Central Angle Calculator

Find a circle's central angle from arc length and radius.

Central angle (°) 80.214

Central angle (rad) 1.4

Formula: θ (rad) = arc ÷ radius

Step-by-step with your numbers:

1. Values used:

2. Arc length = 7

3. Radius = 5

5. Central angle = 80.214°

6. Central angle = Arc length / Radius = 7 / 5 = 1.4rad

Did we solve your problem today?

The central angle subtends an arc at the centre of a circle.

The math behind it

In radians, the central angle equals arc length divided by radius. Multiply by 180/π for degrees.

Arc 7, radius 5 → 1.4 rad ≈ 80.2°.

How is this related to arc length?

Arc length = radius × central angle (in radians).