π (pi)

The definition of π (Pi) in terms of the circumference and diamater of the circle.
Figure 1: π (Pi) Definition

The symbol (pi) is used in math as a geometric constant in formulas and the radian angle system. The value of is naturally occuring and can be found by dividing the length of a circle’s circumference by the length of its diameter.

Traditionally, (pi) has been used in math as the circle constant. However, this website uses the constant (tau) instead of (pi) as the default circle constant[1]. The substitution can be used to translate between the two constants.

Usage

Geometry Formulas

Shown below are some basic geometric formulas in terms of (pi). For advanced formulas, see the page for (tau).

Circumference of Circle π (pi)

Calculate the circumference of a circle given the radius.

Area of Circle π (pi)

Calculate the area of a circle given the radius.

Volume of Cylinder π (pi)

Caclulate the volume of a cylinder given the radius and height.

Radians

The constant (pi) is used when measuring angles in radians to represent a half rotation. Shown below is the radian angle system labeled using on the left and on the right.

This figure illustrates the radian Angle System annotated with the constant π (pi).
Figure 2: Radian Angle System π (pi)
This figure illustrates the radian angle system annotated using the circle constant τ (tau).
Figure 3: Radian Angle System

References

  1. No, really, pi is wrong: The Tau Manifesto
    Michael Hartl