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Taper calculator

Choose a standard taper or enter your own sizes. It gives the angle to set the topslide (compound) and, for turning between centres, how far to offset the tailstock.

Use one unit (mm or inches) for every length; answers come out in the same unit. Morse and Jacobs diameters are shown in both.

Safety: return the tailstock to centre afterwards and check it with a test bar, or later parallel work will turn tapered. Keep the drive dog guarded; dogs catch clothing.
How it works, guides and notes

How it works

Set the topslide (compound) to the half angle: the angle between one side of the taper and the centre line. To turn a long, gentle taper between centres instead, offset the tailstock: the offset is half the diameter change, scaled up by the total work length over the taper length.

Half-angle = atan((D − d) ÷ 2L). Taper per foot (TPF) is the change in diameter over 12": half-angle = atan(TPF ÷ 24). Tailstock offset = (D − d)/2 × total length ÷ taper length; if the taper runs the full length of the work, it is simply (D − d)/2.

Morse tapers are close to, but not exactly, 5/8" per foot, and each size differs slightly. Gauge diameter is at the gauge line on the socket mouth. Jacobs figures are typical published values and are marked EST. Check with a taper gauge or Prussian blue before relying on them.

Worked example: MT2 is 0.59941" per foot, so the half-angle is atan(0.59941 ÷ 24) = 1.431° (1° 25′ 50″). Set the topslide to that and check the fit with blue.

Tailstock offset only works with the work between centres and a centre that suits the angle; a ball-ended centre helps. Indicating the topslide against a known taper (an old drill shank or arbor) is often quicker than trusting the scale.

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