Taper turning calculator
A taper from Ø30 to Ø25 mm over 50 mm is 1:10, and the top slide is set to 2.8624° (tan α = (D − d) / 2L), half the included angle. Enter both diameters and the length, or the taper as a ratio, an included angle or a taper per foot, for the slide setting, the small diameter and, for a part turned between centres, the tailstock set-over.
The taper is drawn to scale with the top slide swung to the angle, and the common tapers load from the table.
HSK 1:10: hollow taper shank.
- Top-slide angle α
- α in degrees, minutes, seconds
- 2°51'44.7"
- Included angle 2α
- Taper
- Taper per foot
How it’s calculated
The taper C = (D − d) / L is written 1:k with k = 1/C, or as 12·C inches per foot; the included angle is 2α. Between centres, a part Lw long tilts as a whole, so the tailstock is set over e = (D − d) / 2 · Lw / L. Here: C = (30.000 − 25.000) / 50.000 = 0.1000, α = atan(0.05000) = 2.8624°.
| Taper | Ratio | Included 2α | α | Per foot (in/ft) | Used for |
|---|---|---|---|---|---|
| Morse 0 | 1:19.212 | 2.9816° | 1.4908° | 0.6246 | Drill and centre shanks, tailstock and spindle sockets |
| Morse 1 | 1:20.047 | 2.8575° | 1.4287° | 0.5986 | Drill and centre shanks, tailstock and spindle sockets |
| Morse 2 | 1:20.020 | 2.8613° | 1.4307° | 0.5994 | Drill and centre shanks, tailstock and spindle sockets |
| Morse 3 | 1:19.922 | 2.8754° | 1.4377° | 0.6023 | Drill and centre shanks, tailstock and spindle sockets |
| Morse 4 | 1:19.254 | 2.9751° | 1.4876° | 0.6232 | Drill and centre shanks, tailstock and spindle sockets |
| Morse 5 | 1:19.002 | 3.0146° | 1.5073° | 0.6315 | Drill and centre shanks, tailstock and spindle sockets |
| Morse 6 | 1:19.180 | 2.9866° | 1.4933° | 0.6257 | Drill and centre shanks, tailstock and spindle sockets |
| Pipe thread 1:16 | 1:16.000 | 3.5798° | 1.7899° | 0.7500 | NPT and BSP taper (R, Rc) threads |
| HSK 1:10 | 1:10.000 | 5.7248° | 2.8624° | 1.2000 | Hollow taper shank |
| Steep taper 7/24 | 1:3.429 | 16.5943° | 8.2971° | 3.5000 | SK, BT and CAT spindle tapers |
| ER collet 8° | 1:3.558 | 16.0000° | 8.0000° | 3.3730 | Collet seat in the holder (16° included) |
Top slide, taper attachment or tailstock set-over?
The top slide (compound) turns any angle, but only as long as its travel, fed by hand: short, steep tapers such as a centre or a chamfer. A taper attachment guides the cross slide along a bar set to the angle, so the saddle feeds a long taper under power. Setting the tailstock over tilts the whole part between centres, which suits long, shallow tapers; the set-over depends on the part’s whole length, so each part must be the same length and centre-drilled to the same depth.