What is Tau? The Full-Turn Circle Constant

Tau (τ) is defined as 2π, approximately 6.28318530717.... It represents the ratio of a circle's circumference to its radius.

Why tau instead of pi?

Pi relates circumference to diameter. But in most formulas, radius appears more naturally. A full turn is 2π radians with pi, but simply τ radians with tau.

Where tau appears

• A full circle is τ radians
• The period of sin and cos is τ
• Euler's identity: e^(iτ) = 1

Key facts

Fact	Value
Decimal value	6.28318530717...
Equal to	2π
Proposed by	Bob Palais, 2001
Tau Day	June 28 (6/28)

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