Machining, Welding & Metal Fabrication CNC Layout, Setup & Metrology ISO 286-1 / ISO 286-2 (hole-basis limits and fits)

ISO Hole & Shaft Fit Tolerance Calculator

A drawing that says ø40 H7/g6 is making four separate statements about size, and this calculator unpacks all of them: the upper and lower limit of the hole, the upper and lower limit of the shaft, the tightest and loosest the assembled pair can be, and whether that makes it a clearance, transition or interference fit. It works on the hole-basis system of ISO 286 — hole letter H or JS with any shaft letter from d to s in grades IT5 to IT11 — using the standard tolerance and fundamental deviation values, not an approximation of them.

Calculator

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Inputs this calculator takes, with typical values
InputWhat to enterExample
Nominal diameterThe basic size shared by the hole and the shaft, from 1 mm to 500 mm.40 mm
Hole tolerance letterH is the hole-basis standard; JS places the tolerance equally either side of nominal.H — lower limit at basic size (hole basis)
Hole IT gradeThe number after the letter: H7 is grade 7. Smaller numbers are tighter.IT7
Shaft tolerance letterLower-case letters are shafts; letters before h give clearance, letters after h give interference.g — sliding
Shaft IT gradeShafts are normally specified one grade tighter than the mating hole.IT6

It returns

  • Maximum clearance — Loosest assembly. A negative value means the pair is interfering even at its loosest.
  • Minimum clearance — Tightest assembly. A negative value is an interference.
  • Hole upper limit
  • Hole lower limit
  • Shaft upper limit
  • Shaft lower limit
  • Hole tolerance band
  • Shaft tolerance band

The formula

Cmax=ESei,Cmin=EIes
i=0.45D3+0.001D

In plain text: Cmax = ES − ei; Cmin = EI − es

  • ESUpper deviation of the hole from basic size (µm)
  • EILower deviation of the hole from basic size (µm)
  • esUpper deviation of the shaft from basic size (µm)
  • eiLower deviation of the shaft from basic size (µm)
  • CmaxMaximum clearance; negative values are interference (µm)

Upper-case deviations belong to holes and lower-case to shafts, which is the whole reason ISO 286 writes hole letters in capitals. The IT grade fixes the width of each band and the letter fixes where that band sits relative to the basic size.

Updated Category CNC Layout, Setup & Metrology Verified against published test cases Reading time 12 min

How to read a symbol like H7/g6

Each half of the symbol is a letter and a number, and they do different jobs. The number is the IT grade, and it sets how wide the tolerance band is — IT7 on a 40 mm feature is 25 µm wide, IT6 is 16 µm, IT11 is 160 µm. The letter is the fundamental deviation, and it sets where that band sits relative to the basic size. Capital letters are holes, lower-case letters are shafts.

H is special: it places the lower limit exactly on the basic size, so an H7 hole at ø40 runs from 40.000 to 40.025 and never goes undersize. That is what makes it the basis of the hole-basis system, which nearly all general engineering uses. You machine one standard hole size, usually with a standard reamer or boring tool, and vary the shaft to change the fit. Only where the shaft is a bought-in standard size — bearing journals, drawn bar, hydraulic rod — does the shaft-basis system with an h shaft make more sense.

Shaft letters run alphabetically from a to zc, and h is the pivot. Letters before h place the whole shaft band below basic size, so the fit is always clearance and the gap grows as you move backwards through the alphabet: g is a close sliding fit, f a running fit, d a loose running fit. Letters after h push the band upward, so k, m and n give transition fits that may go either way, and p, r and s give interference that always requires force.

The four numbers and where they come from

Every fit reduces to four deviations. The hole has an upper deviation ES and a lower deviation EI; the shaft has an upper deviation es and a lower deviation ei. All four are measured in micrometres from the basic size, and all four can be positive, negative or zero.

Maximum clearance occurs when the hole is at its largest and the shaft at its smallest: Cmax = ES − ei. Minimum clearance occurs the other way round: Cmin = EI − es. If Cmin is zero or positive the fit is a clearance fit; if Cmax is zero or negative it is an interference fit; anything in between is a transition fit, where two conforming parts may or may not press together depending on where each one landed inside its band.

The IT grade widths are not arbitrary. ISO 286 builds them from a standard tolerance unit i = 0.45 D1/3 + 0.001 D micrometres, with D the geometric mean of the size range, and then assigns each grade a multiple: IT5 = 7i, IT6 = 10i, IT7 = 16i, IT8 = 25i, and so on in a roughly geometric series, with the results rounded to preferred numbers. The cube-root term reflects manufacturing reality — holding a tolerance gets harder as a part gets bigger, but not in proportion. Below 3 mm the formula stops fitting and the standard simply tabulates the values, which is why the small-size numbers look slightly out of pattern.

The letters have their own formulas. Shaft f is es = −5.5 D0.41, shaft g is −2.5 D0.34, shaft n is +5 D0.34. Those constants are what make each letter behave consistently across sizes: an f shaft leaves roughly the same proportional running clearance at ø10 as at ø200.

Worked example: ø40 H7/g6

A 40 mm shaft that must slide freely in a bore but with almost no play — a gauge plunger, a locating pin, a lightly loaded plain bearing.

  1. Find the size range. 40 mm falls in the 30–50 mm band of ISO 286.
  2. Hole band. IT7 in that range is 25 µm. H puts EI = 0, so ES = +25 µm and the hole is 40.000 / 40.025 mm.
  3. Shaft band. IT6 in that range is 16 µm. The fundamental deviation of g at 30–50 mm is es = −9 µm, so ei = −9 − 16 = −25 µm and the shaft is 39.975 / 39.991 mm.
  4. Maximum clearance. ES − ei = 25 − (−25) = 50 µm = 0.050 mm.
  5. Minimum clearance. EI − es = 0 − (−9) = 9 µm = 0.009 mm.
  6. Classification. The minimum is positive, so this is a clearance fit throughout, running from 9 to 50 µm.

Compare that with ø40 H7/p6, keeping the hole identical. The p deviation at 30–50 mm is ei = +26 µm, so the shaft becomes 40.026 / 40.042 mm. Maximum clearance is 25 − 26 = −1 µm and minimum clearance is 0 − 42 = −42 µm: both negative, so it is an interference fit of 1 to 42 µm. A single letter change turned a part you can push together by hand into one that needs a press or a temperature difference.

Choosing a fit, and reading the one you have

Start from function. If the parts must move relative to each other, you need clearance, and the amount depends on speed, load and lubrication: H7/g6 for a sliding location with minimal play, H7/f7 or H8/f7 for a running fit, H9/d9 or H11/d11 where alignment is loose and dirt is expected. If the parts must locate accurately but be separable, a transition fit — H7/k6 or H7/n6 — centres the part with almost no play and still allows assembly with a mallet or a light press. If the joint must transmit torque by friction alone, you need interference: H7/p6 for a light press, H7/s6 for a shrink fit on a hub or a gear.

Then check the grade against how you will make the part. IT6 on a shaft means grinding or very good turning; IT7 in a hole means reaming, boring or honing; IT9 and above are ordinary turning and milling. Specifying IT5 where IT8 would work is one of the more expensive habits in mechanical design, because cost climbs sharply as the band narrows and inspection gets harder at the same rate.

Two practical checks are worth making on any interference fit. The first is whether the outer member can survive the hoop stress; ISO 286 tells you the dimensions and says nothing about stress. The second is what happens at temperature, because a steel hub on a steel shaft holds its interference while an aluminium hub on a steel shaft loses it as the assembly warms. Neither is captured by the fit symbol.

Finally, remember that the symbol is a size specification, not a form specification. A hole can be perfectly within its H7 limits and still be bell-mouthed, tapered or lobed, and any of those will change how the assembly behaves. Where form matters, it needs its own geometric tolerance on the drawing, and the envelope requirement or a maximum-material condition is what ties size and form together.

Common hole-basis fits at ø40 mm

All values in millimetres, computed from the ISO 286 tolerance and deviation tables for the 30–50 mm size range. Negative clearance is interference.
FitHole limitsShaft limitsClearance rangeCharacter
H11/d1140.000 / 40.16039.760 / 39.920+0.080 to +0.400Loose running
H9/d940.000 / 40.06239.858 / 39.920+0.080 to +0.204Free running
H8/f740.000 / 40.03939.950 / 39.975+0.025 to +0.089Close running
H7/g640.000 / 40.02539.975 / 39.991+0.009 to +0.050Sliding
H7/h640.000 / 40.02539.984 / 40.0000.000 to +0.041Locational clearance
H7/k640.000 / 40.02540.002 / 40.018−0.018 to +0.023Transition
H7/n640.000 / 40.02540.017 / 40.033−0.033 to +0.008Tight transition
H7/p640.000 / 40.02540.026 / 40.042−0.042 to −0.001Light press
H7/s640.000 / 40.02540.043 / 40.059−0.059 to −0.018Shrink / drive

The hole is identical in five of these nine rows. That is the entire point of the hole-basis system: one reamer, one bore programme, and the fit is changed on the shaft.

ISO 286 standard tolerance grades, IT5 to IT11, in micrometres

Width of the tolerance band for each grade and size range. The value is the same whether the feature is a hole or a shaft; only the position differs.
Nominal size (mm)IT5IT6IT7IT8IT9IT10IT11
over 3 to 6581218304875
over 6 to 10691522365890
over 10 to 1881118274370110
over 18 to 3091321335284130
over 30 to 501116253962100160
over 50 to 801319304674120190
over 80 to 1201522355487140220
over 120 to 18018254063100160250
over 180 to 25020294672115185290

Each grade is roughly 1.6 times the one below it, so IT7 is about 2.5 times IT5 and IT11 is about 6.4 times IT7. That geometric spacing is deliberate and matches the way process capability improves.

What the fit symbol does not tell you

  • Nothing about form. A bore can be inside its H7 limits and still be oval, tapered or bell-mouthed. Roundness, cylindricity and straightness need their own geometric tolerances.
  • Nothing about surface finish. A press fit into a rough bore loses interference as the asperities flatten during assembly, so an interference fit needs a specified surface roughness to behave as calculated.
  • Nothing about temperature. The limits are defined at 20 °C. Dissimilar materials change the effective interference as the assembly heats or cools.
  • Nothing about stress. An interference fit generates hoop stress in the outer part and contact pressure between the two; those are a Lamé thick-cylinder calculation, not a tolerance one.
  • Nothing about how you measure it. A 25 µm band needs an instrument with resolution well under 5 µm and a controlled part temperature; a vernier caliper cannot verify an IT7 bore.
  • Nothing about assembly force. Two interference fits with the same interference need very different forces depending on engagement length, materials and lubrication.

Where the ISO system sits alongside the alternatives

ISO 286 is the international limits-and-fits system and is what metric drawings use worldwide. The ANSI/ASME B4.1 inch system covers the same ground with a different vocabulary — RC for running and sliding clearance, LC and LT for locational clearance and transition, FN for force and shrink fits — and ANSI B4.2 restates the ISO system in preferred metric fits. The concepts translate directly: an RC4 is close in spirit to H8/f7, an FN2 to H7/s6. What does not translate is the numbers, so never mix a class from one system with a limit from the other.

Getting a part to an IT7 hole is a process decision as much as a specification. Drilling alone will not do it — a drilled hole is oversize, out of round and not straight — so the sequence is drill, then bore or ream, and the drilling speed and feed calculator handles the first step. Where the hole is threaded rather than fitted, a different rule applies entirely, and the tap drill size calculator sizes it from the thread rather than from a fit class.

Fits also determine how a joint carries load. A press fit transmits torque by friction, which is why gears and pulleys are often mounted H7/s6 with no key at all; a clearance fit relies on a fastener's clamp load instead, and the bolt torque calculator works out what that clamp load actually is. Where a shaft carries a belt or gear drive, the mounting fit and the drive geometry are usually specified together — see the gear ratio calculator for the drive side of that decision.

Frequently asked questions

What does H7/g6 mean?

It is a hole-basis sliding fit. H7 means the hole's lower limit sits exactly on the basic size with a grade 7 tolerance above it; g6 means the shaft's band sits slightly below basic size with a grade 6 tolerance. At ø40 that gives a hole of 40.000/40.025 and a shaft of 39.975/39.991, so the parts always assemble with between 0.009 and 0.050 mm of clearance — free to slide, but with very little play.

What is the difference between a clearance, transition and interference fit?

It depends on the sign of the two extreme cases. A clearance fit has a positive minimum clearance, so the shaft is always smaller than the hole. An interference fit has a negative maximum clearance, so the shaft is always larger. A transition fit straddles zero: two parts that both conform to the drawing may go together with a small gap or need a light press, depending where each one landed within its band.

Which fit should I use for a press fit?

H7/p6 for a light press that can still be dismantled, H7/r6 for a medium drive fit, and H7/s6 for a shrink or heavy drive fit that will transmit torque by friction alone. At ø40 those give 0.001–0.042 mm, 0.009–0.050 mm and 0.018–0.059 mm of interference respectively. Check the hoop stress in the outer part separately: the fit symbol specifies dimensions, not whether the hub survives being pressed on.

What does the IT number actually control?

The width of the tolerance band, and nothing else. IT7 on a 40 mm feature is 25 µm wide whether it is a hole or a shaft and whatever letter goes with it. The letter controls where that 25 µm sits relative to the basic size. Grades are spaced roughly geometrically — each is about 1.6 times the one below — so IT6 to IT7 is a step of about 60% in permitted variation.

Why is the shaft usually one grade tighter than the hole?

Because an external diameter is easier to produce and to measure than an internal one. Turning and grinding a shaft to IT6 is routine; holding IT6 in a bore requires honing or very careful boring, and gauging it requires bore gauges rather than a micrometer. Pairing H7 with a grade 6 shaft puts the tighter half of the work where it is cheaper, which is why H7/g6, H7/k6 and H7/p6 are all written that way.

Is hole basis or shaft basis better?

Hole basis for nearly all general engineering, because you can change the fit by changing the shaft while keeping one standard hole size — and holes are made with fixed-size tooling such as reamers, while shafts are made by turning to whatever diameter you want. Shaft basis makes sense only when the shaft is a bought-in standard size you cannot alter: drawn bar, hydraulic cylinder rod, or a shaft carrying several different components along its length.

Does an ISO fit account for surface roughness?

No, and it matters most on interference fits. The limits describe the measured size, but the peaks of a rough surface flatten during pressing, so some of the calculated interference is lost as the asperities collapse. That is why interference fits usually carry a surface roughness requirement as well, and why a bore finished at Ra 1.6 µm will hold less than one finished at Ra 0.4 µm at the same nominal interference.

What temperature do ISO 286 limits assume?

20 °C, which is the international reference temperature for dimensional metrology. A part measured warm reads large, and on a 500 mm steel dimension a 5 °C error is about 30 µm — enough to fail an IT7 inspection entirely. It also means an assembly of dissimilar materials does not keep the fit it was designed with: an aluminium hub on a steel shaft loses interference as it heats, while a steel hub on the same shaft holds it.

References

  • ISO 286-1 — Geometrical product specifications (GPS): ISO code system for tolerances on linear sizes, Part 1: Basis of tolerances, deviations and fits — International Organization for Standardization
  • ISO 286-2 — Tables of standard tolerance classes and limit deviations for holes and shafts — International Organization for Standardization
  • Machinery's Handbook, 31st Edition — Preferred Metric Limits and Fits — Industrial Press
  • ASME B4.2 — Preferred Metric Limits and Fits — American Society of Mechanical Engineers