Visual demonstration of pi ( π ). Pi is the factor by which the diameter of a circle must be multiplied to get its circumference. Pi is the same for all circles and has a value of about 3.14159265 ... π is irrational (not a ratio of two integers) and is infinitely long, which gives it a special fascination, most brilliantly expressed in Carl Sagan's "Cosmos".

The animation starts with a circle (yellow) with its diameter (d) shown as a black arrow. From this black diameter, arise three lines (1 blue, 2 purple and 3 red) which migrate outwards to map to the edge of the circle. These three diameter lengths almost completely go around the circle but they leave a small gap at the bottom (0.14159 of a diameter). These three diameter lengths + their shortfall then unwrap to form a straight line (green) of length d x 3.14159. When the diameter is 1, then the circumference is π.

Try our circle and area calculator to derive various values from different starting points. This calculator allows you to find values from all starting points. For example, you can start with the volume of a sphere and get the circumference!

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