How do I set a sine bar to an angle?

Stack gauge blocks to H = L·sin(θ), where L is the sine bar's centre-to-centre roll distance — typically 5 in or 100 mm. Place the stack under one roll and the work is set when the top surface is parallel to the reference. For 30° on a 5 in bar, the stack is 2.5000 in.

What are sine bar rolls measured between?

The centre-to-centre distance between the two cylindrical rolls, which is the nominal sine bar length — 5 in, 10 in or 100 mm are the common values. Measuring over the outside of the rolls instead is a common error that makes every angle wrong.

Why is a sine bar not accurate at large angles?

Because the sensitivity dθ/dH = 1/(L·cos θ) grows as the angle approaches 90°. At 60° a 0.0001 in stack error gives about 8 arc-seconds of angle error, twice what it gives at 30°. Most guidance limits sine bars to about 45°.

Can I use a sine bar without gauge blocks?

A sine bar needs a known length to work, so gauge blocks or a calibrated stack are essential. Using a rule or a set of parallels defeats the purpose, since the length is what the angle accuracy depends on.

How do I check an angle with a sine bar?

Set the bar with a stack computed for the nominal angle, place the work on the bar, and measure the gap along the top with a dial indicator. The angle error is the indicated difference divided by the length over which you measured, converted to degrees.

Sine Bar Calculator

Sources and scope for this page: Formulas as shown on this page (standard engineering relationships, no single governing revision), covering every value this calculator produces. No independent source check is recorded for this page: the content rests on the sources listed and on the working shown on the page. Full sources, values and limits on this page.

Page last changed 2026-10-19 · based on n/a — standard engineering relationships, no single governing revision

Quick Answer

The gauge block height is H = L · sin(θ). For a 5 in sine bar set to 30°, that is 2.5000 in. The sine bar converts an angle into a length, which is why it is the most accurate way to set an angle in a machine shop.

Sine Bar Setting

Sine bar length (in)

Angle (degrees)

Actual gauge stack height (in)

The Formulas Used

Gauge block height: H = L · sin(θ)
Angle from a stack: θ = asin(H ÷ L)
Sensitivity: dθ/dH = 1 ÷ (L · cos θ) — the angle is least sensitive to stack error at small angles

Why a Sine Bar Beats a Protractor

A sine bar converts an angle measurement into a length measurement, and length is the quantity a machine shop can generate and verify most accurately. A gauge block stack is accurate to a few millionths of an inch, so the angle a sine bar sets is far more accurate than any angle-measuring instrument in the shop.

The sensitivity formula is the reason sine bars behave differently at different angles. dθ/dH = 1/(L·cos θ) means that at 30° a 0.0001 in stack error produces about 4 arc-seconds of angle error, while at 60° it produces about 8 arc-seconds, and it diverges as the angle approaches 90°. Sine bars are most accurate at small angles and should not be used above about 45°.

Frequently Asked Questions

How do I set a sine bar to an angle?: Stack gauge blocks to H = L·sin(θ), where L is the sine bar's centre-to-centre roll distance — typically 5 in or 100 mm. Place the stack under one roll and the work is set when the top surface is parallel to the reference. For 30° on a 5 in bar, the stack is 2.5000 in.
What are sine bar rolls measured between?: The centre-to-centre distance between the two cylindrical rolls, which is the nominal sine bar length — 5 in, 10 in or 100 mm are the common values. Measuring over the outside of the rolls instead is a common error that makes every angle wrong.
Why is a sine bar not accurate at large angles?: Because the sensitivity dθ/dH = 1/(L·cos θ) grows as the angle approaches 90°. At 60° a 0.0001 in stack error gives about 8 arc-seconds of angle error, twice what it gives at 30°. Most guidance limits sine bars to about 45°.
Can I use a sine bar without gauge blocks?: A sine bar needs a known length to work, so gauge blocks or a calibrated stack are essential. Using a rule or a set of parallels defeats the purpose, since the length is what the angle accuracy depends on.
How do I check an angle with a sine bar?: Set the bar with a stack computed for the nominal angle, place the work on the bar, and measure the gap along the top with a dial indicator. The angle error is the indicated difference divided by the length over which you measured, converted to degrees.

Value Sources

References and calculation methods used for this page are listed below. Numbered markers connect table columns where present. A reference listing does not itself establish that every value has been independently checked.

#	Source	Type	Revision / method
[1]	Values computed in your browser	derived	Evaluated locally from the formulas shown on the page. No data leaves the device.

Data Sources

Standard	Revision	What it covers on this page
Formulas as shown on this page	n/a — standard engineering relationships, no single governing revision	every value this calculator produces

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Derived values — the following values on this page are calculated, not taken directly from the standard:

Value	How it is derived
All outputs	Computed in the browser from the formulas above. No data leaves the device.

Outputs are computed from the formulas shown. Verify against the governing standard for design or acceptance work.

Accuracy and use. Use the source notes and recorded verification scope above to assess each value. Calculated values follow the stated derivations; compilation values may lack a confirmed original document or product condition. No warranty, express or implied, is made as to the accuracy or completeness of this information, and no liability is accepted for any loss or damage arising from its use. Engineering reference data is provided for guidance in preliminary work — before a value is used for design, fabrication or acceptance testing, verify it against the current revision of the governing standard and against your own inspection. The user assumes all risk and responsibility in connection with the use of this information.

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Plain text

Engineering Reference. "Sine Bar Calculator." https://refmanual.com/calculators/sine-bar/ (accessed 2026-11-09). Data from Formulas as shown on this page, n/a — standard engineering relationships, no single governing revision.

BibTeX

@misc{sine-bar,
  title        = {Sine Bar Calculator},
  author       = {{Engineering Reference}},
  howpublished = {\url{https://refmanual.com/calculators/sine-bar/}},
  note         = {Accessed: 2026-11-09},
  source       = {Formulas as shown on this page, n/a — standard engineering relationships, no single governing revision}
}

RIS (EndNote, Zotero, Mendeley)

TY  - ELEC
TI  - Sine Bar Calculator
AU  - Engineering Reference
PB  - Engineering Reference
UR  - https://refmanual.com/calculators/sine-bar/
PY  - 2026
DA  - 2026-11-09
N1  - Source: Formulas as shown on this page, n/a — standard engineering relationships, no single governing revision
ER  -