Equal Areas  Circles vs. Squares
Radius and side lengths of equal areas, circles and squares.
The area of a circle can be expressed as
A_{c} = π r^{2} (1)
where
A_{c} = circle area (m^{2}, ft^{2})
r = circle radius (m, ft)
The area of a square can be expressed as
A_{s} = s^{2} (2)
where
A_{s} = square area (m^{2}, ft^{2})
s = side of square (m,ft)
If the area of the circle is equal to the area of the square  then A_{c} = A_{s} and (1) and (2) can be combined to
π r^{2} = s^{2} (3)
Radius of Circle  Side of Square is known
r = (s^{2}/ π)^{1/2} (4)
Side of Square  Radius of a Circle if known
s = (π r^{2})^{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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