# Sector Area Calculator

Calculate sector area, arc length, chord length, and perimeter from radius and central angle. Free online sector calculator for circle geometry.

## What this calculates

Calculate the area, arc length, chord length, and perimeter of a circle sector. Enter the radius and central angle in degrees to get instant results for all sector properties.

## Inputs

- **Radius** — min 0 — The radius of the circle.
- **Central Angle (degrees)** — min 0, max 360 — The central angle of the sector in degrees.

## Outputs

- **Sector Area** — The area of the sector.
- **Arc Length** — The length of the curved arc.
- **Chord Length** — The straight-line distance between the arc endpoints.
- **Sector Perimeter** — The total perimeter of the sector (arc + 2 radii).

## Details

A sector is a pie-shaped region of a circle bounded by two radii and an arc. Think of it as a slice of pizza or a wedge of a pie chart. The central angle determines what fraction of the full circle the sector represents.

Sector Formulas (radius = r, central angle = theta in degrees):

- Sector Area: A = (theta/360) x pi x r^2

- Arc Length: L = (theta/360) x 2 x pi x r

- Chord Length: c = 2r x sin(theta/2)

- Sector Perimeter: P = arc length + 2r

A sector with theta = 180 degrees is a semicircle, theta = 90 degrees is a quarter circle (quadrant), and theta = 360 degrees is the full circle. The chord connects the two endpoints of the arc in a straight line and is always shorter than or equal to the arc length.

Sector calculations are used in pie charts, windshield wiper coverage, radar sweep areas, irrigation systems, and architectural design elements like arched windows and fan-shaped rooms.

## Frequently Asked Questions

**Q: How do I calculate the area of a sector?**

A: Use the formula: Sector Area = (theta/360) x pi x r^2, where theta is the central angle in degrees and r is the radius. For example, a sector with radius 10 and angle 60 degrees has area = (60/360) x pi x 100 = (1/6) x 314.159 = 52.36 square units.

**Q: What is the difference between arc length and chord length?**

A: Arc length is the distance along the curved edge of the sector (part of the circumference). Chord length is the straight-line distance between the two endpoints of the arc. The arc is always longer than or equal to the chord. They are equal only when the angle is zero (both are zero).

**Q: How do I find the arc length of a sector?**

A: Use the formula: Arc Length = (theta/360) x 2 x pi x r. This is the fraction of the full circumference corresponding to the central angle. For a 90-degree sector with radius 8: arc length = (90/360) x 2 x pi x 8 = (1/4) x 50.265 = 12.566 units.

**Q: What is a sector perimeter?**

A: The perimeter (or boundary length) of a sector consists of the arc plus the two straight radii: P = arc length + 2r. Note this is different from the arc length alone. For a quarter circle with radius 5: P = (1/4)(2 x pi x 5) + 2(5) = 7.854 + 10 = 17.854 units.

**Q: Can the central angle be greater than 180 degrees?**

A: Yes. A sector with an angle greater than 180 degrees is called a major sector (the larger portion of the circle). The formulas work the same way. A 270-degree sector covers three-quarters of the circle, and a 360-degree sector is the full circle.

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Source: https://vastcalc.com/calculators/math/sector-area
Category: Math
Last updated: 2026-04-21