Free · Angle calculators 🕑
Central Angle from Arc Length and Radius
Yes. This model divides positive arc travel by radius and keeps the accumulated angle. It does not reduce the result to a minor arc or one revolution.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
Example in initial displayed units: Arc length (L) 3.141593, Radius (r) 2 gives Central angle (θ) 90, Diameter (2r) 4.
L = rθ with θ in radians; d = 2r
Worked example
Enter these known values and leave the other values blank.
- Arc length (L)
- 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068 m
- Radius (r)
- 2 m
- Diameter (2r)
- 4 m
- Central angle (θ)
- 90 deg
Assumptions and limitations
- Arc length and radius are positive and measured in compatible units. Angle is unwrapped: it can exceed one full turn for accumulated circular travel. The tool does not choose a minor arc or reduce the result modulo 360°.
- Use compatible units and enough independent values. Clear unknowns before solving backward. Original reference drawings are schematic and do not scale to entered values.
Common questions
Can the central-angle result exceed 360 degrees?
Yes. This model divides positive arc travel by radius and keeps the accumulated angle. It does not reduce the result to a minor arc or one revolution.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.