TAHA Engineering Toolsby TAHA Knowledge Lab

Metrology & Quality

Limits of Size & Tolerance Calculator

Maximum and minimum limits, tolerance and mean size from nominal size and deviations.

Inputs

Calculate from
A zero line representing the nominal size with a shaded tolerance zone below it, bounded by the upper and lower limits.nominal size (zero line)tolerance zoneupper dev.lower dev.Tupper limit = nominal + upper deviation
The tolerance zone lies between the lower and upper limits of size. Deviations are measured from the nominal size (zero line); here a shaft whose zone lies below nominal, as for g6. Diagram not to scale.

Signed: + above nominal, − below. For a hole it is written ES, for a shaft es. From the drawing or ISO 286-2 tables.

Signed. For a hole EI, for a shaft ei. Must be lower than the upper deviation.

Result

Upper limit of size (maximum)
25.021
Lower limit of size (minimum)
25
Tolerance (max − min)
21
Mean size (middle of the tolerance)
25.0105
Maximum material size
25
Working
Upper limit = 25 + (21 µm) = 25.021 mm Lower limit = 25 + (0 µm) = 25 mm Tolerance = 21 − (0) = 21 µm

An acceptable part measures between 25 mm and 25.021 mm — a tolerance of 21 µm. Its maximum material size is 25 mm.

Educational estimate — check the assumptions below.

About this calculator

No part can be made to an exact size, so a drawing gives a nominal size and the amount the real size may differ from it. The two limits of size are the largest and smallest acceptable sizes; the difference between them is the tolerance. This calculator turns a nominal size and its deviations — such as 25 +0.021/0 or 50 ± 0.05 — into the limits you measure against.

Deviations are signed: a hole toleranced 25 H7 has deviations +21 µm and 0 µm; a shaft 25 g6 has −7 µm and −20 µm. The deviations for ISO fit codes come from the tables in ISO 286-2 (or the drawing); they are not built in.

Formula

Upper and lower deviation

Upper limit = N + upper deviation    Lower limit = N + lower deviation

Tolerance = upper limit − lower limit = upper deviation − lower deviation

N = nominal size. Hole deviations are written ES (upper) and EI (lower); shaft deviations es and ei. Maximum material size = lower limit for a hole, upper limit for a shaft.

Equal ± tolerance

Limits = N ± t    Tolerance = 2t

N = nominal size, t = equal tolerance either side (a bilateral tolerance).

Worked example

  • Hole 25 H7 (ES = +21 µm, EI = 0): limits 25.021 mm and 25.000 mm; tolerance 21 µm; mean size 25.0105 mm.
  • Shaft 25 g6 (es = −7 µm, ei = −20 µm): limits 24.993 mm and 24.980 mm; tolerance 13 µm.
  • 50 ± 0.05 mm: limits 50.05 and 49.95 mm; tolerance 0.10 mm.

Assumptions and limitations

  • Limits are calculated from the values you enter. The calculator does not look up ISO 286 fit codes; take deviations from ISO 286-2 or the drawing.
  • Sizes are at the standard reference temperature of 20 °C (ISO 1). Measure parts at, or correct them to, 20 °C for close tolerances.
  • Form, orientation and surface texture requirements (GD&T) are separate and not checked here.

References

  • ISO 286-1: Geometrical product specifications — ISO code system for tolerances on linear sizes (terms: nominal size, deviations, tolerance).
  • ISO 1: standard reference temperature 20 °C.