Standard Spur Gear Size
Compute pitch, addendum, base diameters, centre distance, circular & base pitch, ratio, recommended face width and whole depth for standard spur gears.
Inputs
Formula
Fundamentals
Spur gears are the most common type, with teeth parallel to the axis, used for constant-speed drive between parallel shafts.
Ratio $i=Z_2/Z_1$; contact ratio $\varepsilon$ (≈1.4–2.5 for standard) shows how many teeth mesh at once; center distance $a=m(z_1+z_2)/2$.
History
Spur gears are the oldest gear form, seen in ancient Greece and medieval water mills; the Industrial Revolution made them the backbone of mechanical drives with machine tools and steam power.
Engineering applications
Used in garage doors, conveyors, pumps, appliances and general-purpose gearmotors for simple, reliable parallel-shaft, low-to-medium speed drives.
Glossary
| Contact ratio $\varepsilon$ | Number of teeth in mesh at once; higher = smoother. |
| Face width $b$ | Gear width along the axis, affecting load sharing. |
| Pitch circle | Instant rolling circle; coincides with pitch circle at standard mounting. |
How to use
- Fill in Module m, Pinion teeth Z₁, Gear teeth Z₂, Pressure angle α in the Inputs section (watch the unit on each field).
- Click Calculate; the tool evaluates the formula shown above.
- Read Pinion pitch d₁, Pinion addendum da₁, Pinion base db₁, Centre distance a, Circular pitch p, Base pitch pb in the results area.
Formula · Worked Example · Knowledge
Formula
Worked Example
Key Points
- Base circle $d_b$ sets the involute profile.
- Face width $b$ is usually (6–12)m.
- Circular pitch $p=\pi m$, base pitch $p_b=p\cos\alpha$.
Parameters
Inputs
| Parameter | Symbol | Unit | Default |
|---|---|---|---|
| Module m (mm) | m | mm | 2 |
| Pinion teeth Z₁ | Z1 | 20 | |
| Gear teeth Z₂ | Z2 | 40 | |
| Pressure angle α (°) | alpha | ° | 20 |
Outputs
| Result | Symbol | Unit |
|---|---|---|
| Pinion pitch d₁ | d1 | mm |
| Pinion addendum da₁ | da1 | mm |
| Pinion base db₁ | db1 | mm |
| Centre distance a | a | mm |
| Circular pitch p | p | mm |
| Base pitch pb | pb | mm |
| Min face width b_min | bmin | mm |
| Max face width b_max | bmax | mm |
| Whole depth h | h | mm |
Applications
- Common engineering use cases