# What Are Radians?

## What Are Radians?

Radians are a unit of measurement of an angle.

There are 2π radians in a full rotation.

### Dictionary Definition

The Oxford English Dictionary defines a degree as "a unit of angle, equal to the angle subtended at the centre of a circle by an arc equal in length to the radius."

## Definition of a Radian

1 radian is the angle found when the radius is wrapped around the circle. More generally, the angle in radians is equal to:

• the arc length divided by the radius.

• arc length of a circle with radius 1 (the unit circle).

## A Formula to Define a Radian

We have seen that the angle in radians is equal to the arc length divide by the radius. We can use this to define a formula.

The angle in radians is found using the formula: In this formula, θ is the angle in radians, s is the arc length and r is the radius. The image below shows what we mean by angle, arc length and radius: ## Slider

The slider below shows more about the definition of radians.

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## 2π Radians in a Circle

There are 2π radians in a full rotation (a circle). Using the definition of radians, can you work out why there are 2π radians in a circle?

See the Note to find out why.