Sector Calculator

Comprehensively calculate the area, arc length, and perimeter of a circular sector. Just enter the radius and central angle.

Results

Area

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Arc Length

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Perimeter

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Chord Length

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GUIDE

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Automatically Calculate All Sector Values

A sector is a portion of a circle formed by two radii and an arc. This calculator automatically calculates area, arc length, and perimeter by just entering the radius and central angle. This pie-slice shaped figure is frequently used in everyday life and mathematics.

Using Mathematically Accurate Formulas

Area is calculated using the formula (θ/360) × π × r², arc length as (θ/360) × 2 × π × r, and perimeter as arc length + 2r. Enter the central angle in degrees to get precise results.

Essential Tool for Architecture and Design

Sectors are frequently used in architecture and interior design, such as circular stairs, sector tiles, and portions of circular windows. Calculate accurate area and perimeter for material purchasing and construction planning.

Easy to Understand with Visual Diagrams

Visually displays the shape of the sector with SVG diagrams. The radius and arc are clearly marked, making it intuitively understandable.

Optimized for Math Education

Useful for students learning the properties of sectors and circles. You can see in real-time how area and arc length change as you vary the central angle, helping to develop mathematical intuition.

Supports Both Mobile and Desktop

Responsive design allows convenient use on smartphones, tablets, and desktops anywhere. Calculate on-site immediately or use as educational material in the classroom.

Frequently asked questions

How is the area of a sector calculated?

Area is calculated as (central angle/360) × π × radius². For example, a sector with a 10cm radius and 90° angle has an area of (90/360) × π × 10² ≈ 78.5 cm².

What's the difference between arc length and chord length?

Arc length is the length of the curved edge of the sector (a portion of the circle's circumference), while chord length is the straight-line distance between the two endpoints of that arc. The larger the central angle, the bigger the gap between the two values.

How is the perimeter calculated?

The perimeter of a sector equals the arc length plus twice the radius (arc length + 2r) — it's the total length around the curved edge and the two straight radius edges.

Can I enter the central angle in radians?

This calculator expects the central angle in degrees. If you have a value in radians, convert it first using (radians × 180/π) before entering it.

What is a sector calculator useful for?

It's handy for comparing pizza slice sizes, planning circular staircases or sector-shaped tiles, designing portions of round windows, and any real-life or construction situation where you need quick area and length figures.