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Hole and Shaft Fit Calculator (ISO 286)
Choose a nominal size and the hole and shaft tolerance classes, such as H7/g6, H7/k6 or H7/u6. The calculator derives the IT grades and fundamental deviations from the ISO 286-1 formulas and reports limits, maximum and minimum clearance, and the fit type.
ISO 286 hole and shaft fit calculator
Formula-derived values, rounded to 1 µm. Supports 3–500 mm and grades IT5–IT11. Confirm critical limits against ISO 286-2.
| Part | Upper / lower deviation | Max / min size |
|---|---|---|
| Hole | +21 / 0 µm | 25.021 / 25.000 mm (0.98508 / 0.98425 in) |
| Shaft | -7 / -20 µm | 24.993 / 24.980 mm (0.98398 / 0.98346 in) |
Negative clearance means interference.
| Step | Formula | Value |
|---|---|---|
| Size step and geometric mean D | 18 < size ≤ 30 mm; D = √(18·30) | 23.2379 mm |
| Standard tolerance factor | i = 0.45·∛D + 0.001·D | 1.3074 µm |
| Hole tolerance grade | IT7 (rounded to 1 µm) | 21 µm |
| Hole deviations | es = 0; EI = −es = 0; ES = EI + IT7 | +21 / 0 µm |
| Shaft tolerance grade | IT6 (rounded to 1 µm) | 13 µm |
| Shaft deviations | es = −2.5·D^0.34, D = 23.238; ei = es − IT6 | -7 / -20 µm |
| Maximum clearance | ES − ei = 21 − (-20) | 41 µm |
| Minimum clearance | EI − es = 0 − (-7) | 7 µm |
Formulas used
- Geometric mean of the size step
- D = √(D₁·D₂) (mm)
- Standard tolerance factor
- i = 0.45·∛D + 0.001·D (µm)
- Standard tolerance grades
- IT5 = 7i, IT6 = 10i, IT7 = 16i, IT8 = 25i, IT9 = 40i, IT10 = 64i, IT11 = 100i
- Shafts d, e, f, g (upper deviation es)
- d: −16·D^0.44 e: −11·D^0.41 f: −5.5·D^0.41 g: −2.5·D^0.34 h: 0
- Shafts k, m, n, s, u (lower deviation ei)
- k: +0.6·∛D (IT4–IT7), 0 otherwise m: IT7 − IT6 n: +5·D^0.34 s: IT7 + 0.4·D (D > 50) u: IT7 + D
- Holes, general rule
- EI = −es (D–H); ES = −ei (S, U above IT7)
- Holes, special rule
- ES = −ei + Δ, Δ = ITn − IT(n−1) (K, M, N to IT8; S, U to IT7)
- Fit
- max clearance = ES − ei; min clearance = EI − es (negative = interference)
Assumptions and limits
- Sizes above 3 mm up to 500 mm. Inch input is converted at exactly 25.4 mm per inch.
- Each IT grade and fundamental deviation is rounded to the nearest micrometre. ISO 286-2 tables apply the standard's own rounding, so a few values differ by about 1 µm. For acceptance, the tables govern.
- Supported classes: holes D, E, F, G, H, JS, K, M, N, S, U and shafts d, e, f, g, h, js, k, m, n, s, u, grades IT5–IT11. K, M, S and U (and k, m, s, u) are limited to IT8 and finer, and the special-rule holes start at IT6.
- u/U is supported above 18 mm and s/S above 50 mm, using the intermediate size steps. Letters whose standard values are ranges or tables rather than a single formula (j, p, r, and s up to 50 mm) are not offered.
- Limits apply at the reference temperature of 20 °C. Thermal expansion and form errors are not included.
Worked example
A 25 mm shaft must slide in its bore with a small, guaranteed clearance. The fit chosen is H7/g6, a common sliding fit.
| Step | Formula | Value |
|---|---|---|
| Size step and geometric mean D | 18 < size ≤ 30 mm; D = √(18·30) | 23.2379 mm |
| Standard tolerance factor | i = 0.45·∛D + 0.001·D | 1.3074 µm |
| Hole tolerance grade | IT7 (rounded to 1 µm) | 21 µm |
| Hole deviations | es = 0; EI = −es = 0; ES = EI + IT7 | +21 / 0 µm |
| Shaft tolerance grade | IT6 (rounded to 1 µm) | 13 µm |
| Shaft deviations | es = −2.5·D^0.34, D = 23.238; ei = es − IT6 | -7 / -20 µm |
| Maximum clearance | ES − ei = 21 − (-20) | 41 µm |
| Minimum clearance | EI − es = 0 − (-7) | 7 µm |
Result: H7/g6 at 25 mm is a clearance fit: clearance ranges from 7 µm to 41 µm.
How ISO 286 fits work
Tolerance classes: letter plus grade
A tolerance class such as H7 or g6 combines a fundamental deviation, the letter, with a standard tolerance grade, the number. The letter places the tolerance zone relative to the nominal size; the grade sets its width.
Capital letters are holes and lower-case letters are shafts. H holes and h shafts have a deviation of zero at their minimum or maximum material limit respectively.
Hole-basis fits
Most designs use the hole-basis system: the hole is H and the shaft letter sets the fit. a–h shafts give clearance, js–n usually give transition fits, and p onwards give interference. The hole-basis system keeps reamers and plug gauges to standard sizes.
Reading the result
Maximum clearance occurs with the largest hole and the smallest shaft; minimum clearance with the smallest hole and the largest shaft. If both are positive the fit always clears. If both are negative it always interferes. If the signs differ it is a transition fit, and an assembly may be either.
Why compute instead of looking it up?
ISO 286-1 defines the system with formulas, and ISO 286-2 tabulates the rounded results. Showing the formula and every intermediate value lets you see why a limit is what it is. Confirm critical values against your licensed copy of ISO 286-2.
Common mistakes
- Mixing up hole and shaft letters. G7 (hole) and g7 (shaft) sit on opposite sides of the zero line. Case matters.
- Using the wrong size step. A diameter of exactly 30 mm belongs to the 18–30 mm step, not 30–50 mm. Steps include their upper boundary.
- Ignoring the special rule for K, M and N holes. These holes are not mirror images of the k, m and n shafts at fine grades. The Δ correction keeps hole-basis and shaft-basis fits equivalent.
- Forgetting temperature and surface finish. Interference fits assembled with heating or cooling, or rough surfaces that smooth out on assembly, change the effective fit.
- Treating computed values as the table. This tool shows formula-derived values. Where an inspection decision depends on a micrometre, use the ISO 286-2 tables.
Frequently asked questions
What are the limits of H7/g6 at 25 mm?
The hole is +21 / 0 µm and the shaft is −7 / −20 µm, so clearance ranges from 7 µm to 41 µm. This is a close sliding fit.
What is the difference between clearance, transition and interference fits?
A clearance fit always leaves a gap, an interference fit always needs force or heat to assemble, and a transition fit may do either depending on the actual sizes of the parts.
Why do some results differ from my ISO 286 table by 1 µm?
The standard's tables were produced from the same formulas but rounded with ISO 286's own rules and, for some cells, adjusted. This calculator rounds to the nearest micrometre and shows the unrounded working.
Why are p, r and j fits not available?
The standard does not define them with a single closed-form formula: p is given as IT7 plus a range, r as a mean of p and s, and j only as table values. Rather than guess, the calculator leaves them out.
Can I enter the size in inches?
Yes. Select inches and the size is converted at 25.4 mm per inch. ISO 286 itself is metric, so limits are reported in micrometres and millimetres, with inch equivalents for the limits.
Sources
- ISO 286-1:2010, Geometrical product specifications (GPS) — ISO code system for tolerances on linear sizes — Part 1: Basis of tolerances, deviations and fits.
- ISO 286-2:2010, Part 2: Tables of standard tolerance classes and limit deviations for holes and shafts — the authoritative tabulated values.
Results are computed in your browser from the published formulas named above. They are an engineering aid, not a substitute for the governing standard, your drawing, or your customer's requirements.