TAHA Engineering Toolsby TAHA Knowledge Lab

Machining & Workshop

Taper Turning Calculator

Taper angle, compound setting, taper per foot and tailstock offset for turning tapers.

Inputs

Calculate from
Side view of a conical taper, large end diameter D on the left and small end d on the right, length L, half angle alpha.αLDd
A taper from diameter D to d over length L. The half angle α (between the taper surface and the axis) is the compound slide setting; the included angle is 2α. Diagram not to scale.

Only for the tailstock set-over method. Leave empty otherwise.

Result

Half angle (compound slide setting)
2.86241
Included angle
5.72481
Taper ratio 1 : x (x shown)
10
Taper per foot
1.2in/ft
Taper per metre (diameter change)
100mm/m
Working
Taper = (D − d) ÷ L = (50 − 40) ÷ 100 = 0.1 = 1 : 10 Half angle α = arctan[(D − d) ÷ (2L)] = arctan(0.05) = 2.8624°

Set the compound slide to 2.86241 ° from the axis. The taper is 1 : 10 (included angle 5.72481 °).

Educational estimate — check the assumptions below.

About this calculator

A taper is a cone-shaped section of a turned part — used for machine tapers, shaft ends, pins and fits. It can be described in several equivalent ways: two diameters and a length, a taper ratio (such as 1 : 20), a taper per foot (common in inch drawings), an included angle, or the half angle that you set on the lathe’s compound slide. This calculator converts between them and gives the tailstock set-over for turning a long, shallow taper between centres.

Formula

k = (D − d) ÷ L    α = arctan[(D − d) ÷ (2L)]    included angle = 2α

Taper ratio = 1 : (1 ÷ k)    taper per foot = 12 × k (in/ft)    set-over = (D − d) ÷ 2 × Lw ÷ L

D, d = large and small diameters, L = taper length along the axis, α = half angle (compound slide setting), Lw = total workpiece length between centres. From an angle: d = D − 2L tan α.

Worked example

D = 50 mm, d = 40 mm, L = 100 mm:

  • Taper = 10 ÷ 100 = 0.1, i.e. 1 : 10; 1.2 in per foot; 100 mm per metre
  • Half angle = arctan(0.05) = 2.8624° (2° 51′ 45″); included angle 5.7248°
  • Turned between centres on a 200 mm long workpiece: set-over = 5 × 200 ÷ 100 = 10 mm

Assumptions and limitations

  • A straight (conical) taper measured on diameters. Angles are given in decimal degrees.
  • Standard tapers (Morse, Jacobs, metric, ISO/BT/SK tool tapers) have dimensions fixed by their standards; enter the values from the standard or drawing — they are not built in.
  • The tailstock set-over formula is a close approximation for shallow tapers; the centre holes are not perfectly aligned with the offset axis, so check with a test cut. Large offsets damage centre holes.
  • Taper per foot is the change in diameter over 12 inches of length, as used on inch drawings.

References

  • Conical taper geometry: tan α = (D − d) ÷ 2L; taper per foot = 12 (D − d) ÷ L; tailstock set-over (D − d) Lw ÷ 2L (standard machining texts).