Taper, chamfer and nose radius calculator
The three calculations used most for tapers and chamfers: taper angle, chamfer with X/Z points, and tool nose radius compensation.
- Half angle α (compound setting)
- 5.7106° (5° 42′ 38″)
- Included angle 2α
- 11.4212°
- Taper C = (D − d) / L
- 1 : 5.000
- Small diameter d
- 30.000 mm
- Radial depth
- Chamfer face length
- Start point
- End point
- Compensation in Z
- Compensation in X (radius)
- Compensation in X (diameter)
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📘 Free download: CNC machine buyer's guide 2026 (PDF) →- Taper: α = arctan((D − d) / 2L). Chamfer: radial depth = a × tan θ. Nose compensation applies when programming the imaginary tool tip without G41/G42: ΔZ = r × (1 − tan(θ/2)), ΔX (radius) = r × (1 − tan((90° − θ)/2)). Where possible, use G41/G42 with the tool tip direction so the control compensates automatically.
Nose radius compensation by angle (r = 0.4 and 0.8 mm)
| Angle (°) | r (mm) | Compensation in Z | Compensation in X (radius) | Compensation in X (diameter) |
|---|---|---|---|---|
| 15 | 0.4 | 0.347 | 0.093 | 0.186 |
| 15 | 0.8 | 0.695 | 0.186 | 0.372 |
| 20 | 0.4 | 0.329 | 0.120 | 0.240 |
| 20 | 0.8 | 0.659 | 0.240 | 0.480 |
| 30 | 0.4 | 0.293 | 0.169 | 0.338 |
| 30 | 0.8 | 0.586 | 0.338 | 0.676 |
| 45 | 0.4 | 0.234 | 0.234 | 0.469 |
| 45 | 0.8 | 0.469 | 0.469 | 0.937 |
| 60 | 0.4 | 0.169 | 0.293 | 0.586 |
| 60 | 0.8 | 0.338 | 0.586 | 1.171 |
| 75 | 0.4 | 0.093 | 0.347 | 0.695 |
| 75 | 0.8 | 0.186 | 0.695 | 1.389 |