Sine Bar Calculator

Enter a sine bar's length and an angle in degrees, minutes and seconds to get the gauge block stack height — or enter the stacks to get the angle. Inches or millimetres.

Construction & DIYWorldwideSource: Sine bar formula, Manufacturing Processes 4-5 (open textbook, CC BY)Free, no sign-up

Common angles for a 5-inch sine bar (from the source)

5°	0.4358″
10°	0.8682″
15°	1.2941″
20°	1.7101″
25°	2.1131″
30°	2.5000″
35°	2.8679″
40°	3.2139″
45°	3.5355″
50°	3.8302″
55°	4.0958″
60°	4.3301″

How to set up a sine bar

Enter the sine bar length. Use the distance between the centres of the two rolls — 5 in, 10 in, 100 mm or whatever your bar is marked — not its overall length.
Choose what you want to find. The block height for an angle you need, or the angle that a stack you already have produces.
Enter the angle or the stacks. Angles can be entered in degrees, minutes and seconds. For the reverse calculation, enter the stack under each roll; use 0 for a roll resting on the surface plate.
Read the result. Height = length × sin(angle); angle = asin(height difference ÷ length). The arithmetic is printed with the answer.
Build the nearest stack. Wring together the gauge blocks that make up the height as closely as your set allows, and place them under one roll on a clean surface plate.

10 situations where a sine bar calculation is needed

Setting up a part to grind an angle

A 5-inch sine bar for a 15° face needs a 1.2941" stack. Getting the stack right is the difference between an angle that checks and one that does not.

Checking a machined angle on the surface plate

Set the bar to the nominal angle, put the part on it, and indicate across the face. The tool gives the stack for the nominal angle.

Finding the angle a known stack produces

With a 1.500" stack under a 5-inch bar, the angle is 17° 27′ 27″. Useful when inspecting a set-up someone else built.

Working to an angle in degrees, minutes and seconds

Drawings often call out angles like 12° 30′. The tool converts and returns the stack directly.

Using a metric sine bar

For a 100 mm bar at 12° 30′, the stack is 21.644 mm. Enter mm and the result stays in mm.

Setting up a sine plate or sine vise

The same formula applies to sine plates and sine vises; enter the roll-centre distance of the plate.

Raising both rolls on blocks

When the low roll also sits on a stack, the angle depends on the difference between the stacks. Enter both heights.

Teaching precision measurement

The page shows the formula and the source's own table of common angles for a 5-inch bar.

Preparing a set-up sheet

Calculate the stacks for each angle a job needs before going to the surface plate.

Double-checking a mental calculation

A quick sin × length check avoids building the wrong stack from a mistyped calculator entry.

Where the formula comes from

The method is from the open textbook Manufacturing Processes 4-5 (Virasak), Unit 3: Sine Bar, published on Workforce LibreTexts under a CC BY licence: to set a sine bar to an angle, take the sine of the angle and multiply it by the sine bar length — the distance between the centres of the gauge pins. The unit's worked example sets a 5.0-inch bar to 30°: sin 30° = 0.5000, × 5.0 = 2.5000 inches. It also gives sin θ = H / L for finding an angle, and (H1 − H2) / L when both rolls sit on blocks.

The unit's Table 1 lists common angles for a 5-inch bar — 0.4358" at 5°, 1.2941" at 15°, 2.5000" at 30°, 3.5355" at 45°, 4.3301" at 60°, and others. This page reproduces every row of that table to four decimal places, and the table is shown under the tool.

Everything is calculated in your browser; nothing is sent or stored.

The arithmetic is exact, but a physical set-up is only as good as the bar's roll spacing, the gauge blocks and the surface plate. Results are rounded to 0.0001 inch or 0.001 mm.

This page is a calculation aid. It does not choose gauge blocks for you or replace inspection of the finished set-up.

Sources

Workforce LibreTexts — Manufacturing Processes 4-5, Unit 3: Sine Bar (CC BY) — Formula, worked example and the 5-inch common-angle table

Frequently asked questions

What is the sine bar formula?

Gauge block height = sine bar length × sin(angle), where the length is the distance between the roll centres. For the angle: sin(angle) = height ÷ length.

What height for 30° on a 5-inch sine bar?

2.5000 inches, because sin 30° is exactly 0.5. The source uses this as its worked example.

Is the length the overall bar length?

No. It is the distance between the centres of the two rolls — the figure the bar is sold by, such as 5 in or 100 mm.

How do I enter an angle like 12° 30′?

Enter 12 in degrees, 30 in minutes and 0 in seconds. The tool converts to decimal degrees for the calculation.

What if both rolls are on blocks?

Choose the angle mode and enter both stacks. The angle is asin((H1 − H2) ÷ L), as the source gives.

Can I use this for a sine plate?

Yes — the same relationship applies. Enter the plate's roll-centre distance as the length.