# Arcs and sectors

A sector is a slice of a circle, like a pizza wedge. An arc is the curved edge of that slice. Both are fractions of the whole circle.

Maths (school) · Part 05: Angles and area · Card 6 of 8 · Last updated 2026-10-19

## Analogy

Like cutting a pie: a quarter of the pie has a quarter of the area and a quarter of the crust.

## Example

**Sector 90 degrees, r = 6**

Fraction = 90 / 360 = 1/4
Area = 1/4 x pi x 6^2 = 9 x pi = 28.3
Arc = 1/4 x 2 x pi x 6 = 3 x pi = 9.4

## In practice

Pie charts are built from sectors, and each angle shows a share of the total.

## Practice

### Flashcards

- **What fraction of a circle is a 90 degree sector?** One quarter, because 90 / 360 = 1/4.

## Questions people ask

### How do you find the area of a sector?

Work out the fraction of the circle: the angle divided by 360. Then multiply that fraction by the area of the whole circle, pi x r^2. A 90 degree sector is 1/4 of the circle, so it takes a quarter of the area.

### What is the difference between an arc and a sector?

An arc is only the curved line along the edge, so its length is part of the circumference. A sector is the whole slice, including the area inside between the two straight radii. You find arc length and sector area using the same fraction.

## Related concepts

- [Circles](https://studyvisually.com/learn/science/maths-school/maths-school-part-5/maths-school-part-5-concept-5)
- [Circle theorems](https://studyvisually.com/learn/science/maths-school/maths-school-part-5/maths-school-part-5-concept-8)

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