How do I calculate taper?

Taper C = (large diameter − small diameter) ÷ taper length, written as 1:k (k = L ÷ (D − d)). Angle: included (full) angle = 2 × atan((D − d)/2L); the lathe compound slide is set to the half angle.

Is the Morse taper 1:20?

Not a single ratio: MT0–MT6 each fall roughly between 1:19.2 and 1:20.05, so check the standard table for that size before machining.

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Q: What is the angle of a 7:24 taper?

The included (full) angle is about 16.60° (16°36′) and the half angle is about 8.30°; it is the standard for BT/NT spindle tapers.

Enter the large diameter, small diameter and taper length to instantly get the taper ratio, the included (full) angle and the half angle. Includes a common taper angle table (trigonometric computed values).

Large diameter D (mm)

Small diameter d (mm)

Taper length L (mm)

Taper ratio—1 : k

Included angle (full)——

Half angle (per side)—for lathe compound-slide setting

Formula

Taper C = (D − d) ÷ L = 1 : k, k = L ÷ (D − d)

Full angle θ = 2 × atan( (D − d) ÷ 2L ); half angle = θ ÷ 2

When turning a taper on a lathe, the compound slide is rotated to the half angle; when inspecting the included angle, note whether the drawing dimensions the full angle or the half angle.

Common taper angle table (computed values)

Taper	Full angle	Half angle
7:24 (BT/NT spindle taper)	16.5943°	8.2971°
1:10	5.7248°	2.8624°
1:20	2.8642°	1.4321°
1:30	1.9097°	0.9548°
1:50 (dowel/locating pin)	1.1459°	0.5729°

Morse tapers (MT0–MT6) have different ratios for each size (roughly 1:19.2–1:20.05) rather than a single ratio; check the MT standard table before machining to get the exact value for that size.

FAQ

What is the angle of a 7:24 taper?

The full angle is about 16.60° (16°36′) and the half angle is about 8.30°. 7:24 is the standard taper for BT/NT spindle tapers.

How many degrees do I set the lathe to for a 1:20 taper?

Half angle = atan(1/40) ≈ 1.4321°, so the compound slide is rotated by about 1°26′.

What does a 1:10 taper mean?

For every 10 mm of axial length the diameter changes by 1 mm. Converted to an angle: full angle = 2 × atan(1/20) ≈ 5.72°.

Further reading: Turning and mill-turn machining · Measuring tools primer (taper inspection) | More tools: Tools hub

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