Taper calculator
Enter the large diameter and the taper length, plus the small diameter, the angle or the taper ratio. The calculator works out the rest and gives you the contour points for the program.
Quick answer
Taper ratio C = (D − d) / L, half angle α = atan(C / 2). Example: D = 30, d = 25, L = 50 mm → C = 1:10, α ≈ 2.862°. Morse taper MT3 (1:19.922) — α ≈ 1.438°.
Result
- Large Ø D
- —
- Small Ø d
- —
- Half angle α
- —
- Included angle 2α
- —
- Taper ratio
- —
- Taper per unit length
- —
- Taper per foot (TPF)
- —
Contour points (G7, zero at the face)
Who needs it and why
Drawings specify tapers in different ways: by angle, by ratio 1:N, by two diameters and a length, or by a Morse number. A program needs two diameters and a length; setting the compound slide on a manual lathe needs the angle. The calculator turns any of these into all the others.
- Writing a program by hand — get the small diameter and the contour points from an angle or a ratio.
- Morse tapers — arbors, centers and drill shanks: diameter and ratio with one click.
- Tapered pipe threads — 1:16 (NPT, BSPT) — what the diameter is at the other end.
- On a manual lathe — what angle to set the compound slide to.
The formulas
- taper ratio
C = (D − d) / L = 1 : N - half angle
α = arctg((D − d) / (2 · L)), included angle 2α - small diameter
d = D − 2 · L · tg α = D − L / N
The half angle α is the angle between the taper surface and the part axis — the one you set the compound slide to on a manual lathe. On a CNC lathe you don't need the angle at all: two contour points are enough, the machine moves in a straight line between them.
Tapered threads (1:16 pipe threads and others) are covered in Tapered threads on a CNC lathe. In the Turn G-code app the Taper and Taper threading cycles split the stock into passes and show them in the 2D simulator.