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Central Angle Theorem Calculator

Online arc length calculator. Enter the radius and central angle in degrees to compute the arc length (radius × angle in radians), with degree-to-radian conversion—ideal for circles.

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Arc l=πrθ/180 (degrees); l=rθ (radians)
θ
Radius
Angle at center

📖 Tutorial | Central Angle

1. Definition
A central angle has its vertex at the center.
2. Formula & Notation
rRadius
θCentral angle
lArc, πrθ/180
3. Properties & Laws
  • Equal angles subtend equal arcs and chords;
  • l=πrθ/180;
  • In radians l=rθ;
  • Sector area πr²θ/360.
4. Steps
  1. Enter r and θ;
  2. Click "Find Arc";
  3. Or click "Load Example".
5. Worked Examples
Example: r=6, θ=60°.
Solution: l = 2π ≈ 6.28.
6. Common Pitfalls
Convert degrees before multiplying r;
θ≤360;
Arc is not chord.

❓ FAQ | Central Angle

Central angle?
Vertex at the center.
Arc length?
l=πrθ/180.
r=6,θ=60?
≈6.28.
Angle and arc?
Equal angles, equal arcs.
Sector area?
πr²θ/360.
Radians?
l=rθ; 180°=π.