Math

Central Angle Calculator

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

Calculated Output

Central angle (°) 80.214

Central angle (rad) 1.4

Formula: θ (rad) = arc ÷ radius

Step-by-Step Breakdown

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

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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).