CNC / machinist calculator
Sine Bar Calculator
Set a precise angle for inspection or grinding with a sine bar and a stack of gage blocks. Enter the angle you want and the sine bar length and this calculator gives the exact stack height to place under one roll. It also works the other way, turning a known stack into the angle it produces. It is the standard way to hold an angle far more accurately than a protractor.
How it works
A sine bar is a hardened bar with two precision rolls a fixed distance apart, usually five or ten inches center to center. Resting one roll on the surface plate and lifting the other on a stack of gage blocks tilts the bar by an angle whose sine is the stack height divided by the roll spacing. That is the whole principle: the bar turns the hard problem of holding an angle into the easy problem of stacking precise lengths.
To set an angle, multiply the sine of the angle by the sine bar length to get the stack height, then build that height from gage blocks. To read an angle from a known stack, take the inverse sine of the stack divided by the bar length. A ten inch bar gives finer resolution than a five inch bar because the same block error spreads over a longer base.
Sine bars lose accuracy above about thirty to forty degrees, where the sine changes slowly and small block errors become large angle errors; for steep angles a sine plate or angle blocks are better.
Worked example
To set 30 degrees on a 5 in sine bar, stack 5 x sin 30 = 2.4999999999999996 in of gage blocks under one roll.
Frequently asked questions
How does a sine bar work?
A sine bar has two rolls a fixed distance apart. Lifting one roll on a gage block stack tilts the bar, and the sine of the tilt angle equals the stack height divided by the roll spacing, so stacking precise blocks sets a precise angle.
How do I calculate the gage block stack for an angle?
Multiply the sine of the desired angle by the sine bar length. For a 30 degree angle on a 5 inch bar the stack is 5 times sine 30, which is 5 times 0.5, so 2.5 inches of gage blocks.
What sine bar length should I use?
Five and ten inch bars are standard. A ten inch bar spreads the same block error over a longer base, so it resolves an angle more finely; a five inch bar is more compact for small parts.
Why are sine bars inaccurate at steep angles?
The sine of an angle changes very slowly near ninety degrees, so a tiny error in the gage stack turns into a large error in angle. Above about thirty to forty degrees a sine plate or angle gage blocks hold the angle better.
Can I set metric angles with an inch sine bar?
Yes. The angle is unitless, so any sine bar works for any angle as long as the stack and the bar length are in the same units. Enter the bar length in whatever unit your gage blocks use.
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Sources
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