Sine Bar Calculator (Gauge Block Stack for an Angle)
The gauge block stack that tilts a sine bar to a wanted angle, the angle a given stack produces, and how much a small error in the stack throws the angle off.
Results
Gauge block stack needed
50.0000
mm
Angle given by that stack
14.4775
°
Angle error from 0.01 mm error in the stack
23.8
″
Taper over 100 mm of length
57.735
mm
What this tool does
A sine bar is a precision bar with two rollers a known distance L apart; raise one roller by a stack of gauge blocks of height H and the bar tilts to the angle whose sine is H ÷ L. A 100 mm bar needs 50 mm of blocks for 30°. The method is most accurate at small angles: as the angle grows, the same error in the stack moves the angle more, which is why sine bars are rarely used above about 45°. Use the distance between roller centres, not the overall length of the bar.
Formula
stack height H = L × sin θ · θ = asin(H ÷ L) · angle error per 0.01 mm = 0.01 ÷ (L cos θ)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
bl | Length of the sine bar (between roller centres) | mm |
an | Angle to set | ° |
ht | Gauge block stack you have (to read the angle) | mm |
H | Gauge block stack needed | mm |
AN | Angle given by that stack | ° |
ER | Angle error from 0.01 mm error in the stack | ″ |
TP | Taper over 100 mm of length | mm |
Worked example
- Length of the sine bar (between roller centres)100 mm
- Angle to set30 °
- Gauge block stack you have (to read the angle)25 mm
- Gauge block stack needed50.0000 mm
- Angle given by that stack14.4775 °
- Angle error from 0.01 mm error in the stack23.8 ″
- Taper over 100 mm of length57.735 mm
Limitations
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.