Taper Calculator
Taper calculator for machining and woodworking in Malta: enter major diameter, minor diameter, and taper length to get the taper angle and taper ratio.
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.
A machine shop in Malta that turns a tapered workpiece — a shaft, dowel, or toolholder — to spec typically charges around €40-€170 for the job, depending on the material, tolerance, and finish required.
