# Diameter of a circle

The diameter of a circle is a straight line which passes through the center of the circle and terminates at both ends at the circumference of the circle.

Notice the diameter's twice the length of the radius of the circle.

So you can now write ...

## ... a formula for calculating the diameter of a circle from its radius

where

• d = diameter of circle
• r = radius of circle

Say the radius r is 5cm (centimeters), then the diameter d is 2r (i.e. 2 x r) = 2 x 5 = 10cm.

Another example?

If r = 2.5m (meters), d = 2 x 2.5 = 5m.

## Next consider how to calculate the circle's diameter from its circumference

• d = diameter of circle
• C = circumference of circle
• π = pi

For instance, if the circle's circumference C = 30cm, then its diameter d = 30/π (30 divided by π) = 9.5cm to 1 d.p. (one decimal place).

The key strokes on your calculator are 30, divide sign (÷), pi sign (π), equals sign (=), giving 9.549296586, which is 9.5 to 1 d.p. - you may need to press a shift or 2nd function button to access π

How about a circle with circumference C = 9m?

Diameter of circle   d  =  9/π  =  2.86m to 2 d.p.

Entering 9, divide sign (÷), pi sign (π), equals sign (=) on your calculator gives 2.864788976 = 2.86 to 2 d.p. (two decimal places).

## Now let's work out the diameter of a circle from its area

• d = diameter of circle
• = square root
• π = pi

If the area of the circle A = 60cm² (square centimeters), its diameter d = 2 (60/π) = 8.7cm to 1 d.p.

Use your calculator's left and right bracket signs

Press left bracket sign, 60, divide sign (÷), pi sign (π), right bracket sign, square root sign (), multiply sign (x), 2 to give 8.740387445 or 8.7 to 1 d.p.

What about a circle with area A = 3m² (square meters)?

Diameter of circle   d  =  2 (3/π)  =  1.95m to 2 d.p.

Your calculator key strokes are the same except enter 3 instead of 60 - the display should show 1.954410048 = 1.95 to 2 d.p.

If you've not already done so, read here about the radius of a circle. Otherwise learn in depth about the circumference of a circle and the area of a circle.

For more on the circle click: