What is the difference between the two methods?

The compound-rest method tilts the top slide to the taper half-angle and cuts short, steep tapers any angle you like, but only as long as the slide travel. The tailstock set-over method offsets the tailstock to turn long, gentle tapers along the whole bed, but only shallow angles.

How is the compound-rest angle found?

The compound is set to the half-angle of the taper, measured from the lathe axis. The half-angle is the arctangent of the radius change divided by the length, which equals arctangent of (taper per inch divided by two).

How is tailstock set-over calculated?

Set-over equals the total workpiece length between centers times the taper per inch, divided by two. Equivalently, it is overall length times (large diameter minus small diameter) divided by twice the tapered length. It only works when the taper runs the full length.

What is taper per foot?

Taper per foot is the change in diameter over twelve inches of length, a common way to specify standard machine tapers. Taper per inch is that figure divided by twelve. Both describe the diameter change, not the radius change.

Why does the set-over use total length, not tapered length?

The tailstock offsets the far center of the whole part, so the geometry depends on the full distance between centers. If only part of the length is tapered, the set-over method distorts the taper, which is why the compound method is preferred for partial tapers.

Lathe Taper Calculator

Cutting a taper on a lathe means picking a method and a number. This calculator gives you both numbers — the compound-rest angle and the tailstock set-over — from whichever way the taper is specified on your drawing, so you can choose the right method and dial it in directly.

How it works

Every taper reduces to a diameter change over a length. From that, define taper per inch as the diameter change divided by the tapered length:

taper per inch    = (large dia − small dia) / length
taper per foot    = taper per inch × 12
included angle    = 2 × atan( (taper per inch) / 2 )
compound angle    = included angle / 2 = atan( (taper per inch) / 2 )
tailstock setover = (overall length × taper per inch) / 2

The compound is always set to the half-angle measured from the lathe axis. The set-over uses the full distance between centers because the tailstock pivots the far end of the whole part, not just the tapered section.

Choosing a method

Use the compound rest for short or steep tapers and for any taper that does not run the full length of the part — it can cut any angle but only over the slide travel. Use tailstock set-over for long, shallow tapers along the whole bed, but never for steep angles, because large offsets ride the centers badly and chew up the center holes.

Example and tips

A Morse-style taper of 0.600 inch per foot is 0.050 inch per inch, so the compound angle is atan(0.050 / 2) = 1.43 degrees and the included angle is 2.86 degrees. For an 8-inch part the set-over is 8 × 0.050 / 2 = 0.200 inch. Steep tapers like 30 or 45 degrees can only be done on the compound — at those angles the set-over would exceed the tailstock travel and destroy the center holes.