Trigonometry · Released
Taper and Angle Calculator
Calculate taper dimensions and angles for turned parts, toolholders, and tapered features. Enter any three of the four values (large diameter, small diameter, length, included angle) and the calculator solves the fourth. Also shows taper per 100 mm and the half-angle for programming.
Large diameter D
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Small diameter d
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Length L
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Included angle α
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Taper per 100 mm
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Half-angle (program side)
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Formula and use
The taper is defined by the diameter change over length:
- Included angle: α = 2·atan((D − d) / (2·L))
- D = d + 2·L·tan(α/2)
- d = D − 2·L·tan(α/2)
- L = (D − d) / (2·tan(α/2))
- Taper per 100 mm = (D − d) / L × 100
On a lathe, the compound rest is swivelled to the half-angle (α/2), not the included angle. When programming a CNC lathe, the toolpath uses the half-angle as well. Standard tapers (Morse, Metric 1:50, etc.) are defined by their taper ratio, not the angle.
Common uses: turning tapered shafts, boring tapered holes, setting up taper-turning attachments, checking Morse taper dimensions, and verifying toolholder tapers (BT/CAT).