How does the Arc Length Calculator work?

Circular arc: L = rθ (θ in radians) or L = (θ/360°) × 2πr (degrees) Then: General curve: L = ∫ √(1 + (dy/dx)²) dx (calculus) Then: Approximations: straight line distance for small arcs Then: Chord vs. arc: arc always longer except in limit.

Can you give an example of how to use the Arc Length Calculator?

Example: Input r=5, theta=π/3 gives a result of Arc 5.236.

Is the Arc Length Calculator free to use?

Yes — completely free with no registration, download, or subscription required. All calculations happen instantly in your browser.

How accurate is the Arc Length Calculator?

Our Arc Length Calculator uses verified mathematical formulas and is accurate to multiple decimal places. Results are calculated in real-time using the same methods used by professionals.

Mathematics

Arc Length Calculator

Arc Length

Radius (r)

Central angle (θ radians)

Calculates arc length along curve or circular arc from radius and angle.

Symbol	Name	Unit	Description
L	∫ √(1 + (dy/dx)²) dx (calculus)	—	∫ √(1 + (dy/dx)²) dx (calculus)

Difficulty:intermediate

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Did You Know?

Arc length element ds = √(dx² + dy²) = |r'(t)| dt along parametric curves.

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Arc Length Calculator

Arc Length

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