← AskMachinist · Guides · Calculator · 🔎 Search
How to Cut a Taper with the Compound
Guide · Updated October 28, 2026
The compound rest is the quickest way to cut short tapers and steep angles. Set it to half the included angle, lock the carriage and hand-feed the compound. The length is limited to compound travel.
Measure the taper
Use a sine bar and gage blocks or a micrometer over two points. The free Gage Block Calculator builds the stack.
Step by step
- Find the angle: Half-angle = atan(taper per foot ÷ 24).
- Set the compound: Rotate to that angle from the axis.
- Fine set with an indicator: Indicate a known taper or travel along a test bar.
- Lock the carriage: Lock it to avoid movement.
- Feed by hand: Steady hand feed on the compound.
- Measure: Check diameters at two points.
- Adjust: Small angle corrections as needed.
Worked example
A Morse taper #2 is about 0.5994 in per foot. Half-angle = atan(0.5994 ÷ 24) = atan(0.02498) = 1.431°. Check: over a 2.000 in length the diameter should change 0.5994 × 2 ÷ 12 = 0.0999 in. If you measure 0.1020 in, the angle is too steep by about 0.0021 ÷ 2 ÷ 2.000 = 0.0005 rad, or 0.03°; tap the compound back slightly.
Indicating the angle
Mount an indicator on the compound and run it along a test bar or the taper of a known center while feeding the compound; adjust until the indicator change matches the target per inch.
Common problems
Mismatch from protractor error; indicate instead. Tool off center gives a hyperbolic profile. Uneven finish from hand feed rhythm.
Tips
- Other methods: cut a taper on a lathe.
- Measure: measure a taper.
- Sine bar: sine bar with gage blocks.
Worked example: setting the compound for a 3° included taper
A part needs a 3° included taper. The compound is set to half the included angle, 1.5°, measured from the spindle axis; on lathes whose compound scale reads from the cross slide, that is 88.5° on the dial. Over a 2.000 in taper length, the change in diameter is 2 × 2.000 × tan 1.5° = 4 × 0.02619 ≈ 0.105 in.
For a Morse taper No. 2 (about 0.04995 in/in on diameter, or 0.599 in/ft), the half angle is about 1.43°. Take a light cut, check with a taper ring gage and bluing, and correct the compound by small amounts until contact runs the full length.
Fuller worked example: a 1:20 taper on the compound
A taper of 1:20 on diameter has a half-angle of atan(1 ÷ 40) = 1.432°, so the compound is set 1.432° from the spindle axis. Feeding the compound 2.000 in along its slide changes the radius by 2.000 × sin 1.432° = 0.0500 in, which is 0.100 in on diameter, matching 2.000 ÷ 20.
For a 7° half-angle, each 1.000 in of compound travel changes diameter by 2 × sin 7° = 2 × 0.1219 = 0.2437 in. Check the first cut with a mic at two marked points 1.000 in apart; a 0.002 in error on diameter over 1 in means the angle is off by about atan(0.001) ≈ 0.057°.
FAQ
What angle do I set?
Half the included angle.
How do I convert taper per foot?
Half-angle = atan(TPF ÷ 24).
Is it limited in length?
Yes, by compound travel.
Why is my taper curved?
Tool off center.
How do I check it?
Sine bar or mic at two points.
Related guides and calculators
- How to Cut a Taper on a Lathe
- How to Measure a Taper
- How to Use a Sine Bar with Gage Blocks
- How to Set Tool Height on a Lathe
- How to Use a Bevel Protractor
- How to Cut Metric Threads on an Inch Lathe
- 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.