By Zencalcy Editorial TeamLast reviewed About us
A taper is defined by how much the diameter changes over a length. The half-angle — what you set on a compound rest — comes from the radius change over the length, not the diameter change, which is the mistake that ruins a first taper.
Taper angle, ratio and offset for a turned part.
half angle = atan((D − d) ÷ (2L)) taper per inch = (D − d) ÷ L
Taper per foot is 12 × taper per inch. A Morse taper #2 has a taper of about 0.0500 in/ft. The compound rest is set to the half angle because it turns the tool along the side of the cone.
| Symbol | Meaning |
|---|---|
| D, d | Large and small diameters. |
| L | Length of the tapered section. |
| α | Half angle. |
Half angle = atan(0.5 ÷ 6) = 4.76°, taper 0.1667 in/in or 2.0 in/ft.
Continue with the Beam Deflection Calculator, Beam Load Calculator, Bending Stress Calculator, or the Wood Beam Span Calculator — or browse more structural & workshop and all construction calculators.
Yes. The half angle is measured from the axis of the work, which is where the compound swivel reads.
Results use standard construction estimating arithmetic: volumes from measured area and depth, unit weights from published material densities, and code-referenced spans or clearances where the page names a code. Quantities are rounded up to whole saleable units and include the stated waste allowance. These tools are planning aids, not structural design, and do not replace a licensed engineer, a local code check, or a contractor's site measurement.
Reference material used to build and check this calculator:
Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026