ISO 286 Fit Calculator
ISO 286 Fit Calculator
Hole limits, shaft limits and the real clearance or interference range for any ISO 286 pair — H7/g6, H7/n6, H8/f7, H11/c11 and 700 more — with the class of fit, the hole-basis and shaft-basis equivalence, and every band computed from the standard’s own rules rather than copied from a table.
ISO 286 limits and fits
A Ø25 mm H7 hole and a g6 shaft — the sliding fit, with both parts assumed to come out in the middle of their bands
Two bands, four limits, and a subtraction
- D
- nominal size. Both parts are dimensioned from the same number; the letters and grades say where each band sits relative to it
- ES, EI
- the hole’s upper and lower deviations from the nominal size, in micrometres. Capitals for a hole, always
- es, ei
- the shaft’s upper and lower deviations. Small letters for a shaft
- IT(grade)
- the standard tolerance for that grade at that size step — the WIDTH of the band. It is the same number for a hole and a shaft of the same grade, and it is the check that catches a mis-copied table: ES − EI must equal it
- Δ
- the correction ISO 286 applies to hole letters J to ZC, equal to IT(n) − IT(n−1) above 3 mm and zero at and below it. It is what makes hole basis and shaft basis give the same fit
- i
- the standard tolerance factor, 0.45·∛D + 0.001·D micrometres, evaluated at the geometric mean of the size step. Every IT grade is a fixed multiple of it
Worked example
A Ø25 mm H7 hole and a g6 shaft — the sliding fit, with both parts assumed to come out in the middle of their bands
Find the size step. 25 mm falls in “over 18 to 30”, whose geometric mean is √(18 × 30) = 23.238 mm. Every diameter in that step gets the same tolerance, so a Ø18.5 shaft and a Ø30 shaft share these numbers
The standard tolerance factor there is i = 0.45·∛23.24 + 0.001 × 23.24 = 1.307 µm, so IT7 = 16i = 20.9 and IT6 = 10i = 13.1. The standard rounds those to 21 and 13 µm, and those are the two band widths
The hole is H, so its LOWER deviation is zero by definition: EI = 0 and ES = +IT7 = +21 µm. The hole runs 25.0000 to 25.0210 mm
The shaft is g, whose fundamental deviation is its UPPER one: es = −2.5·D0.34 = -7.29, which the standard rounds to −7 µm. Then ei = es − IT6 = −20 µm. The shaft runs 24.9800 to 24.9930 mm
Now subtract. The biggest hole meets the smallest shaft: maximum clearance = ES − ei = 21 − (−20) = 41 µm. The smallest hole meets the biggest shaft: minimum clearance = EI − es = 0 − (−7) = 7 µm
Both ends are positive, so this is a CLEARANCE fit and it will always come apart. The spread is 34 µm, which is just IT7 + IT6 — the two grades added. That is always true and it is the cheapest sanity check there is: if your loosest and tightest clearances do not differ by exactly the sum of the two grades, one of the four deviations is wrong
The loosest clearance is 5.9 times the tightest, and that ratio is the real difficulty with fits. A bearing designed for 7 µm of running clearance gets up to 41, and the oil film, the running temperature and the noise are all different at the two ends. Tighten it by going to H6/g5 and the spread falls to 22 µm, for a real cost in machining
Change nothing but the shaft letter and watch the character change. With n6 the range is -28 to 6 µm — interference at one end and clearance at the other, which is what TRANSITION means. With p6 it is -35 to -1 — interference at both ends, but only just
The ten preferred fits, with the clearance each gives at Ø25 mm in micrometres
| Hole basis | Shaft basis | What it is called | Clearance at Ø25 mm (µm, negative is interference) | Class of fit | What it is for |
|---|---|---|---|---|---|
| H11/c11 | C11/h11 | Loose running | 110 to 370 | clearance | Wide commercial tolerances or allowances on external members: pivots, latches, parts affected by corrosion, heat or contamination. |
| H9/d9 | D9/h9 | Free running | 65 to 169 | clearance | Not for use where accuracy is essential, but good for large temperature variations, high running speeds or heavy journal pressures. |
| H8/f7 | F8/h7 | Close running | 20 to 74 | clearance | Running on accurate machines and accurate location at moderate speeds and journal pressures. |
| H7/g6 | G7/h6 | Sliding | 7 to 41 | clearance | Not intended to run freely, but to move and turn freely and locate accurately. |
| H7/h6 | H7/h6 | Locational clearance | 0 to 34 | clearance | A snug fit for locating stationary parts that can still be freely assembled and disassembled. |
| H7/k6 | K7/h6 | Locational transition | -15 to 19 | transition | Accurate location, a compromise between clearance and interference. |
| H7/n6 | N7/h6 | Locational transition | -28 to 6 | transition | More accurate location where greater interference is permissible. |
| H7/p6 | P7/h6 | Locational interference | -35 to -1 | interference | Rigidity and alignment with prime accuracy of location, but without special bore pressure requirements. |
| H7/s6 | S7/h6 | Medium drive | -48 to -14 | interference | Ordinary steel parts, or shrink fits on light sections; the tightest fit usable with cast iron. |
| H7/u6 | U7/h6 | Force | -61 to -27 | interference | Parts that can be highly stressed, or shrink fits where the heavy pressing forces required are impractical. |
Hole basis against shaft basis at Ø25 mm — where the identity holds, and where it quietly does not
| Hole basis | Its clearance range (µm) | Shaft basis | Its clearance range (µm) | Agreement | H7 with the shaft at grade 7 (µm) | The hole letter at grade 7 with h7 (µm) |
|---|---|---|---|---|---|---|
| H7/k6 | -15 to 19 | K7/h6 | -15 to 19 | identical | -23 to 19 | -15 to 27 |
| H7/m6 | -21 to 13 | M7/h6 | -21 to 13 | identical | -29 to 13 | -21 to 21 |
| H7/n6 | -28 to 6 | N7/h6 | -28 to 6 | identical | -36 to 6 | -28 to 14 |
| H7/p6 | -35 to -1 | P7/h6 | -35 to -1 | identical | -43 to -1 | -35 to 7 |
| H7/r6 | -41 to -7 | R7/h6 | -41 to -7 | identical | -49 to -7 | -41 to 1 |
| H7/s6 | -48 to -14 | S7/h6 | -48 to -14 | identical | -56 to -14 | -48 to -6 |
| H7/u6 | -61 to -27 | U7/h6 | -61 to -27 | identical | -69 to -27 | -61 to -19 |
Seven fits across all thirteen ISO 286 size steps, in micrometres of clearance
| Nominal size step (mm) | Geometric mean D (mm) | H7/g6 | H7/h6 | H7/n6 | H7/p6 | H7/s6 | H8/f7 | H11/c11 |
|---|---|---|---|---|---|---|---|---|
| over 1 to 3 | 1.73 | 2 to 18 | 0 to 16 | -10 to 6 | -12 to 4 | -20 to -4 | 6 to 30 | 60 to 180 |
| over 3 to 6 | 4.24 | 4 to 24 | 0 to 20 | -16 to 4 | -20 to 0 | -27 to -7 | 10 to 40 | 70 to 220 |
| over 6 to 10 | 7.75 | 5 to 29 | 0 to 24 | -19 to 5 | -24 to 0 | -32 to -8 | 13 to 50 | 80 to 260 |
| over 10 to 18 | 13.42 | 6 to 35 | 0 to 29 | -23 to 6 | -29 to 0 | -39 to -10 | 16 to 61 | 95 to 315 |
| over 18 to 30 | 23.24 | 7 to 41 | 0 to 34 | -28 to 6 | -35 to -1 | -48 to -14 | 20 to 74 | 110 to 370 |
| over 30 to 50 | 38.73 | 9 to 50 | 0 to 41 | -33 to 8 | -42 to -1 | -59 to -18 | 25 to 89 | 120 to 440 |
| over 50 to 80 | 63.25 | 10 to 59 | 0 to 49 | -39 to 10 | -51 to -2 | -72 to -23 | 30 to 106 | 140 to 520 |
| over 80 to 120 | 97.98 | 12 to 69 | 0 to 57 | -45 to 12 | -59 to -2 | -93 to -36 | 36 to 125 | 170 to 610 |
| over 120 to 180 | 146.97 | 14 to 79 | 0 to 65 | -52 to 13 | -68 to -3 | -125 to -60 | 43 to 146 | 210 to 710 |
| over 180 to 250 | 212.13 | 15 to 90 | 0 to 75 | -60 to 15 | -79 to -4 | -159 to -84 | 50 to 168 | 260 to 840 |
| over 250 to 315 | 280.62 | 17 to 101 | 0 to 84 | -66 to 18 | -88 to -4 | -202 to -118 | 56 to 189 | 330 to 970 |
| over 315 to 400 | 354.96 | 18 to 111 | 0 to 93 | -73 to 20 | -98 to -5 | -226 to -133 | 62 to 208 | 360 to 1,080 |
| over 400 to 500 | 447.21 | 20 to 123 | 0 to 103 | -80 to 23 | -108 to -5 | -272 to -169 | 68 to 228 | 440 to 1,240 |
The inch system’s fit classes, and why they are not a translation of these
| Family | What ANSI/ASME B4.1 says it is for | Does it map onto an ISO class? |
|---|---|---|
| RC1 to RC9, running and sliding | Intended to provide a similar running performance, with suitable lubrication allowance, throughout the range of sizes | No, and that sentence is the reason. An RC class holds a PERFORMANCE constant across the size range; an ISO letter holds a DEVIATION RULE constant. Those cannot both be true of the same ladder |
| LC1 to LC11, locational clearance | Intended for parts which are normally stationary, but which can be freely assembled or disassembled | Loosely comparable to the H/h and H/g families in intent, and not equal to any of them in numbers |
| LT1 to LT6, locational transition | A compromise between clearance and interference fits, for application where accuracy of location is important, but either a small amount of clearance or interference is permissible | The same idea as H7/js6, H7/k6 and H7/n6 — and note that the inch system needs six grades where the ISO preferred set uses two |
| LN1 to LN3, locational interference | Used where accuracy of location is of prime importance and for parts requiring rigidity and alignment with no special requirements for bore pressure | The same idea as H7/p6. The phrase to notice is “no special requirements for bore pressure”, which is the inch standard saying the same thing ISO says by making p’s minimum interference zero |
| FN1 to FN5, force and shrink | Force or shrink fits constitute a special type of interference fit, normally characterized by maintenance of constant bore pressures throughout the range of sizes | No. A constant bore pressure across the size range is a different construction from a constant deviation rule, and it is why an FN2 at half an inch and an FN2 at four inches are not the same ISO class |
The letter moves the band, the number widens it, and transition means transition
A fit is a range, and the code on the drawing is a rule for generating it. H7/g6 on a Ø25 feature is not “a bit of clearance”. It is 7 to 41 µm, because the hole may be anywhere in a 21 µm band and the shaft anywhere in a 13 µm one, and the two ends of that range are what the design has to work at. The capital letter and the small letter say where each band sits relative to the nominal size; the numbers are IT grades and say how wide each band is. Those are two independent decisions and people routinely conflate them — a tighter grade does not move the fit, it only narrows it, and if the clearance is wrong the letter is what needs changing.
ISO 286 is the one standard on this site whose values can be derived rather than copied, and this page derives them. The standard tolerance factor is i = 0.45·∛D + 0.001·D micrometres, evaluated at the geometric mean of the size step; IT7 is 16i, IT6 is 10i, and IT(n+5) is exactly ten times IT(n) from IT7 upward. Each letter’s fundamental deviation has its own rule: g is −2.5·D0.34, f is −5.5·D0.41, m is IT7 − IT6 exactly, n is 5·D0.34, and a hole letter’s is the shaft letter’s with the sign reversed plus a correction Δ. Every one of those was checked here against published tables before it was trusted, and the check is the trivial one that no shifted column survives: ES − EI must equal the IT grade. It rejected four separate fetches in the making of this page, including ISO 286-2’s own published preview. The dowel pin and hole calculator on this site uses the same machinery for the one fit a dowel pin is allowed.
Clearance, transition, interference — and transition really is both. If the smallest hole is still bigger than the biggest shaft, the fit is a clearance fit and it always comes apart. If the biggest hole is still smaller than the smallest shaft, it is an interference fit and it never goes together by hand. In between, the bands overlap and the SAME designation gives interference on one pair of parts and clearance on the next. H7/k6 and H7/n6 are both like this, and it is the most misread thing in the standard: you cannot promise an assembler that an H7/n6 will press together and you cannot promise it will not. This page reports the split as a percentage — computed exactly, as a ratio of areas over the two bands — and lets you put each part anywhere in its own band to see the actual clearance change sign.
Hole basis and shaft basis, and the identity that is narrower than people think. H7/n6 and N7/h6 give the same fit. That is exact — it holds at every size step and for every interference letter, which is 120 pairs checked here — but it is not a fact about the letters. It holds because Δ is exactly IT(n) − IT(n−1) and because the preferred pairs put grade n on the hole and grade n−1 on the shaft. Put both members at grade 7 and H7/n7 allows 6 µm of clearance where N7/h7 allows 14. Go below 3 mm, where the standard sets Δ to zero, and the identity fails even for the preferred pairs. Which basis to use is a manufacturing question: hole basis for general machining, because a reamer and a plug gauge fix the hole and the shaft is easy to turn to suit; shaft basis where the shaft is already fixed, by drawn bar, a bought ground shaft, a bearing journal or a standard spindle.
What this page is not. It gives limits, not consequences. For the contact pressure, torque capacity, hub stress and assembly temperature of an interference fit, the interference fit and shrink fit calculator does the Lamé solution and subtracts the surface roughness the faces lose on assembly. For what happens when the assembly is not at 20 °C, the thermal effect on fit calculator moves both bands. For the grade you can actually hold on a given machine, and what a grade costs, the IT grade tolerance calculator. And for the plug and ring gauges that accept or reject the parts, the go / no-go gauge tolerance calculator, which is where you find out how much of your band the gauges themselves eat.
Frequently asked questions
What clearance does an H7/g6 fit give?
A range, not a number. At Ø25 mm it is 7 to 41 µm of diametral clearance: the hole is 25.0000 to 25.0210 and the shaft is 24.9800 to 24.9930. The tight end is the smallest hole against the biggest shaft and the loose end is the other way round. The spread between them, 34 µm, is exactly IT7 + IT6 — the two grades added — and that identity is the quickest check that all four limits are right.
Is H7/n6 a press fit?
No. It is a transition fit, and at Ø25 it runs from 28 µm of interference to 6 µm of clearance. About nine in ten pairs will interfere and about one in ten will drop together, so it locates well and it carries no guaranteed torque. If you need torque from the fit itself you want s6 or u6, and you want the Lamé calculation that goes with them. If you only need the parts concentric, n6 is an excellent choice and the occasional loose one does no harm.
Does H7/n6 really give the same fit as N7/h6?
Yes, exactly, at every size from 3 mm to 500 mm — and it is worth knowing why, because the reason tells you when it stops. The hole letter’s fundamental deviation is the shaft letter’s with the sign reversed, plus a correction Δ equal to IT(n) − IT(n−1). Work the algebra through and the two clearance ranges coincide provided the hole is one grade coarser than the shaft, which every preferred pair is. Make both grade 7 and they part company: H7/n7 allows 6 µm of clearance and N7/h7 allows 14. Below 3 mm they part company too, because Δ is zero there.
Which basis should I use, hole or shaft?
Hole basis for general machining, and it is the default for a good manufacturing reason: a hole is made by a reamer, a boring bar or a broach and checked with a plug gauge, all of which come in fixed sizes, so it is much cheaper to keep the hole at H and vary the shaft. Shaft basis where the shaft is the fixed thing — drawn bar used as bought, a ground shaft to a standard diameter, a bearing journal, a commercial spindle — because then it is the bore that is easy to adjust. Do not mix bases within an assembly if you can help it; the tooling savings are the whole point and they disappear.
Can I get the inch RC, LC, LT, LN and FN classes here?
Their meanings, yes; their numbers, deliberately not. The five inch families and what ANSI/ASME B4.1 says each is for are in a table on this page, and so is the reason they do not map onto the ISO letters: B4.1’s own words are that an RC class is “intended to provide a similar running performance … throughout the range of sizes” and an FN class is “characterized by maintenance of constant bore pressures throughout the range of sizes”. Those hold a PERFORMANCE constant across the size range, where an ISO letter holds a deviation formula constant. No single ISO class tracks an RC or an FN class across the range, so any table claiming a one-to-one equivalence is wrong somewhere in the middle.
Why does a Ø30 and a Ø30.5 shaft get different limits for the same class?
Because ISO 286 quantises size into thirteen steps and 30 mm is the last size in one of them. The tolerance for a step is computed once, at the geometric mean of the step’s two limits, and applied to every size inside it. So h6 is 0/−13 µm up to and including Ø30 and 0/−16 µm from just above it. The series on this page plots the staircase. It is also a real trap on a drawing: a feature nominally at a step boundary can have its band change if somebody rounds the nominal size.
The two parts are made to the same nominal size — how can there be clearance at all?
Because the nominal size is a reference, not a target. Neither part is required to be 25.000 mm and neither will be. The letters say which side of 25 each band sits on and the grades say how wide each band is, and the fit is whatever the arithmetic gives. H/h is the interesting case: H’s lower deviation and h’s upper deviation are both exactly zero, so the tightest H7/h6 pair is metal-to-metal at precisely the nominal size and every other pair has clearance. It is the only fit in the preferred set that is guaranteed to assemble and guaranteed not to be loose.
Related calculators
References
- ISO 286-1:2010, Geometrical product specifications (GPS) — ISO code system for tolerances on linear sizes — Part 1: Basis of tolerances, deviations and fits. Cited by number; the standard is copyrighted and its tables are not reproduced here. What this page uses from it is its STRUCTURE, which is not a table: the standard tolerance factor i = 0.45·∛D + 0.001·D evaluated at the geometric mean of each nominal size step, the grade multipliers (IT5 = 7i, IT6 = 10i, IT7 = 16i, IT8 = 25i, IT9 = 40i, IT10 = 64i, IT11 = 100i and so on), the rule that IT(n+5) is ten times IT(n) from IT7 upward, the formulas for each letter’s fundamental deviation, and the Δ correction for hole letters J to ZC. Every one of those is checked here against a published table rather than trusted.
- ISO 286-2:2010, … Part 2: Tables of standard tolerance classes and limit deviations for holes and shafts. Cited, and its freely published preview was fetched and then DISCARDED. The extract returned an upper-deviation column belonging to a different letter and a lower-deviation column mixed from several size steps — g6 as −10/−68 where it is −6/−17, h6 as 0/−58 where it is 0/−11, js6 as ±29 where it is ±5.5. The identity ES − EI = IT rejected every row. Recorded because this is the second batch on this site to have the same document shift a column on it, and because it is the strongest possible argument for deriving the values instead.
- Machining Doctor. Tolerance charts by fundamental deviation letter (one page per letter, hole and shaft, stated as ISO 286-1:2010). The source for the fundamental deviations of c, d, e, f, g, k, m, n, p, r, s and u on this page, fetched one letter at a time so a shifted column could not hide in a wide table. Every row of every letter satisfies es − ei = IT(grade) exactly — 220 independent checks — and its N7 hole column reproduces the Δ = IT(n) − IT(n−1) rule at all thirteen size steps. Its u6 column also agrees with the interference-fit page already on this site at all sixteen steps that page covers, which cross-validates both.
- RoyMech. ISO 286-2 shaft tolerances and ISO hole limits and fits tables. The second source for the hole column: its whole 18–30 mm row (E6 to R7, twenty-four classes) is reproduced here exactly from the Δ rule, which is what proves Δ is IT(n) − IT(n−1) and not IT(n) − IT6. Its SHAFT table was fetched too and partly rejected: it returned a11’s deviations in the c11 row (−290/−470 against c11’s −95/−205 at 10–18 mm) and IT9 in the lower column of the d9 and e8 rows. Its upper column is right at every row and is used as the independent confirmation of d, e, f and g.
- AmesWeb. Preferred fits and tolerances charts (ISO and ANSI metric standards), attributing its descriptions to ISO 286-1 and ANSI B4.2-1978. The source for the ten preferred hole-basis fits, their shaft-basis twins and the description of each — loose running, free running, close running, sliding, locational clearance, two locational transitions, locational interference, medium drive and force. Cross-read against Wikipedia’s Engineering fit tables, whose wording is different and whose meaning agrees at all ten rows.
- MetricMech. ISO 286 fits chart: H7/g6 to H7/s6 tolerances. The independent worked check at Ø25 mm: H7 +21/0, g6 −7/−20, h6 0/−13, k6 +2/+15, n6 +15/+28, p6 +22/+35, s6 +35/+48, and the resulting clearance and interference ranges for all six fits. Every one is reproduced here from the derivation, which is the check that the derivation is the standard’s and not merely self-consistent.
- Wikipedia, Engineering fit. Used for two things and checked on both. Its c11 and H11 columns are the second source for the loose-running fit, and one row of them is wrong: it repeats the 10–18 mm lower deviation of c11 (−205) on the 6–10 mm row, where ES − EI = IT11 gives −170. Its worked clearances at Ø50 for H8/f7 (+0.025 to +0.089), H7/k6 (+0.023 to −0.018) and H7/p6 (−0.001 to −0.042) are reproduced here exactly and are three of the page’s assertions.
- Firat Bearing. ISO 286 — IT tolerance grades reference. The source for the IT01 to IT4 and IT12 to IT16 rows. The IT12 to IT16 rows turned out to be EXACTLY ten times IT7 to IT11 at all sixty-five cells, which is ISO 286-1’s own rule, so IT17 and IT18 are derived from it here rather than copied. The IT2, IT3 and IT4 rows satisfy the standard’s other construction rule — a geometric progression from IT1 to IT5 — at twelve of the thirteen size steps.
- ANSI/ASME B4.1-1967 (R1994), Preferred Limits and Fits for Cylindrical Parts, and ANSI B4.2-1978 for its metric twin. The source for the five inch fit families and, crucially, for their own statements of intent: the RC classes are “intended to provide a similar running performance, with suitable lubrication allowance, throughout the range of sizes” and the FN classes are “normally characterized by maintenance of constant bore pressures throughout the range of sizes”. Those two sentences are why an inch class cannot map onto an ISO letter: the inch classes hold a PERFORMANCE constant across the size range and the ISO letters hold a DEVIATION RULE constant, and the two cannot both be true of the same ladder. Descriptions quoted via AmesWeb’s published ANSI preferred-fits charts; the numeric limit tables were not reproduced.
