Calculate the area of the square first by multiplying its side length by itself. For example, suppose the side of your square is 10 cm. Multiply 10 cm x 10 cm to get 100 square centimeters.
Calculate the circle's radius. Because the circle fits entirely inside the square, the diameter is 10 cm. The radius is half the diameter, which is 5 cm.
Calculate the area of the circle using the equation pi x radius squared. Pi's value is 3.14, so the equation becomes 3.14 x 5 cm squared. So you have 3.14 x 25 cm squared, equaling 78.5 square centimeters.
Subtract the area of the circle (78.5 cm squared) from the area of the square (100 cm squared) to determine the area outside the circle, but still within the square. This becomes 100 cm squared - 78.5 cm squared, equaling 21.5 cm squared.