Circumference of a circle (perimeter of a circle)


The circumference of a circle is its boundary line or perimeter.



Given a circle's radius, diameter or area, you can easily work out the length of the circumference.



Circumference of circle from radius of circle




where

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


So if r = 8cm (centimeters), C = 2π x 8 = 50.3 cm to 1 d.p. (one decimal place).


On your calculator, press 2, multiply sign (x), pi sign (π), multiply sign (x), 8, equals sign (=) to give 50.26548246 = 50.3 to 1 d.p. - you may need to press a shift or 2nd function button to access π


What about the circumference C of a circle with radius r = 11m (meters)?


C = 2π x 11 = 69.12m to 2 d.p. (two decimal places).


Grab your calculator again and enter 2, multiply sign (x), pi sign), multiply sign (x), 11, equals sign (=). The display should show 69.11503838 which is 69.12 to 2 d.p.



Circumference of circle from diameter of circle




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


First let's consider a circle with diameter d = 2.5cm

Circumference of circle   C  =  π  x  2.5  =  7.9cm to 1 d.p.


Your calculator key strokes are pi sign (π), multiply sign (x), 2.5, equals sign (=). The display should show 7.853981634 = 7.9 to 1 d.p.


Next what's the circumference C of a circle with diameter d = 50m?

C  =  π  x  50  =  157.08m to 2 d.p.


Press the pi sign (π) on your calculator, followed by the multiply sign (x), enter 50, then press the equals sign (=). 157.0796327 should be displayed which is 157.08 to 2 d.p.



Circumference of circle from area of circle




  • C = circumference of circle
  • π = pi
  • = square root
  • A = area of circle


Say the area A of a circle is 100cm² (square centimeters), then its circumference C = 2π (100/π) = 35.4cm to 1 d.p.


Use the left and right bracket signs on your calculator



Enter carefully left bracket sign, 100, divide sign (÷), pi sign (π), right bracket sign, square root sign (), multiply sign (x), 2, multiply sign (x), pi sign (π), equals sign (=) to give 35.44907702 = 35.4 to 1 d.p.


And if the area A's 11m² (square meters)?


Circumference C = 2π (11/π) = 11.76m to 2 d.p.


The key strokes on your calculator are the same except enter 11 instead of 100. The display should show 11.75712876 which is 11.76 to 2 d.p.


Let's 'round' off circumference of a circle!


Hopefully, having worked through the above examples, you now feel confident about calculating the circumference of a circle.


Check out in more detail the radius, diameter and area of a circle.


For more on the circle click:

Radius of a circle

Diameter of a circle

Area of a circle

Pi (π)


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