Equal Areas - Circles vs. Squares
Radius and side lengths of equal areas, circles and squares.
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
