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Central Angle (degrees)

Arc Length

Radius

Diameter

Central Angle Calculator

Our Central Angle Calculator finds a circle's central angle, arc length, or radius — give it any two of the three, and it finds the third.

What Is a Central Angle?

A central angle is the angle formed at a circle's center by two radius lines drawn to the endpoints of an arc. The arc it "cuts off" — the arc length (L) — grows directly with both the angle and the radius: a bigger circle or a wider angle both mean a longer arc.

Central Angle Formula

θ (radians) = L ÷ r
L = θ × r
r = L ÷ θ

Where θ is the central angle in radians, L is the arc length, and r is the radius. Multiply radians by 180÷π to convert to degrees.

Example Calculation

Radius = 10, Arc Length = 15

θ = 15 ÷ 10 = 1.5 radians ≈ 85.94°

✓ Central Angle ≈ 85.94°

Features of Our Central Angle Calculator

✅ Solves for angle, arc length, or radius

✅ Labeled diagram for quick visual reference

✅ Instant, accurate results

✅ Free to use, no sign-up required

Who Can Use This Calculator?

Students & Teachers – For geometry and trigonometry homework

Engineers & Machinists – For arcs, gears, and curved layouts

Designers – For pie charts, dials, and circular layouts

Everyday Users – For quick circle-geometry questions

👉 Try our Central Angle Calculator to solve for any circle's angle, arc, or radius instantly.