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Circles and Squares - Equal Areas

Radius and side lengths of equal areas, circles and squares

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The area of a circle can be expressed as

Ac = π r2                             (1)

where

Ac = circle area (m2, ft2)

r = circle radius (m, ft)

The area of a square can be expressed as

As = s2                                 (2)

where

As = square area (m2, ft2)

s = side of square (m,ft)

If the area of the circle is equal to the area of the square - then Ac = As and (1) and (2) can be combined to

π r2 = s2                             (3)  

Radius of Circle - Side of Square is known

r = (s2/ π)1/2                              (4)

Side of Square - Radius of a Circle if known

s = (π r2)1/2                               (5)

Example - Circle and Square with equal Area

The side length of a square with the same area as a circle with radius 2 m can be calculated as

s = (π (2 m)2)1/2   

  = 3.54 m

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