tau

Represents the mathematical constant equal to 2π (approximately 6.28318), defining the ratio of a circle's circumference to its radius.

Overview

A fundamental mathematical constant gaining popularity as an alternative to pi, particularly valued for its natural relationship to circular and periodic phenomena.

Increasingly preferred in modern mathematics education for its more intuitive representation of full circle rotation
Common in physics and engineering for angular frequency and periodic motion
Appears frequently in trigonometry, signal processing, and quantum mechanics
Simplifies many mathematical formulas where 2π would traditionally appear

Examples

Express the circumference of a circle in terms of radius using tau.

C = \tau r

C = \tau r

Show the relationship between tau and pi.

\tau = 2\pi

\tau = 2\pi

Express the period of a simple harmonic oscillator using tau.

T = \tau\sqrt{\frac{m}{k}}

T = \tau\sqrt{\frac{m}{k}}