What is the formula for arc length?

Arc length L = r × θ, where r is the radius and θ is the central angle in radians. If your angle is in degrees, convert first: θ(rad) = θ(deg) × π / 180.

What unit is the arc length in?

The arc length is in the same unit as the radius. If you enter the radius in centimeters, the arc length is also in centimeters.

What is the difference between arc length and chord length?

Arc length is the curved distance along the circle's edge between the two endpoints. Chord length is the straight-line distance between those same two endpoints.

The sector is the "pie slice" region bounded by two radii and the arc. Its area is A = ½ × r² × θ (θ in radians).

Can I enter angles greater than 360 degrees?

Yes. The calculator accepts any positive angle. An angle greater than 360° (or 2π rad) represents more than one full revolution around the circle.

How do I convert degrees to radians?

Multiply degrees by π/180. For example, 90° = 90 × π/180 = π/2 ≈ 1.5708 radians. This tool accepts either unit and converts automatically.

Can it find the arc length of a curve like y = x²?

No. This calculator handles arcs of a circle. The length of a general curve needs the integral L = ∫ √(1 + (dy/dx)²) dx over your interval, which a calculus tool or computer algebra system can evaluate.

How do I find the angle from the arc length?

Divide the arc length by the radius to get the angle in radians, then multiply by 180/π for degrees. An arc of 10 on a radius of 10 is 1 radian, or 57.30°.

Arc Length Calculator

Enter a radius and central angle (degrees or radians) to instantly get arc length, chord length, and sector area.

Arc length = radius × angle in radians.

Inputs

Radius (r)

Central Angle (θ)

Angle Unit

Enter radius and angle, then click Calculate.

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Quick answer

Arc length = radius × angle in radians. For a 10 cm radius and a 90° angle that is 10 × π/2 = 15.708 cm. The tool takes degrees or radians and also gives the chord (14.1421 cm here) and the sector area (78.5398 cm²).

Examples

Radius	Angle	Arc length	Chord	Sector area
10	90°	15.708	14.1421	78.5398
10	60°	10.472	10	52.3599
5	180°	15.708	10	39.2699
12	120°	25.1327	20.7846	150.796
1	1 rad	1	0.958851	0.5

Enter the radius and angle.

Summary

The Arc Length Calculator computes the length of a circular arc given a radius and a central angle. Enter the angle in degrees or radians and get the arc length, the straight-line chord length between the two endpoints, and the area of the circular sector — all in one click. Results update in real time with the underlying formulas shown.

How it works

Enter the radius of the circle in any unit (the result uses the same unit).
Enter the central angle and choose degrees or radians.
The tool computes arc length using L = r × θ (angle in radians).
Chord length is calculated as C = 2r × sin(θ/2).
Sector area is calculated as A = ½ × r² × θ.
All three results appear instantly with formula breakdowns.

Use cases

Determine the length of a curved road or track segment.
Calculate material needed for a curved architectural element.
Solve geometry homework involving circles and arcs.
Find the arc length for a given slice of a pie chart.
Design curved furniture or woodworking pieces.
Compute sector area for irrigation or land-use planning.
Verify hand calculations in engineering or physics problems.

Frequently Asked Questions

Last updated: 2026-05-29 · Reviewed by Nham Vu