# 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*