Sine Bar Angle Calculator
Calculate the precise gauge block height for any angle on your sine bar. Supports degrees-minutes-seconds input and inch/metric units.
✓ DMS angle input
✓ 5” and 10” sine bar support
✓ 4-decimal precision
Degrees, minutes, seconds
Gage Block Height
2.5000 in
= 63.5000 mm
Quick reference — Gage block heights (inches)
| Angle | 5″ bar | 10″ bar |
|---|---|---|
| 5° | 0.4358 | 0.8716 |
| 10° | 0.8682 | 1.7365 |
| 15° | 1.2941 | 2.5882 |
| 20° | 1.7101 | 3.4202 |
| 25° | 2.1131 | 4.2262 |
| 30° | 2.5000 | 5.0000 |
| 35° | 2.8679 | 5.7358 |
| 40° | 3.2139 | 6.4279 |
| 45° | 3.5355 | 7.0711 |
How Sine Bar Angle Calculation Works
A sine bar uses the fundamental trigonometric relationship H = L × sin(θ) to create precise angles for inspection and machining setups. The sine bar sits on a surface plate with gauge blocks elevating one end.
The Formula
Height = Sine Bar Length × sin(Angle)
5” bar at 15°30': H = 5 × sin(15.5°) = 5 × 0.26724 = 1.3362”
10” bar at 15°30': H = 10 × sin(15.5°) = 10 × 0.26724 = 2.6724”
Common Sine Bar Angles & Heights (5” Bar)
- 5°: 0.4358”
- 10°: 0.8682”
- 15°: 1.2941”
- 30°: 2.5000”
- 45°: 3.5355”
Accuracy Considerations
- Use Grade A or AA gauge blocks for inspection-quality setups
- Clean all contact surfaces thoroughly before assembly
- For angles under 15°, use a 10” sine bar for better height resolution
- Avoid angles above 60° — a sine bar becomes inherently less accurate at steep angles due to the cosine error
⚠️ Practical Limit
Sine bars are most accurate between 0° and 60°. Above 60°, small height errors produce large angle errors. For steep angles, consider a sine plate or direct angular measurement.