Shaft/Hole Tolerance

Calculate the upper deviation, lower deviation, and limit sizes for shafts and holes in accordance with JIS B 0401-1:2016 or ISO 286-1:2010.

Inputs

D

Nominal Size

IT

IT Grade

\text{Zone}

Fundamental Zone

Formula Interpretation

Common Tolerance Zones for Holes

Common Tolerance Zones for Shafts

Core Relation

\Delta = \Delta_0 \pm IT

First find IT-size range and deviation-size range from nominal size, then compute the unknown deviation from the known side and IT value.

Shaft a~h (known es)

a\sim h:\; es\;\Rightarrow\;ei=es-IT

For shaft zones c/d/e/f/g/h, upper deviation es is known; lower deviation ei = es - IT.

Shaft k/m/p (known ei)

k,m,p:\; ei\;\Rightarrow\;es=ei+IT

For shaft zones k/m/p, lower deviation ei is known; upper deviation es = ei + IT.

Hole C~H (known EI)

C\sim H:\; EI\;\Rightarrow\;ES=EI+IT

For hole zones C/D/E/F/G/H, lower deviation EI is known; upper deviation ES = EI + IT.

Hole M/P (known ES)

M,P:\; ES\;\Rightarrow\;EI=ES-IT

For hole zones M/P, upper deviation ES is known; lower deviation EI = ES - IT.

Knowledge Points

Size ranges come from different tables

IT-grade table and fundamental-deviation table do not share identical size intervals, so they must be matched independently.

Deviation unit vs size unit

Fundamental deviations and IT values are usually in μm, while limit sizes are in mm. Conversion: 1000 μm = 1 mm.

Band position and width

The letter defines tolerance zone position relative to the zero line; IT grade defines tolerance width. Both are required for final upper/lower deviations.

Example

Given shaft code h6 and nominal size D = 20 mm, find upper deviation, lower deviation, and limit sizes.

Step 1 — Look up known deviation and IT value

h6,\;D=20\text{ mm}:\; es=0\,\mu m,\;IT6=13\,\mu m

Step 2 — Compute upper/lower deviations

\Delta_{upper}=es=0\,\mu m,\;\Delta_{lower}=es-IT6=0-13=-13\,\mu m

Conclusion: h6 at 20 mm gives upper deviation 0 μm and lower deviation -13 μm; limit sizes are 20.000 mm and 19.987 mm.

Extended Knowledge

•In fit design, hole-basis (e.g., H7/g6) and shaft-basis (e.g., h6/H7) systems are commonly used to simplify tolerance chains.
•At the same nominal size, larger IT grades mean wider tolerance zones: easier manufacturing but lower fit precision.
•For practical fit checks, also evaluate max clearance/min interference, plus thermal and assembly factors.