Parts of a circle

What is a circle?

You have seen circles everywhere. They have a perfectly round shape, which makes them great for hula hooping!

Every circle has a center, a point that lies exactly in the middle of the circle.

A circle is a shape where the distance from the center to the edge is always the same, no matter which way you go. That distance has a name: the radius.

Now imagine a straight line that goes from one edge of the circle, through the center, to the other edge. That line is called the diameter. The diameter is made of two radii end to end, so the diameter is always 2 times the radius. If the radius is 4 cm, the diameter is 8 cm.

One more word to know: the circumference. That is the distance all the way around the outside of the circle, like the circle's perimeter. If you walked along the edge of a circle all the way back to where you started, you walked the circumference.

What is circumference?

The circumference is the distance around the outside of a circle. It is the circle's perimeter.

To find the circumference of a circle, you can use either of these two rules:

Circumference = π x diameter

Circumference = 2 x π x radius

Both rules give the same answer, because the diameter is always 2 times the radius. The symbol π (called pi) is a special number, about 3.14, that shows up whenever you measure around a circle.

For example, if a circle has a diameter of 10 cm, its circumference is about 3.14 x 10 = 31.4 cm. If a circle has a radius of 5 cm, its diameter is 10 cm, so its circumference is about 31.4 cm too.

Need to find the diameter of a circle? It is easy once you know the radius, the circumference, or the area.

Using the radius: The radius is the distance from the center of the circle to its edge. The diameter is twice the radius, so just double it. If the radius is 4 cm, the diameter is 4 x 2 = 8 cm.

Using the circumference: The circumference is the distance around the circle. Divide it by π (about 3.14) to get the diameter. If the circumference is 15.7 cm, the diameter is about 15.7 / 3.14 = 5 cm.

Using the area: Divide the area by π, find the square root of that to get the radius, then double it to get the diameter.

Why do we learn about circles?

Circles show up everywhere in the real world. Architects use curved arcs when designing buildings, and engineers use circles when designing gears and wheels.

What is the difference between a radius and a diameter?

The radius is the distance from the center of the circle to its edge. The diameter goes all the way across the circle, passing through the center, from one edge to the other. So the diameter is always exactly 2 times the radius.

That one simple rule lets you switch between the two: double the radius to get the diameter, or halve the diameter to get the radius.

In this lesson, you discover the special connection between a circle's diameter and its circumference. If you measure the distance across many circles and the distance around them, you will find something surprising: the circumference is always a little more than 3 times the diameter. That little-more-than-3 number is π, about 3.14.

Then you practice finding the circumference when you are given the diameter or the radius. Remember, if you only know the radius, double it first to get the diameter, then multiply by π.