What does a 1:20 taper mean?

The diameter changes by 1 unit for every 20 units of length — for example, a 1mm reduction over 20mm of taper length. It is a ratio commonly used for dowel pins and some machine tapers.

How do I convert a taper ratio to a taper angle?

Half-angle = arctan(ratio / 2). For a 1:20 taper, that is arctan(0.025) = 1.43 degrees — double it for the full included angle.

How much does it cost to have a taper turned by a machine shop in Australia?

A typical Australian machine shop charges roughly AUD 70-270 to turn a tapered workpiece (arbor, dowel, or toolholder) to spec, depending on the material, required tolerance, and surface finish.

Taper Calculator — Taper Angle and Ratio from Diameters

Taper Calculator: Taper Ratio, Taper Angle and 1:x Notation

A taper is how much a workpiece's diameter changes over a set length — the geometry behind lathe-turned shafts, drill and toolholder tapers, dowel pins, and tapered joints. Enter the major diameter, minor diameter, and taper length to get the taper ratio (as a 1:x figure), the taper-per-foot equivalent, and the half-angle in degrees.

How to use the taper calculator

Enter the major diameter (Dl), the larger end of the workpiece, and its unit.
Enter the minor diameter (Ds), the smaller end, and its unit.
Enter the taper length (Tl), then read off the taper ratio, 1:x notation, taper-per-foot equivalent, and half-angle in degrees.

The taper formulas, explained

Taper per unit length (TPI) = (Dl - Ds) / Tl, using one consistent length unit for all three — a dimensionless ratio, not literally "per inch."

Half-angle (theta) = arctan(TPI / 2); double it for the full included angle. Taper per foot = 12 x TPI, the traditional US machinist convention.

Worked example: 25mm major diameter, 20mm minor diameter, 100mm taper length. TPI = (25 - 20) / 100 = 0.05, a 1:20 taper. Half-angle = arctan(0.025) = 1.43 degrees, so the full included angle is about 2.86 degrees.

Tips and common mistakes

Convert every dimension to the same unit first — mixing a millimetre diameter with an inch taper length gives a meaningless ratio.

Check whether a spec means the half-angle (centerline to surface) or the full included angle — the two differ by a factor of two.

An Australian machine shop that turns a tapered workpiece — a shaft, dowel, or toolholder — to spec typically charges around AUD 70-270 for the job, depending on the material, tolerance, and finish required.