To determine the area of a circle from its diameter, divide the diameter by two, square it and multiply by π. The formula for calculating the area of a circle is: A = πr^{2}, where r is the radius of the circle.

Mathematician Archimedes (287-212 B.C.E) was first to calculate the area of a circle. He recognized that the area of a hexagon inscribed inside a circle was a gross approximation of the area of the circle. The area of a hexagon is calculated by breaking it into six equilateral triangles where the base of the triangle is the length of one side of the hexagon and the other two legs of the triangle are equal to the radius of the circle.

Archimedes realized that as the number of sides on a polygon approaches infinity, the area is equal to the square of the radius of the circle times a constant, to which he assigned the Greek letter π.