Sine Bar Calculator
Calculate the gage block height needed to set a sine bar to any angle, or find the angle from a known stack height. Supports DMS input/output, inches & millimeters.
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 a sine bar works
A sine bar uses the relationship sin(θ) = opposite / hypotenuse. The bar length is the hypotenuse, and the gage block stack under one roller is the opposite side.
To find the angle from a known height:
Example: For a 5-inch sine bar at 30°, the gage block height is 5 × sin(30°) = 5 × 0.5000 = 2.5000 inches.
When to use a sine bar
Angle inspection
Verify machined angles on tapers, dovetails, and chamfers during quality inspection.
Precision grinding
Set workpieces to exact angles on surface grinders for tooling and fixture work.
Milling setups
Tilt workpieces for angular milling operations when a rotary table isn't available.
CMM verification
Cross-check CMM angle measurements with a mechanical reference standard.
Tool & die work
Set press-brake punches, die inserts, and cutting tools to specified relief angles.
Calibration
Calibrate angle-measuring instruments like protractors and digital inclinometers.
Frequently asked questions
What is a sine bar?
A sine bar is a precision metrology tool used by machinists and quality inspectors to measure or set accurate angles. It consists of a hardened steel bar with two precision-ground cylinders (rolls) at each end, set a fixed distance apart — typically 5 inches, 10 inches, 100 mm, or 200 mm.
How do I calculate gage block height for a sine bar?
Use the formula: Height = Bar Length × sin(Angle). For example, for a 5-inch sine bar at 30°: Height = 5 × sin(30°) = 5 × 0.5 = 2.5000 inches. Stack gage blocks to this height under one roller.
What is DMS format?
DMS stands for Degrees, Minutes, Seconds — a way to express angles more precisely than decimal degrees. One degree = 60 arc-minutes, one arc-minute = 60 arc-seconds. For example, 30° 15' 45" means 30 degrees, 15 minutes, and 45 seconds.
Why does accuracy decrease above 45°?
Above 45°, the sine function's rate of change decreases (its derivative, cosine, gets smaller). This means small errors in gage block height produce larger angular errors. For angles above 45°, consider using a sine plate, compound angles, or the complementary angle approach.
What is the difference between a sine bar and a sine plate?
A sine plate has a wider working surface (a plate instead of a narrow bar) and often includes clamping features. Sine plates are better for larger workpieces and angles above 45°. The math is identical — both use Height = Length × sin(Angle).
Can I use metric and imperial units?
Yes. This calculator supports both inches and millimeters. Common sine bar lengths include 5 in, 10 in (imperial) and 100 mm, 200 mm, 300 mm (metric). Results automatically show both unit conversions.
How accurate are gage block stacks?
High-quality (Grade B) gage blocks are accurate to ±0.000050 inches (50 millionths). Grade 0 blocks are accurate to ±0.000002 inches. Combined with a precision sine bar, you can achieve angle accuracy of a few arc-seconds.
What if my height exceeds the bar length?
The gage block height can never exceed the sine bar length — that would require an angle greater than 90°, which is physically impossible. If you need a very large angle, use a shorter bar or a compound angle setup.
How do I convert between DMS and decimal degrees?
Decimal = Degrees + (Minutes ÷ 60) + (Seconds ÷ 3600). For example, 30° 15' 45" = 30 + 15/60 + 45/3600 = 30.2625°. This calculator handles the conversion automatically.
What is a compound sine angle setup?
A compound sine setup uses two sine bars oriented 90° to each other to set an angle in two planes simultaneously. This is required when a workpiece needs both tilt and rotation. The math involves calculating two separate gage block heights for each axis.