What is the sine bar formula?

The gauge-block stack height equals the sine bar length times the sine of the desired angle: H = L x sin(theta). For a 5-inch sine bar set to 30 degrees, the stack is 5 x 0.5 = 2.5000 inches. The roll-to-roll center distance is the length L.

Why is a sine bar so accurate?

Because it converts an angle into a linear height that can be set with gauge blocks accurate to millionths of an inch. The sine relationship is most sensitive near 90 degrees and least sensitive near 0, so sine bars are most accurate for small to moderate angles.

Can I use any gauge-block combination?

You stack blocks to reach the target height as closely as your set allows. The tool reports the exact required height so you can wring together blocks that sum to it. A standard 81-piece set reaches almost any height to 0.0001 inch.

How do I convert decimal degrees to minutes and seconds?

Multiply the decimal part by 60 to get minutes, then multiply the leftover decimal by 60 for seconds. The tool does this automatically so you can match an angle stated in degrees-minutes-seconds on a drawing.

What is a sine plate?

A sine plate is a wider sine bar with a hinged top surface for holding workpieces during grinding or inspection. The same formula applies: stack height equals the plate's hinge-to-roll length times the sine of the angle. Compound sine plates set two angles with two stacks.

Sine Bar / Sine Plate Setup Calculator

A sine bar turns a precise angle into a precise height you can set with gauge blocks, making it one of the most accurate ways to establish or check an angle. This calculator gives the exact gauge-block stack height for any angle, and reverses the math to read an angle from a measured stack.

How it works

The sine bar relationship is exact for a bar of known roll-center length L:

height to angle:  H = L * sin(theta)
angle to height:  theta = arcsin(H / L)

Because the relationship uses sine, the height changes most per degree near 90 and least near 0, so a sine bar is most precise for small and moderate angles. The tool also splits the decimal angle into degrees, minutes, and seconds to match drawing callouts.

Example and tips

For a 5-inch sine bar set to 15 degrees, the stack height is 5 x sin(15 degrees) = 1.2941 inches; wring gauge blocks that sum to that height under the elevated roll. Conversely, a measured 2.5000-inch stack under a 5-inch bar back-calculates to exactly 30 degrees. Keep the bar, blocks, and surface plate clean and wrung tight, and for angles above about 60 degrees consider an angle gauge block set, where the sine method loses sensitivity.