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Taper per Foot to Angle
Guide · Updated October 28, 2026
Tapers are often specified as taper per foot (TPF), the change in diameter over 12 in of length. Lathes, compound slides, and sine bars need an angle instead. Because TPF is a change in diameter, each side moves half as much, so the half-angle (angle to the centerline) is atan(TPF ÷ 24). The included angle is twice that.
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Step by step
- Get the taper per foot: From the drawing, or from (D − d) × 12 ÷ L when you have two diameters and a length.
- Find the half-angle: Half-angle = atan(TPF ÷ 24).
- Find the included angle: Included = 2 × half-angle.
- Set the machine: Set the compound or taper attachment to the half-angle.
- Verify: Check with a sine bar, taper gage, or by measuring two diameters.
Worked examples
- 1/2 in/ft: atan(0.5 ÷ 24) = 1.193° half, 2.387° included
- 0.600 in/ft: atan(0.025) = 1.432° half, 2.864° included
- 3/4 in/ft (NPT-style 1:16): atan(0.03125) = 1.790° half, 3.580° included
- 1-1/2 in/ft: atan(0.0625) = 3.576° half, 7.153° included
The 3/4 in/ft line matches the 1:16 taper on diameter used for NPT pipe threads: 0.75 ÷ 12 = 0.0625 = 1/16.
Worked example: from two diameters
A part measures 1.000 in at one end and 0.875 in at the other over 2.500 in. TPF = (1.000 − 0.875) × 12 ÷ 2.500 = 0.125 × 4.8 = 0.600 in/ft, so the half-angle is 1.432°.
To check it on a 5 in sine bar at the half-angle, the stack height is 5 × sin 1.432° ≈ 0.1250 in. A 0.125 in block from an 81-piece set does it in one block.
Angle back to taper per foot
TPF = 24 × tan(half-angle). A 2° half-angle gives 24 × 0.03492 = 0.838 in/ft. For a taper per inch, divide TPF by 12.
Worked example: tailstock offset
When turning a taper by offsetting the tailstock, offset = TPF × L ÷ 24, where L is the overall length of the work between centers in inches. For a 0.600 in/ft taper on a part 6.000 in long between centers, offset = 0.600 × 6 ÷ 24 = 0.150 in. On a 12.000 in part, the same taper needs 0.300 in.
Tailstock offset only suits shallow tapers and needs a ball-ended or bell center to avoid wearing the center holes. Measure the offset with a dial indicator on the tailstock quill, not by the witness marks alone.
Quick shop check
Common problems: setting the compound to the included angle instead of the half-angle, mixing taper per foot with taper per inch, and measuring diameters at positions that are not the stated length apart.
FAQ
How do I convert taper per foot to degrees?
Half-angle = atan(TPF ÷ 24); included angle is twice that.
Why 24 and not 12?
TPF is diametral, so each side moves half the amount over 12 in.
What angle is 3/4 in per foot?
About 1.790° half-angle, 3.580° included.
How do I check the angle?
Use a sine bar with gage blocks; build the stack free at gageblockcalc.com.
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General shop information only — follow your drawing, tool maker's data and your quality system.