Lathe Taper Calculator
Enter the large diameter, small diameter and length to get the compound angle, included angle, taper ratio, taper per foot and the diameter at any point. Or work backward from an angle. Free, no sign-up.
1. Choose what to solve for
2. Enter the numbers
Results
Tapers are exactly where nose radius error shows up.
Program the taper to the drawing and the round nose of the insert leaves it off size. LATHE-NC compensates the nose radius automatically when it builds the G-code from your drawing, and lets you check the cut in 3D before the spindle turns. It runs in the browser.
How it works
Metric example: D 20, d 16, L 40 mm → tanθ = 4 ÷ 80 = 0.05 → half angle 2.8624°, included angle 5.7248°, taper ratio 1:10. 20 mm from the small end the diameter is 18.000 mm.
Inch example: D 1.250, d 1.000, L 3.000 in → taper per foot 1.0000 in/ft (0.0833 in per inch), half angle 2.3859°, ratio 1:12.
On a manual lathe, swing the compound rest to the half angle, not the included angle. On a CNC lathe, use the diameter at z to get the X/Z end points for a G01 taper move or an angled chamfer — then remember that the insert nose radius still shifts the cut surface unless you use G41/G42 or compensated coordinates (see the nose radius calculator).
FAQ
Do I set the compound rest to the half angle or the included angle?
The half angle. The compound (top slide) swings from the spindle axis, and each side of the taper is inclined by half the included angle, so you set it to atan((D − d) / 2L).
How do I calculate taper per foot?
Taper per foot = (D − d) / L × 12, with D, d and L in inches. For example, D 1.25 in, d 1.00 in over 3 in gives 0.25 / 3 × 12 = 1.000 in per foot.
What does a taper ratio of 1:10 mean?
The diameter changes by 1 unit for every 10 units of length. It is (D − d) / L written as 1 : L / (D − d), and it is the same in inches or millimeters.
Why does my taper come out the wrong size on a CNC lathe?
Usually tool nose radius. The program drives the imaginary tool tip, but the round nose of the insert does the cutting, so on a taper the actual surface shifts unless nose radius compensation (G41/G42) or compensated coordinates are used.