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How to Use a Sine Bar with Gage Blocks
Guide · Updated October 27, 2026
A sine bar turns a gage block stack into an exact angle. Put blocks under one roll, leave the other on the surface plate, and the bar's top sits at a precise angle. The only math is one sine, and the only skill is building the right stack.
Skip the trig
The free sine bar calculator gives the stack height for any angle, and the Gage Block Calculator builds the stack. Free, no login.
The formula
Stack height = L × sin(angle), where L is the distance between the roll centers (commonly 5 in, 10 in, 100 mm or 200 mm).
Worked examples
| Bar | Angle | Height | Stack |
|---|---|---|---|
| 5 in | 10° | 0.8682 in | 0.650 + 0.118 + 0.1002 (81-piece) |
| 5 in | 30° | 2.5000 in | 2.000 + 0.500 (81-piece) |
| 100 mm | 15° | 25.882 mm | 20 + 3.5 + 1.38 + 1.002 (88-piece) |
Each stack is worked digit by digit. The method is in how to build a gage block stack, and the metric version is in metric gage block stacks.
Step by step
- Work out the height: Multiply the sine bar length by the sine of the angle.
- Build the stack: Build the fewest-block stack for that height, rounded to your set's smallest step.
- Wring and clean: Clean the plate, rolls and blocks, then wring the stack.
- Set the bar: Put the stack under one roll and rest the other roll on the plate.
- Check and clamp: Sweep the top with an indicator to confirm the angle, then clamp the work.
Tips for accurate angles
- Round the height to your set's smallest step (0.0001 in or 0.001 mm). On a 5 in bar, 0.0001 in is about 4 arc-seconds.
- Keep the stack short and use the fewest blocks. Wear blocks are optional here, but add them in the math if you use them.
- Let the blocks reach the plate's temperature. See temperature compensation.
- Stay under about 45° when you can. Steeper angles magnify height errors.
- Wring properly so the stack doesn't shift: how to wring gage blocks.
FAQ
How do you work out the gage block height for a sine bar?
Height = sine bar length × sin(angle). For a 5 in sine bar at 10°: 5 × 0.173648 = 0.8682 in.
What stack makes 10 degrees on a 5 inch sine bar?
0.8682 in. From an 81-piece set: 0.650 + 0.118 + 0.1002, three blocks.
Where do the gage blocks go under a sine bar?
Under one roll only, with the other roll resting directly on the surface plate. The bar length is the roll center distance.
Why do sine bars get less accurate at steep angles?
As the angle approaches 45° and beyond, a small height error makes a bigger angle error, and the setup gets less stable. Most shops keep sine bar work under about 45° or use a compound setup.
Is there a free sine bar calculator?
Yes. The AskMachinist sine bar calculator gives the stack height for any angle and bar length, and the Gage Block Calculator at gageblockcalc.com builds the stack. Both are free, no login.
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Build your stack in seconds
The free Gage Block Calculator finds the fewest-block combination for inch and metric sets, with wear blocks. No login.
Questions? Ask a machinist.
General shop information only — follow your gage manufacturer's instructions and your quality system.