How to use this calculator
- Choose the mode. Pick "Find gauge stack (from angle)" if you know the angle, or "Find angle (from gauge stack)" if you know the stack height.
- Enter the bar length. Enter the sine bar roll-centre length L (5 in / 127 mm, 100 mm or 200 mm).
- Enter the known quantity. Enter either the target angle θ or the measured gauge-block stack height h.
- Read the result. Read the gauge stack height to wring up, or the resulting set angle.
How it works
A sine bar is a precision bar with two equal rolls a known distance apart.
Raising one roll on a stack of gauge blocks tilts the bar by a right-triangle
relationship: the stack height is the opposite side, the roll-centre length is
the hypotenuse, so
h = L · sin θ
where L is the roll-centre distance and θ the set angle
(with θ in radians, θrad = θdeg · π/180).
To go the other way — reading the angle from a measured stack — invert it:
θ = asin(h / L). Because sin θ ≤ 1, the stack can never
exceed the bar length; ask for h > L and the angle is geometrically
impossible, so the calculator clamps it to 90° and warns.
Worked example
Verified against the live calculator
A 100 mm sine bar set to 30° needs a stack of
h = 100 × sin 30° = 50.000 mm. Wring up a 50 mm gauge-block stack
under one roll and the bar sits at exactly 30°. Conversely, a measured 50 mm
stack under that 100 mm bar reads back as
θ = asin(50 / 100) = 30°. Those are the numbers the calculator
shows for these inputs.
Frequently asked questions
How do you calculate a sine bar gauge block stack?
The gauge-block stack height is h = L · sin θ, where L is the sine bar roll-centre length and θ is the angle you want to set. For a 100 mm bar at 30°, h = 100 × sin 30° = 50.000 mm — wring up a 50 mm stack of gauge blocks under one roll and the bar sits at exactly 30°.
How do I find the angle from a known gauge stack?
Invert the formula: θ = asin(h / L). Divide the stack height by the bar length and take the inverse sine. A 50 mm stack under a 100 mm bar gives θ = asin(50 / 100) = asin(0.5) = 30°.
What is the length of a sine bar?
The length L is the roll-centre distance — the centre-to-centre spacing of the two precision rolls — not the overall bar length. Common sizes are 5 in (127 mm), 100 mm and 200 mm. Always use the rated roll-centre length in the formula, which is marked on the bar.
Why can a sine bar not set angles up to 90 degrees easily?
Because h = L · sin θ, the stack height grows toward L as the angle approaches 90°, and sin θ can never exceed 1, so the stack can never exceed the bar length. Above roughly 45–60° the sine function flattens, so small stack errors cause large angle errors — sine bars are most accurate for small to moderate angles.
Does a sine bar work in metric and imperial?
Yes. Enter the bar length and stack in mm or inches and the math is identical, because h = L · sin θ is dimensionless in the sine term. A 5 in bar at 30° needs a 2.5 in stack; a 100 mm bar at 30° needs a 50 mm stack. Toggle SI/Imperial in the header.
Method & assumptions
- The length
Lis the roll-centre distance (centre-to-centre of the two rolls), not the overall bar length — common bars are 5 in (127 mm), 100 mm and 200 mm. - Assumes a flat, clean surface plate and gauge blocks wrung into a single stack with no dirt or burrs between faces.
- Sine bars are most accurate at small to moderate angles; as θ approaches 90° the sine flattens and small stack errors blow up the angle error.
- For angles above about 45° a sine plate or compound stack is usually preferred over a plain sine bar.