The formula for pi relates the circumference and diameter of a circle. It can be used to calculate the value of pi if the measurements of circumference and diameter of a circle are given. Pi is a Greek letter, its symbol is π and in geometry, it is the ratio of the circumference of any circle to the diameter of that circle. In decimal form, the value of pi is approximately 3.14159... It cannot be written as an exact decimal as it has digits that go on forever. The pi formula can be expressed as, Pi (π) formula = (Circumference / Diameter) .

There are many formulas of pi of many types, including series, products, geometric constructions, limits, special values, and pi iterations. Pi is intimately related to the properties of circles and spheres. For a circle of radius r, the circumference and area are given by 2πr and πr^2, respectively. Similarly, for a sphere of radius r, the surface area and volume enclosed are 4πr^2 and (4/3)πr^3, respectively.

Here are some examples of formulas involving pi:

• The perimeter of a circle with radius r is 2πr.
• The area of a circle with radius r is πr^2.
• The volume of a sphere with radius r is (4/3)πr^3.
• The surface area of a sphere with radius r is 4πr^2.
• Machins formula: π/4 = 4 arctan(1/5) - arctan(1/239).
• The Bailey–Borwein–Plouffe (BBP) formula: π = ∑(k=0 to infinity) [16^-k (4/(8k+1) - 2/(8k+4) - 1/(8k+5) - 1/(8k+6))].
• The Ramanujan formula: 1/π = (2√2)/9801 ∑(k=0 to infinity) [(4k)!(1103+26390k)/(k!)^4 396^(4k)].

Note that pi is an irrational number, meaning that it cannot be expressed exactly as a ratio of two integers, although fractions such as 22/7 are commonly used to approximate it.