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


  • 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 = 70m² (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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