Arc Length, Chord Length, and Area of a Sector Calculator

An easy to use online calculator to calculate the arc length \( s \), the length \( d \) of the chord and the area \( A \) of a sector given its radius \( r \) and its central angle \( t \).

Formulas for Arc Length, Chord and Area of a Sector

The formulas of the arc length \( s \), the area \( A \) and the length \( d \) of the chord of the sector with angle \( \theta \) within a circle of radius \( r \), shown below, are given by:

\[ s = r \theta \]

\[ A = \frac{1}{2} \theta r^2 \]

\[ d = 2 r \sin(\theta/2) \]

Sector of a Circle
Figure 1. Sector of a Circle showing radius (r), angle (θ), arc length (s), and chord (d)

About the Calculator

Enter the radius and central angle \( \theta \). The two angle inputs are synchronized - change one and the other updates automatically. The angle should be between:

If you enter a value outside these ranges, it will be automatically adjusted to the nearest valid value.

The outputs are:

Tip: Click on the preset buttons (π/6, 30°, etc.) for common angles.

Use the Sector Calculator

Circle Sector Calculator

Enter radius and central angle \( \theta \) (radians and degrees are synchronized)

Radius must be positive
π/6 π/4 π/3 π/2 π
Angle must be between 0 and 2π (≈6.283)
30° 45° 60° 90° 180° 360°
Angle must be between 0 and 360

Click on preset buttons for common angles. Values outside limits will be adjusted.

Results

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More References and Links

Sectors and Circles Problems
Circles, Sectors and Trigonometry Problems with Solutions and Answers
Online Geometry Calculators and Solvers