Machining and Fastener Charts
Sine bar gauge block height.
Choose a sine bar length and enter the angle you want to set, or the gauge block stack you have. You get the stack height or the angle. Runs in your browser; nothing is sent or stored.
Inputs
Result
Fill the form and press Calculate.
Answer first. Gauge block height = bar length x sin(angle). A 5 inch sine bar set to 30 degrees needs 2.500 inches of gauge blocks; a 100 mm bar set to 15 degrees needs 25.882 mm.
Worked example
You want 12 degrees on a 10 inch sine bar. sin(12 degrees) = 0.207912, so the stack is 10 x 0.207912 = 2.07912 in. Build it from gauge blocks as close to 2.0791 in as the set allows, then check the angle with a dial indicator along the work.
How it works
The bar. A sine bar is a hardened bar with two precision rollers a fixed distance apart (commonly 100 mm, 5 in or 10 in). Raising one roller on a gauge block stack tilts the bar. The side opposite the angle is the stack, the hypotenuse is the roller distance, so sin(angle) = stack / length.
Reverse. To find the angle from a stack, use angle = asin(stack / length).
Practical note. The method is exact on paper, but the result depends on a flat surface plate, accurate gauge blocks and a dial gauge or level to confirm the top surface is flat. Rounding in the stack height becomes angle error, and a longer bar gives finer control for the same stack error.
Sources
- Sine bar - Wikipedia (principle, standard lengths) (opened 2026-10-16)
The sine relationship and the common bar lengths of 100 mm, 5 in and 10 in come from this page. Stack height = length x sin(angle) is that relationship with the bar length as the hypotenuse.
FAQ
What is the sine bar formula?
Gauge block height = length of the bar between roller centres x sine of the angle. In reverse, angle = arcsine of height divided by length.
What are the common sine bar sizes?
100 mm, 5 inch and 10 inch bars are common. A 5 inch (127 mm) bar is the most common size in the U.S.
How do I set 30 degrees on a 5 inch sine bar?
Stack gauge blocks to 2.500 inches: 5 x sin(30 degrees).
Why use a longer sine bar?
For the same error in the stack, a longer bar gives a smaller angle error, so it is easier to set an angle precisely.
Can I use millimetres and inches together?
No. Keep the bar length and the stack height in the same unit.