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How to Check a Taper with a Sine Bar

Guide · Updated October 28, 2026

A sine bar and gage blocks set a precise angle. Tilt the sine bar to the taper half-angle, rest the part on it and the taper surface becomes parallel to the surface plate. Sweep it with an indicator and any reading change is taper error.

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Step by step

  1. Find the half-angle: Half-angle = atan(TPF ÷ 24).
  2. Calculate the stack: Stack = L × sin(half-angle).
  3. Set the sine bar: Put the stack under one roll on a surface plate.
  4. Hold the part: Set the part on the bar or between bench centers with the bar holding them.
  5. Sweep: Sweep the top line of the taper with an indicator on a height stand.
  6. Read: A reading change is taper error.
  7. Correct: Adjust the taper setting and recut.

Worked example: 3/4 in per foot

Half-angle = atan(0.750 ÷ 24) = 1.790°. Included angle = 3.580°. On a 5 in sine bar: stack = 5 × sin 1.790° = 0.1562 in. Sweep 2.000 in along the taper; if the indicator changes by 0.0004 in, the error is 0.0004 ÷ 2.000 = 0.0002 in per inch on radius, or 0.0004 in per inch on diameter.

Radius vs diameter

The indicator reads along one side, so its reading is radial. Double it for diameter taper error.

Which way to correct

If the reading rises toward the large end, the half-angle is too large. Reduce it.

Common problems

False reading: indicator not on the top line. Wrong stack: used included angle instead of half angle. Part rocks: dirt.

Tips

Worked example: 5 in sine bar for a 7° angle

Gage block height = L × sin θ. For a 5.000 in sine bar at 7°, sin 7° = 0.12187, so the stack is 0.6093 in. Build 0.1003 + 0.109 + 0.400 = 0.6093 in. Indicate along the taper; if the indicator moves 0.0005 in over 2 in, the taper is out about 0.00025 in per inch.

Angles above about 45° lose accuracy because small errors in the stack produce larger angle changes; use a complementary setup instead.

Second worked example: 3° half-angle on a 5 in sine bar

To set a 5 in sine bar to 3°, the stack height is H = 5 × sin 3° = 5 × 0.05234 = 0.2617 in. From an 81-piece set: 0.1007 + 0.111 + 0.050 = 0.2617 in. Indicate along the taper; zero end to end means the half-angle matches.

For a taper given as taper per foot, half-angle = atan(TPF ÷ 24). A 0.600 in/ft taper gives atan(0.025) ≈ 1.432°, so H = 5 × sin 1.432° ≈ 0.1250 in. If the indicator changes by 0.0005 in over 2.000 in of travel, the angle error is about 0.0005 ÷ 2 = 0.00025 rad, or 0.014°.

Quick shop check

Common problems: unclean gage blocks or a burr on the sine bar roll throws off the angle. Clean all contact surfaces and use the same indicator preload at each end.

FAQ

Half angle or included?

Half angle for one side of the taper.

What is the formula?

Stack = L × sin(half-angle).

What is 3/4 TPF on a 5 in bar?

0.1562 in.

Is the indicator reading diameter?

No, radius; double it.

Which way to correct?

Rising toward the large end means too steep.

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