How to use this calculator
- Enter the diameters. Enter the large and small finished diameters of the taper.
- Enter taper length. Enter the axial length over which the diameter changes.
- Enter center distance. For tailstock setover, enter the distance between centers. Use zero if you only need taper and angle.
- Read the setup values. Use taper per foot for drawing/shop notation, compound angle for one-side cutting and setover for between-centers turning.
How it works
Taper per foot is a diametral taper. Start with the diameter
change DeltaD = D1 - D2, divide by the taper length L,
then scale that slope to the reference length you want:
TPF = (DeltaD / L) x 12 in.
The calculator also shows the same slope as taper per inch and taper per 100 mm.
A lathe compound slide is set to the half angle of the taper, not the included
cone angle. The half angle is
alpha = atan(DeltaD / (2L)), and the included angle is
2alpha. For tailstock turning between centers, the required
setover is S = DeltaD x C / (2L), where C is the
center distance.
Worked example
Verified against the live calculator
A shaft tapers from 2.000 in to 1.500 in
over 6.000 in. The diameter change is
DeltaD = 0.500 in, so
TPF = 0.500 / 6 x 12 = 1.000 in/ft. The compound angle is
atan(0.500 / (2 x 6)) = 2.3859 degrees, and the included angle is
4.7719 degrees. With 18 in between centers,
the tailstock setover is 0.500 x 18 / (2 x 6) = 0.750 in.
Frequently asked questions
How do you calculate taper per foot?
Use the diametral change divided by taper length, then scale it to 12 inches: TPF = (D1 - D2) / L x 12. D1 and D2 are the large and small diameters, and L is the axial taper length. The same slope can be shown as taper per inch or taper per 100 mm.
Is taper per foot based on diameter or radius?
Shop taper per foot is normally diametral taper: the change in diameter over the length, not the change in radius. The compound angle uses half that change because the cutting tool follows one side of the cone.
How do I calculate the lathe compound angle from taper per foot?
First find the diameter change DeltaD = D1 - D2. The compound angle from the part centerline is alpha = atan(DeltaD / (2L)). The included angle of the cone is twice that value.
How do you calculate tailstock setover for a taper?
For a between-centers taper, setover S = DeltaD x C / (2L), where DeltaD is the diameter change, C is the distance between centers and L is the taper length. The sign tells which direction the tailstock must move relative to the spindle centerline.
What does a 1:12 taper ratio mean?
A taper ratio of 1:12 means the diameter changes by one unit over twelve units of axial length. This calculator reports N in 1:N as taper length divided by absolute diameter change.
Method & assumptions
- Taper per foot uses diameter change, not radius change. If your print gives side slope, convert it before comparing.
- The compound angle is measured from the workpiece centerline. Some machines or drawings label the complementary angle; verify the setup convention before cutting.
- Tailstock setover assumes the work is turned between centers and the entered center distance is the actual distance between centers for the setup.
- The calculator is geometry only. It does not account for tool deflection, work spring, taper attachment error, tailstock alignment, centre wear or inspection tolerance.