Circle Sector & Arc Length Calculator

Calculate arc length, sector area, chord length, and segment properties in real-time with our bidirectional geometry tool. Perfect for students, engineers, and designers.

°
units

Calculation Results

Arc Length
10.47 units
Sector Area
52.36 units²
Chord Length
10.00 units
Segment Area
2.36 units²
All values calculated in real-time

Understanding Circle Sectors & Arc Lengths

A circle sector is a portion of a circle enclosed by two radii and an arc. Our calculator helps you determine key properties of circle sectors including arc length, sector area, chord length, and segment area.

The arc length (s) is the distance along the curved line of the sector. It's calculated using the formula: s = r × θ where r is the radius and θ is the central angle in radians. Since our calculator uses degrees, we automatically convert to radians for calculations.

The sector area is the region enclosed by the two radii and the arc. It's calculated with: A = (θ/360) × πr² or equivalently A = (1/2) × r² × θ (with θ in radians).

The chord length is the straight-line distance between the two points where the radii meet the circle. It's calculated using: c = 2r × sin(θ/2).

This tool is invaluable for geometry students, engineers, architects, and designers working with circular components. The real-time bidirectional calculations allow you to work flexibly with any known parameters.

Frequently Asked Questions

What is a circle sector?

A circle sector is a portion of a circle bounded by two radii and the included arc. It resembles a "pizza slice" of the circle.

How is arc length different from chord length?

Arc length is the distance along the curved section of the circle between two points. Chord length is the straight-line distance between those same two points.

Can I calculate with radians instead of degrees?

Our calculator automatically handles conversions between degrees and radians. Just enter your angle in degrees and we'll convert to radians for the calculations.

What practical applications does this have?

Circle sector calculations are essential in engineering (gear design), architecture (arch and dome calculations), physics (angular motion), and even in everyday applications like pizza slicing or pie chart creation.