Machining and Fastener Charts
Taper per foot and angle.
Enter the large and small diameters and the length of the taper. You get taper per foot (inches) or per 100 mm, the 1:n ratio, the half angle for a compound slide and the included angle. Runs in your browser; nothing is sent or stored.
Inputs
Result
Fill the form and press Calculate.
Answer first. Taper per foot = 12 x (D - d) / L with all dimensions in inches. The half angle is arctan((D - d) / (2L)); the included angle is twice that.
Worked example
A bar tapers from 1.5 in to 1.0 in over 10 in. Taper per inch = 0.5 / 10 = 0.05, so taper per foot = 0.6 in. The ratio is 1:20, and the half angle = arctan(0.025) = 1.432 degrees, so the included angle is 2.864 degrees. On a lathe with a compound slide set from the axis, 1.432 degrees is the setting.
How it works
Per unit length. The diameter change per unit of length is (D - d) / L. Multiply by 12 for inches per foot. In metric, multiply by 100 for mm per 100 mm.
Half angle versus included angle. The included angle is the angle between opposite sides of the cone. The half angle is the angle between one side and the axis, and is what a compound rest or taper attachment is set to.
Standard tapers. Published tapers such as Morse have defined taper per foot values and tolerances. The Morse #2 value of about 0.5994 in per foot gives roughly 2 degrees 51.7 minutes included. Use the controlling table or ASME B5.10 for the real values; this tool only does the geometry.
Sources
- Taper Calculations for Machinists - ToolGrit (taper per foot and angle formulas) (opened 2026-10-16)
- Taper Calculator - Omni Calculator (taper formula cross-check) (opened 2026-10-16)
Taper per foot = (D - d) x 12 / L and half angle = arctan(TPF / 24) are from these pages. The two pages label taper per inch and per foot inconsistently; this tool follows the first.
FAQ
What is taper per foot?
It is how much the diameter changes over 12 inches of length. Taper per foot = 12 x (large diameter - small diameter) / length, with inches.
How do I find the compound slide angle for a taper?
Use the half angle: arctan((D - d) / (2L)). It is the angle between one side of the taper and the axis.
How do I convert taper per foot to an angle?
Half angle = arctan(taper per foot / 24). Double it for the included angle.
What does a 1:20 taper mean?
The diameter changes by 1 unit for every 20 units of length. That is a taper per inch of 0.05 and a taper per foot of 0.6 inch.
Can I use millimetres?
Yes. Pick the millimetre option. The tool reports mm per 100 mm instead of per foot; the ratio and the angles do not depend on the unit.