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Squaring the Circle - Calculator

Calculator for the edge length of a square and the radius of a circle, if both have the same area. Also the perimeter will be calculated. Squaring a circle geometrically is in fact impossible, a circle can't be constructed from a square and vice versa. Also the exact calculation can't be done, because the value of π (pi) can't be given exactly. But it can be calculated with an approximation at any accuracy.
If circle and square should have the same area, the edge length of the square has to be root-of-pi-times the circle radius, a = √π r.
Please enter one value, the other values will be calculated. Also pi can be entered or something like 2*pi.

Edge length:

Round to    decimal places.

The unit is the same for edge length, radius and perimeter. The area has this unit squared. For example, length in centimeters, area in square centimeters.

Square and circle with the same area

Example: square and circle with almost the same area. The circle radius is 100 pixels. The edge length of the square is 177 pixels, because there are no fractions of pixels.

Squaring the circle is an insoluble problem of classical geometry in the antique. The term goes back to Anaxagoras, who worked in ancient Greece, and dates back to around 430 BCE. The impossibility of the solution refers to the fact that no square can be constructed that has the same area as a given circle. This is equivalent to stating that π is a transcendent number, i.e. an irrational number that cannot be calculated as fraction or root of whole numbers. In this calculator, as in all others, an exact calculation is impossible due to the infinite decimal places of π, only an approximation. But in all practical cases an approximation is sufficient.

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