π (Pi)

Circle Definition of π (Pi)

The greek letter (pi) is a geometric constant that traditionally appears in numerous formulas relating to circles and angles. 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.

Usage

Note: Traditionally, the constant (pi) is used throughout math in formulas relating to the circle. However, this website uses the constant (tau) instead of (pi) as the default circle constant for reasons discussed here. The substitution can be used to translate between the two constants.

Geometry Formulas

Shown below are some basic geometric formulas in terms of (pi).

Area of Circle π (pi)

The traditional formula for the area of a circle is given in terms of the geometric constant π (pi).
Volume of Cylinder π (pi)

The volume of a cylinder is equal to PI multiplied by its radius squared and its height.

Radians

The constant (pi) traditionally shows up when measuring angles in radians, the preferred unit for measuring angles[1]. Shown to the left below is the circle annotated using (pi). On the right is the circle annotated using (tau) which is the preferred constant for this website.

Radian Angle System π (pi)
Figure 1: Radian Angle System π (pi)
Radian Angle System
Figure 2: Radian Angle System

Advanced Formulas

While (pi) currently appears in advanced formulas through text books and on the web, they are omitted here. See instead the page for (tau) for advanced circle formulas.

links

Τ (Tau) | Concept

The circle constant τ (tau) is a geometric constant approximately equal to 6.283. The numeric value is defined as the length of any circle's circumference divided by the length of its radius.

Radians | Concept

Radians are a unit that measure angle using the radius of a circle. One radian is equal to the amount of rotation required to travel the length of one radius along the circumference of the circle.

references

  1. Radians Versus Degrees
    Wumbo (internal)