Describing a taper
A taper is a gradual change in diameter along a part, as on a lathe center, a drill shank or a tapered pin. It can be described in several equivalent ways, all derived from the large diameter D, the small diameter d and the length L:
- Taper per inch = (D − d) ÷ L
- Taper per foot = (D − d) ÷ L × 12, the usual US description
- Taper ratio 1 : x, where x = L ÷ (D − d), the usual metric description
- Half angle = arctan[(D − d) ÷ (2L)], the angle to set on the compound rest of a lathe
- Included angle = 2 × half angle
Example
A part tapers from 1 in to 0.75 in over 3 in. The taper per inch is 0.25 ÷ 3 = 0.0833, which is 1 inch per foot. The ratio is 1:12, the half angle 2.386° and the included angle 4.772°.
Common standard tapers
| Taper | Approximate taper per foot | Use |
|---|---|---|
| Morse | about 5/8 in/ft (about 1:20) | drill shanks, lathe centers |
| Jarno | 0.6 in/ft | small machine spindles |
| Brown & Sharpe | about 1/2 in/ft | milling machine arbors |
| Taper pins | 1/4 in/ft | pins and dowels |
| NPT pipe threads | 3/4 in/ft (1:16) | tapered pipe threads |
| Steep taper (CAT, BT, SK) | 7/24 | machining center tool holders |
Each Morse size has its own slightly different taper; check the table for the exact value.
Turning a taper
- Compound rest: swing it to the half angle and feed by hand. Suitable for short, steep tapers.
- Tailstock offset: offset the tailstock by L_total × (D − d) ÷ (2L) for work between centers. Suitable for long, gentle tapers.
- Taper attachment: guides the cross slide along a set angle for accurate, repeatable tapers.
- CNC: program the two diameters and the length directly.
Checking a taper
Blue the part, try it in the matching socket or ring gauge and look at the contact pattern. Full-length contact means the angle is right; contact at one end means it needs adjusting.