Worked example
To set a 5 in sine bar to 30°, h = 5 × sin 30° = 5 × 0.5 = 2.5 in. With a 200 mm bar and a 100 mm stack the angle is arcsin(100 / 200) = arcsin(0.5) = 30°, again exactly, because sin 30° is exactly one half.
Stack heights for common angles
From h = L × sin α for the usual bar lengths (5 and 10 in in inches, 100 and 200 mm in millimetres).
| Angle | 5 in bar | 10 in bar | 100 mm bar | 200 mm bar |
|---|---|---|---|---|
| 5° | 0.4358 | 0.8716 | 8.716 | 17.431 |
| 10° | 0.8682 | 1.7365 | 17.365 | 34.730 |
| 15° | 1.2941 | 2.5882 | 25.882 | 51.764 |
| 20° | 1.7101 | 3.4202 | 34.202 | 68.404 |
| 25° | 2.1131 | 4.2262 | 42.262 | 84.524 |
| 30° | 2.5000 | 5.0000 | 50.000 | 100.000 |
| 45° | 3.5355 | 7.0711 | 70.711 | 141.421 |
How a sine bar is used
- The bar rests on one roll on the surface plate and the other on the gauge block stack. The workpiece sits on the bar; its top face is then at the set angle to the plate.
- Past about 45° a sine bar loses accuracy: a small error in the stack height makes a larger error in the angle, because cos α gets small. Use a sine plate or a compound sine fixture for steep angles.
- For a measured angle, put the bar on the part and adjust the stack until an indicator reads the same at both ends, then read the angle from the stack height.
- Check that the surface plate, rolls and gauge blocks are clean: a speck of dirt is a wrong angle.
Frequently asked questions
How do I calculate sine bar height?
Height h = L × sin α, where L is the distance between the roll centres. For a 5 in bar at 30°: 5 × 0.5 = 2.5 in.
How do I find the angle from the gauge block height?
α = arcsin(h / L). A 100 mm stack under a 200 mm bar gives arcsin(0.5) = 30°.
What length is a sine bar?
Common bars are 5 in, 10 in, 100 mm and 200 mm between the roll centres. The calculator takes any length, as long as height and length use the same unit.
Why is a sine bar less accurate at steep angles?
Above roughly 45° the sine curve flattens against the cosine: the same error in stack height produces a larger angle error. A sine plate or a compound fixture is better for steep angles.
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Making parts for a customer who wants paperwork?
Automotive and aerospace customers ask for proof that the parts match the drawing. See first article inspection (FAI), PPAP explained and the true position calculator.