← AskMachinist · Guides · Calculator · 🔎 Search
How to Cut a Taper on a Lathe
Guide · Updated October 28, 2026
There are three common ways to turn a taper: swing the compound rest, offset the tailstock, or use a taper attachment. Each one needs the same thing first: the taper expressed as a half-angle or a taper per foot.
Check the taper
Measure diameters at two points a known distance apart, or check with a sine bar on gage blocks. The free Gage Block Calculator builds the stack.
Step by step
- Find the taper: Get the taper per foot (TPF) or included angle from the drawing or a taper table.
- Convert it: Half-angle = atan(TPF ÷ 24). The compound is set to the half-angle, not the included angle.
- Pick a method: Short, steep tapers: compound. Long, shallow tapers between centers: tailstock offset. Long tapers on chucked work: taper attachment.
- Set tool height: Set the tool exactly on center; an off-center tool cuts the wrong taper and a curved profile.
- Rough the taper: Take passes leaving about 0.010 in on diameter.
- Check the taper: Blue the mating part or gage, test-fit, and look at the rub pattern, or mic two diameters.
- Adjust and finish: Correct the angle in small amounts, then take the finish pass.
Worked example
A Morse taper #2 is about 0.5994 in per foot. Half-angle = atan(0.5994 ÷ 24) = 1.431°, so swing the compound to about 1° 26′. Because a compound dial is hard to set that finely, set it close, take a pass, then indicate along the taper with a test indicator on the carriage: over 2.000 in of travel the needle should move 2.000 × tan(1.431°) = 0.050 in on the radius. If it moves 0.054 in, bring the compound back a little and check again.
Tailstock offset formula
Offset = (TPF × overall part length) ÷ 24, with lengths in inches. A 6 in long part with 0.500 in/ft taper needs 0.500 × 6 ÷ 24 = 0.125 in of offset. The taper depends on overall part length, so every part must be the same length and center-drilled the same depth.
Taper attachment
The attachment guides the cross slide from a bar set to the taper, so you can cut long tapers on chucked work with power feed. Take up the backlash in the attachment before each pass by moving in the same direction.
Tips
- Measuring: measuring a taper.
- Angles: sine bar with gage blocks.
- Tool height: setting tool height.
FAQ
Do I set the compound to the included angle?
No. Set it to the half-angle; the included angle is twice that.
How do I convert taper per foot to an angle?
Half-angle = atan(TPF ÷ 24).
What is the tailstock offset formula?
Offset = TPF × part length ÷ 24, all in inches.
Why does my taper look curved?
The tool is not on center height.
What is the easiest way to check a taper fit?
Blue the mating part, twist it on, and look for even contact along the length.
Related guides and calculators
- How to Measure a Taper
- How to Set Tool Height on a Lathe
- How to Align a Lathe Tailstock
- How to Use a Sine Bar with Gage Blocks
- How to Use a Dial Test Indicator
- Turning Speeds and Feeds
- How to Use a Follow Rest
- How to Cut a Radius on a Lathe
- How to Cut a Taper with the Compound
- How to Cut a Taper with a Taper Attachment
- All free machinist calculators
Build your stack in seconds
The free Gage Block Calculator finds the fewest-block combination for inch and metric sets, with wear blocks. No login.
Questions? Ask a machinist.
General shop information only — follow your machine and tooling manufacturer's instructions and your shop's safety rules.