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Cosine Error with Indicators

Guide · Updated October 27, 2026

When an indicator isn't aligned with the direction of movement, it reads wrong. On a dial indicator, a plunger at an angle to the movement under-reads. On a test indicator, a stylus tilted away from parallel to the surface gives a reading that needs correcting by the cosine of the angle.

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Step by step

Align the dial indicator: Keep the plunger in line with the movement.
Set the test indicator angle: Keep the stylus close to parallel to the surface, within about 10–15°.
If you can't: Correct the reading: true ≈ reading × cos(angle) for a test indicator.
Verify: Check the setup against a known gage block step.
Record: Note the angle on critical setups.

Factors

10° → ×0.985 (1.5%)
20° → ×0.940 (6%)
30° → ×0.866 (13%)
45° → ×0.707 (29%)

Worked example: correcting a 15° indicator tilt

Cosine error is corrected by multiplying the indicated reading by cos θ. A test indicator with its stylus 15° off parallel to the surface reads 0.0100 in; the true movement is 0.0100 × cos 15° = 0.0100 × 0.9659 ≈ 0.0097 in, so the error is about 0.0003 in. At 30° the factor is 0.8660 and the same reading is really 0.0087 in, an error of 0.0013 in.

A quick rule: below about 10° (cos 10° = 0.9848) the error is under 2% of the reading, which is often negligible for small readings. For larger tilts, either reposition the stylus or apply the correction factor. Note that some test indicators are built with a contact point designed for a specific angle; check the maker’s instructions.

Second worked example: a 20° tilt on a small reading

A test indicator at 20° reads 0.0020 in. True movement = 0.0020 × cos 20° = 0.0020 × 0.9397 ≈ 0.00188 in, an error of about 0.00012 in. On a 0.0002 in tolerance, that is over half the tolerance, so either straighten the stylus or apply the factor.

For a dial indicator plunger tilted 10° to the travel, the indicator over-travels relative to the true movement: true movement = reading × cos 10° = reading × 0.985. A 0.0500 in reading is really about 0.0492 in of travel, a 0.0008 in error.

Quick shop check

Common problems: forgetting to check the contact angle when moving a test indicator to a new setup.

FAQ

What is cosine error?

A measurement error from an indicator that's misaligned with the movement. It scales with the cosine of the angle.

How do I correct it?

For test indicators, true ≈ reading × cos θ. It's better to align the setup.

Does it matter at small angles?

Under 10° it's about 1.5% of the reading, which is often fine for zeroing comparisons.

How do I prove a setup?

Indicate a known step built from gage blocks. Build any reference size free with the Gage Block Calculator at gageblockcalc.com.

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Questions? Ask a machinist.

General shop information only — follow your gage manufacturer's instructions and your quality system.