One full revolution = τ radians. τ/4 = 90°. τ/2 = 180° = π radians. The circumference of a circle is C = τr.
Comparison of formulas using tau vs pi
| Formel | mit π | mit τ |
|---|---|---|
| Umfang | 2πr | τr |
| Kreisfläche | πr² | τr²/2 |
| Volle Drehung | 2π rad | τ rad |
| Eulers Identität | eⁱπ+1=0 | eⁱτ=1 |
| Gaußsches Integral | √(2π) | √τ |
With π, a quarter turn is π/2: half of the full-turn constant. With τ, a quarter turn is τ/4: literally one quarter. Every fraction of a turn maps directly to the same fraction of τ.
Tau τ is irrational. Its decimal expansion never ends and never repeats. Every digit shown below is computed from the definisi lingkaran.