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Math • Arc Length Calculator

Arc Length Calculator

Calculate the arc length of a circle from its radius and central angle in degrees.

Arc Length (L = rθ)
10.472
θ in radians = 1.0472
Sector Area (A = ½r²θ)
52.360
Semicircle Reference (θ = 180°, radius 10)
Area = ½πr²
157.080
Perimeter = πr + 2r
51.416
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Calculation Guide & Reference

Circle Arc Length Mathematics

Arc length calculator computes the length of a circular arc from its radius and central angle in degrees.

Standardized Mathematical Formula
L = r × θ (θ in radians)

Arc length is the fraction of a circle's circumference swept out by the central angle. Since a full circle (360°, or 2π radians) has circumference 2πr, any angle θ (in radians) sweeps out a proportional arc length of r × θ.

Variables:
r:Radius of the circle
θ:Central angle, converted from degrees to radians (θ × π/180)
How It Works (Step-by-Step)
  • 1Enter the circle's radius (r).
  • 2Enter the central angle (θ) in degrees.
  • 3View the arc length, computed as r times the angle in radians.
Real-World Numerical Example
Radius 10, Central Angle 60°

A circular arc has a radius of 10 units and spans a central angle of 60°.

•Convert angle to radians: 60 × π/180 ≈ 1.047 rad.
•Arc length: L = 10 × 1.047 ≈ 10.47 units.
Result: The arc length is approximately 10.47 units.
Calculation Best Practices & Tips
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In statistical analysis, always check both the mean and median to identify if data distribution is skewed by outliers.
When calculating percentage changes, ensure you divide by the original starting baseline value: ((New - Old) / Old) * 100.

Frequently Asked Questions (FAQ)

The formula L = rθ only works when θ is measured in radians, because a radian is defined as the angle that produces an arc length exactly equal to the radius — this makes the relationship a simple direct proportion.

A full circle is 2π radians, so its arc length equals r × 2π — which is exactly the circumference formula, C = 2πr.

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