## What is the Radius of a Circle?

The radius of a circle is the distance from the center of the circle to the circumference of the circle. The Latin word “radius” means “straight rod; spoke of a wheel; beam of light” and it is the root word for “radiate”, “radio”, and “ray”.

Ancient mathematicians chose this word because, just like the spoke of a wheel or a ray of light radiating from the sun, the radius of a circle starts at the center of the circle and beams straight out until it reaches the circumference of the circle.

## Radius and Diameter

The diameter of a circle is a chord that passes through the center of the circle. Because it passes straight through the center of the circle, the diameter is basically two radii stuck together.

If you are given the diameter and you need to find the radius, you can split the diameter in half.

If you are given the radius and you need to find the diameter, you can double the radius.

## Examples

What is the diameter?

The radius is \(\green 5\,m\) and the diameter is always twice as long as the radius.

\[2\times5=10\]

So, the diameter is \(\green 10\,m\).

What is the radius?

The diameter is \(\blue 3\, ft\) and the radius is always half as long as the diameter.

\[3\div2=1.5\]

So, the radius is \(\blue 1.5\,ft\).

## When Will I Use the Radius of a Circle?

When you calculate the circumference of a circle, you will plug the radius measurement into the circumference formula.

When you calculate the circumference of a circle, you will plug the radius measurement into the area formula.

The radius is part of the equation of a circle includes because the radius defines how big or small the circle will be.

The unit circle is a circle with a radius of 1 centered at the origin. It is used to define sine, cosine, and tangent in trigonometry.

Radians are one way that you can measure angles. They are defined as the number of radii that the arc length is equal to.