# Radius of a circle

The radius of a circle is a straight line between the center and circumference of the circle.

It's half the length of ...

## ... the diameter of a circle

Therefore, if r = radius of circle and d = diameter of circle

For instance, if d = 4cm (centimeters), r = 4 / 2 (4 divided by 2) = 2cm.

*What about if the diameter d is 15cm?*

In this case, the radius r = 15 / 2 = 7.5cm.

*Try to work out the radii (plural for radius) of circles with diameters 6cm, 1m (meter), 40cm and 20m using the formula above.*

The correct answers are 3cm, 0.5m, 20cm and 10m. How did you get on?

Next let's work out the circle radius from ...

## ... the circumference of a circle

where

- r = radius of circle
- C = circumference of circle
- π = pi

Say C = 10cm, then r = 10 / (2π) [10 divided by 2π] = 1.6cm to 1 d.p. (one decimal place).

On your calculator, you'll need to use the left bracket sign

and the right bracket sign

when performing the 2π (2 x π) part of the calculation.

Enter in order 10, divide sign (÷), left bracket sign, 2, multiply sign (x), pi sign (π), right bracket sign, equals sign (=). You may need to press a shift or 2nd function button to access π.

1.591549431 should be displayed which is 1.6 to 1 d.p.

*How about if the circle circumference C is 2m?*

**Radius of circle r = 2 / (2π) = 0.32m to 2 d.p.**

Entering 2, divide sign (÷), left bracket sign, 2, multiply sign (x), pi sign (π), right bracket sign, equals sign (=) on your calculator gives 0.318309886 = 0.32 to 2 d.p. (two decimal places).

Last but not least, how to find the radius of a circle from ...

## ... the area of a circle

For example, if A = 25cm² (square centimeters), r = √ (25 / π) = 2.8cm to 1 d.p.

Press the left bracket sign on your calculator, enter 25, press the divide sign (÷) followed by the pi sign (π), then press the right bracket sign followed by the square root sign (√).

2.820947918 should be displayed which is 2.8 to 1 d.p.

*What about the radius of a circle with area A = 70m**² (meters squared)?*

**Radius of circle r = ****√ (70 / π) = 4.72m to 2 d.p.**

The key strokes on your calculator are the same except enter 70 instead of 25. The display should show 4.720348719 = 4.72 to 2 d.p.

## In other words, there are lots of ways of working out the radius of a circle!

Now move on to study further the diameter, circumference and area of a circle.

For more on the circle click:

Diameter of a circle

Circumference of a circle (perimeter of a circle)

Area of a circle

Pi (π)

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Radius of a circle