Inspection and GD&T
Sine bar calculator
Stack height H = L x sin(angle); 30° on a 5 in sine bar is a 2.5000 in stack.
Technical review pending. Formulas and values are cited. This notice comes down after a machinist review.
Stack height
in
H = L x sin(A) = 5 x sin(30°) = 2.5000 in
2.5000 in (63.500 mm). Angle 30° 0' 0".
The gage block stack calculator builds 2.5000 in from the 81-piece inch set.
Source: Machinery's Handbook (sine bar)
How it works
H = L x sin(A); A = asin(H / L)
| Symbol | Meaning | Unit |
|---|---|---|
| H | Gage block stack height under the raised roll | in or mm |
| L | Sine bar length, center to center of the rolls | in or mm |
| A | Angle of the bar top to the surface plate | ° |
Inch stacks show 4 places; metric stacks show 0.001 mm. Angles show 4 decimal places and D-M-S to 1 second.
Worked example: 30° on a 5 in bar
Set a 5 in sine bar to 30°.
- sin(30°) = 0.50000.
- H = 5 x 0.50000 = 2.5000 in.
- Build it from 0.500 in + 2.000 in blocks.
Result: 2.5000 in (63.500 mm) stack, two blocks.
Worked example: 12° on a 5 in bar
Set a 5 in sine bar to 12°.
- sin(12°) = 0.20791.
- H = 5 x 0.20791 = 1.0396 in.
- Build it from 0.1006 in + 0.139 in + 0.800 in blocks.
Result: 1.0396 in (26.405 mm) stack, three blocks.
Worked example: angle from a stack
A 1.2500 in stack sits under a 5 in sine bar.
- H / L = 1.2500 / 5 = 0.2500.
- A = asin(0.2500) = 14.4775°.
- 0.4775° x 60 = 28.65 min, so 28 min; 0.65 x 60 = 39 sec.
Result: 14.4775° (14° 28' 39").
Which bar length
A 5 in bar handles small parts and small angles. A 10 in bar gives better angular resolution: the same stack error moves the angle half as much. Metric bars come in 100 mm and 200 mm on the same logic; 15° on a 100 mm bar is a 25.882 mm stack.
Shop notes
- Sine error grows at steep angles. Rule of thumb: above about 45°, set the complement and turn the part if the setup allows.
- Wring clean blocks and let them reach room temperature before you trust the stack.
- L is the distance between roll centers, not the overall length of the bar.
- Angles from a drawing in degrees, minutes and seconds convert to decimal degrees with the degree converter, or enter the minutes and seconds above.
FAQ
What is the gage block stack for a given angle on a 5 in sine bar?
H = 5 x sin(angle). For 12° that is 5 x 0.20791 = 1.0396 in; for 30° it is 2.5000 in.
5 in or 10 in sine bar?
A 10 in bar gives finer angle resolution, because the same stack error is spread over twice the length. A 5 in bar suits small parts and small setups. The same 30° takes a 5.0000 in stack on a 10 in bar.
What stack do you need for 15° on a 100 mm sine bar?
25.882 mm: 100 x sin(15°) = 100 x 0.25882.
How do you find the angle from a stack you already have?
A = asin(H / L). A 1.2500 in stack under a 5 in bar gives asin(0.2500) = 14.4775°, or 14° 28' 39".
Is a single gage block worth it for a home shop?
A single calibrated block checks micrometers. A full set is for building sine bar and height setups.
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