Documentation / @interstellar-tools/constants / TWO_PI

Variable: TWO_PI

const readonly TWO_PI: number;

Defined in: math.ts:69

The circle constant τ (tau), equal to 2π (≈ 6.283185307179586). Useful for full rotations, radians-per-turn calculations, angular velocity, and other periodic math where factors of 2 arise naturally.

$$\tau =2\pi$$$$1\text{turn}=\tau \text{radians}={360}^{\circ }$$$${\theta }_{\text{rad}}=t\tau (\text{turn fraction }t\in [0,1))$$$${\theta }_{\mathrm{deg}}=\frac{{180}^{\circ }}{\pi }{\theta }_{\text{rad}}={360}^{\circ }t$$$$\omega =2\pi f=\tau f\text{(angular frequency)}$$$$T=\frac{2\pi }{\omega }=\frac{\tau }{\omega }\text{(period)}$$

INFO

• Using τ often simplifies formulas that involve full cycles (e.g., Fourier analysis, rotations, oscillator phase), eliminating stray factors of 2.
• TWO_PI is a runtime numeric constant; do not compare floating-point results using === when they involve trigonometric operations-prefer tolerance checks.

See

• https://en.wikipedia.org/wiki/Tau\_(mathematics)
• https://en.wikipedia.org/wiki/Radian

Examples

import { TWO_PI } from '@interstellar-tools/constants';

// A quarter turn (π/2 radians)
const quarterTurn = 0.25 * TWO_PI; // ≈ 1.5707963267948966

// Point on the unit circle at 1/8 of a turn
const t = 1 / 8;
const angle = t * TWO_PI; // τ/8 = π/4
const x = Math.cos(angle); // ≈ 0.7071
const y = Math.sin(angle); // ≈ 0.7071

// Wrap any angle (radians) to [0, τ):
function wrapTau(theta: number): number {
  const tau = TWO_PI;
  return ((theta % tau) + tau) % tau;
}

// Convert turn fraction to radians:
const radiansFromTurns = (turns: number) => turns * TWO_PI;

// Angular frequency from frequency (Hz):
const omega = (f: number) => TWO_PI * f; // ω = τ f