Diameters
in- Pitch diameterd
- 2.000
- Outside diameterda
- 2.200
- Root diameterdf
- 1.750
- Base diameterdb
- 1.879
Spur gears
Spur gear calculator
Diametral pitch (or module) and number of teeth: every dimension to cut and inspect the gear, the gear pair and the DXF of the profile.
Gear data
Spur, involute, ISO 53 basic rack.
1 System
3 Pressure angle
Mating gear (optional)
Units
Profile generated by simulating generation with the ISO 53 rack (true involute, root fillet and undercut), in mm. REFERENCE layer with the pitch circle.
Gear DP 10 · N20
Spur, α = 20° · ISO 53 · equivalent m 2.540 mm
Inspection with a caliper
in- Span measurement over 3 teethW3
- 0.766
- Chordal tooth thicknesssc
- 0.157
- Chordal addendum (for gear tooth caliper)hc
- 0.103
Wk: span 3 teeth with the flat jaws of the caliper. Chordal thickness is measured with a gear tooth caliper set to the chordal addendum hc.
Tooth
in- Circular pitchp
- 0.314
- Tooth thickness at pitch circle (arc)s
- 0.157
- Whole depthh
- 0.225
- Addendum / dedendumha/hf
- 0.100 / 0.125
- Bottom clearancec
- 0.025
Stock material (steel)
- Cut Ø
- 2.318 in
- Cut length / thickness
- 0.906 in
- Stock weight
- 0.49 kg
- Approx. finished weight
- 0.28 kg
Check
- No undercut at the tooth root.
ISO 53 / DIN 867 formulas for external spur gears. Check tolerances and backlash for your application.
Frequently asked questions
How do you calculate the outside diameter of a spur gear?
In diametral pitch: pitch diameter = N ÷ DP and outside diameter = (N + 2) ÷ DP. A 10 DP gear with 20 teeth has a 2.000" pitch diameter and a 2.200" outside diameter. In metric: d = m·N and da = m·(N + 2).
How do I find the diametral pitch of a gear I have?
Measure the outside diameter and count the teeth: DP ≈ (N + 2) ÷ OD (in inches). Round to the nearest standard DP (4, 5, 6, 8, 10, 12, 16…). If it does not land on a standard value, it may be a metric gear: module m ≈ OD ÷ (N + 2) in mm.
What is the span measurement (Wk)?
It is the practical way to check tooth thickness with a caliper: span k teeth with the flat jaws. For 20° and no profile shift, k ≈ N/9 + 0.5. The calculator gives k and the exact value of Wk.
What is profile shift (x)?
Moving the cutter out (positive x) or in (negative x) when generating the teeth. It avoids undercut on pinions with few teeth (below 17 at 20°) or adjusts the center distance. It changes the outside and root diameters, tooth thickness and Wk.