Analytic results Circumference Main article: Circumference The ratio of a circle's circumference to its diameter is π (pi), an irrational constant approximately equal to 3.141592654. Thus the circumference C is related to the radius r and diameter d by: 𝐶 = 2 𝜋 𝑟 = 𝜋 𝑑 . Area enclosed Area enclosed by a circle = π × area of the shaded square Main article: Area of a circle As proved by Archimedes , in his Measurement of a Circle , the area enclosed by a circle is equal to that of a triangle whose base has the length of the circle's circumference and whose height equals the circle's radius, [11] which comes to π multiplied by the radius squared: A r e a = 𝜋 𝑟 2 . Equivalently, denoting diameter by d , A r e a = 𝜋 𝑑 2 4 ≈ 0.7854 𝑑 2 , that is, approximately 79% of the circumscribing square (whose side is of length d )....