerance grade, and it is the same width for every letter at a given size — IT7 on a 25 mm feature is 21 µm whether that feature is a bore or a spindle. That is why H7/p6 presses together and H7/g6 slides: the arithmetic of the two zones says so, and no chart is needed to see it. The width itself comes from one expression, i = 0.45 ∛D + 0.001 D, with every grade from IT5 up a fixed multiple of it — 7i, 10i, 16i, 25i, 40i, 64i — which is why the columns grow so regularly and why they stop being regular in the smallest sizes, where the committee rounded up to numbers the formula does not give.
Hole basis exists because holes are expensive to change and shafts are not. One reamer, one plug gauge and one inspection routine covers every fit at a given size, and the fit is altered by turning the shaft to a different letter — a tool offset rather than new tooling. Where the joint is an interference rather than a clearance, the limits this page prints are only half the story: the overlap between them is metal that has to go somewhere, and the press fit calculator turns it into a contact pressure, an assembly force and a hoop stress in the hub. It is also worth knowing that a designation says nothing about roughness, and roughness eats interference — the peaks of both surfaces flatten on assembly, so a bore left at the finish a drill leaves delivers less interference than it measures. The surface finish chart gives the Ra each process actually holds.
The stack-up panel exists because most calculators return one number and hide the argument. Worst case adds the tolerances and is true of every part ever made; it also describes a coincidence a hundred-piece run will not produce, and a designer who works to it on a ten-member chain buys tolerances nobody needs. Root-sum-square takes the square root of the sum of the squares and assumes each contributor is independent, centered, and spread so its ± band is three standard deviations — three assumptions that fail quietly. Features cut in one setup share their fixturing error. A tool wearing through a run puts every piece on the same side of nominal. A supplier sorting parts to ship what is nearest a limit hands over a distribution with a hole in the middle. The honest use of the two columns is as bounds: if worst case is affordable, take it; if it is not, the RSS figure is what you are betting on, and the bet is about the process rather than the geometry. Nothing here is a stamped design — the fits, the chain and the assembly method are the engineer's call, and this page is the arithmetic underneath it.
Where the drawing you type stays
Every number on this page is worked out by JavaScript running in the tab you are reading it in. Nothing you type — loads, lengths, nameplate ratings, the rates your utility charges you — is uploaded, logged or kept, which is also why the calculators carry on working in a mechanical room with no signal.
Sizes, designations and the rows of a stack-up chain live in the page's own memory for as long as the tab is open and are gone when it closes. There is nothing to save and no account to save it to, which is deliberate: a tolerance chain is usually somebody's unreleased part.