basic

Central Angle from Arc Length and Radius Calculator

θ = s / r (radians); θ_deg = s/r · 180/π.

Compute the central angle subtended at the centre of a circle by an arc of given arc length, using the radius: θ_radians = s / r; θ_degrees = θ_radians · 180/π. Inverse of the standard arc-length formula s = r·θ.

Daniel Oh By Daniel Oh
Published Last reviewed 1 min read

Inputs

Results

Enter values and click Calculate to see results.
Was this helpful?

How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

θ_rad = s / r; θ_deg = θ_rad · 180/π.

In depth

Compute the central angle subtended at the centre of a circle by an arc of given arc length, using the radius: θ_radians = s / r; θ_degrees = θ_radians · 180/π. Inverse of the standard arc-length formula s = r·θ.