Calculator
Convert angular displacement (θ) and radius (r) into linear displacement (s).
Example data table
Use these samples to verify your inputs.
| θ (deg) | Radius (cm) | θ (rad) | Arc length s (cm) | Chord length c (cm) | Sector area A (cm²) |
|---|---|---|---|---|---|
| 90 | 10 | 1.57079633 | 15.707963 | 14.142136 | 78.539816 |
| 180 | 5 | 3.14159265 | 15.707963 | 10.000000 | 39.269908 |
| 45 | 20 | 0.78539816 | 15.707963 | 15.307337 | 157.079633 |
These examples use s = rθ with θ in radians.
Formula used
Angle values are converted to radians before calculation.
- Arc length: s = r × θ
- Degree conversion: θ(rad) = θ(deg) × π / 180
- Chord length: c = 2r · sin(θ/2)
- Sector area: A = ½ r² θ
- Turns: turns = θ / (2π)
Radians are unitless, so s uses the same length unit as r.
How to use this calculator
Follow these steps for consistent results.
- Enter angular displacement θ and choose its unit.
- Select radius mode and enter radius or diameter.
- Choose the radius unit and an output unit.
- Press Calculate to show results above the form.
- Use Download CSV or Download PDF from results.
Tip: Use the effective radius at the contact surface.