What Are Radius, Diameter, and Circumference?

This is, you guessed it, a circle. 😂 

To draw a circle, pick a point to be the center.

Then decide how far the edge will be from the center.

      The distance from the center to the edge of a circle is called the radius.

Diameter

      The length from one edge of a circle through the center to the other side is the diameter.

      The diameter is twice the length of the radius.

2 × radius = diameter

Another way to write this formula is like this:

diameter = 2r

Tip: In math, if you write a number in front of a variable, you don't have to write the × in between. It still means multiplication. 

It's just shorter and easier, since we multiply a lot in math.

Super tip: The 2 is call a coefficient. You'll see that word a lot in the next few years of math. A coefficient is just a number that multiplies a variable, like r.

Tip: You can also find the diameter by adding the radius to itself.

radius + radius = diameter

Finding the Radius

What is the radius of the circle above? 🤔

      Divide the diameter by 2 to get the radius.

14 ÷ 2 = 7

The radius of this circle is 7. ✔️

Finding the Diameter

Can you find the diameter of this circle?

👉 Just double the radius to get the diameter.

diameter = 2r = 2 × 12 = 24

Our diameter is 24! ✔️

Circumference

      The circumference is the total distance around a circle.

Tip: Circumference is similar to the perimeter of a rectangle or square. Our math ancestors just gave it a special name. 🧙‍♂️

Circles have a special property:

      If you divide the circumference of any circle by its diameter, you get the number 3.14159....

This special number goes on forever, and it's the exact same for every circle!

Even more special, its digits after the decimal point never repeat a pattern!

It's such a special number that it gets its own name, pi!

Pi is usually written with the Greek symbol π.

π = about 3.14
Memorise this! 👆

      To find the circumference of a circle, just multiply the diameter by pi, or 3.14!

Circumference = π × d

So the distance around any circle is just its diameter times the number 3.14159... 🤯 It's awesome how the universe works like that!

Math people usually write the formula even shorter, like this:

c = πd

Tip: even though π looks like a variable, it's actually called a constant. It's just a shortcut for the never-ending number 3.141592653589....

Finding the Circumference from the Radius

Remember:

d = 2r
diameter = 2 × radius

We can actually rewrite the circumference equation using radius instead of diameter:

c = πd = π(2r)

Mathematicians usually write it like this:

c = 2πr

      The formula for circumference of a circle is 2πr.

Let's use this formula to find the circumference of the circle below.

c = 2πr

We plug in the value of the radius.

c = 2π × 6

c = 12π

We can just leave our answer in terms of pi. 😅

If you're curious, 12π is ~37.8.

Tip: ~ means about, or approximately. It's called a "tilde".

Great job learning about radius, diameter and circumference of a circle! 😀🎉

Now, complete the practice to help you master working with radius, diameter, and circumference! 😀 

These are important skills, and the practice will help you remember for long.