Bearings, headings, and azimuths

When you know two geographic points, distance is one useful quantity — but direction is equally important. A bearing tells you which compass direction to face to look from one point toward another. It's the foundation of navigation, drone flight paths, sector queries ("show me restaurants to the north of me"), and directional UI elements like compass indicators.

The bearing (or forward azimuth) is the angle, measured clockwise from north, from one point toward another. Use the calculator below to build intuition before the formula.

Initial bearing formula

$$\theta = \arctan2\Big(\sin\Delta\lambda \cdot \cos\varphi_2,\;\; \cos\varphi_1 \cdot \sin\varphi_2 - \sin\varphi_1 \cdot \cos\varphi_2 \cdot \cos\Delta\lambda\Big)$$

The result is in radians, in the range $[-\pi, \pi]$. Convert to degrees and normalize to $[0, 360)$:

$$\text{bearing} = \left(\theta \cdot \tfrac{180}{\pi} + 360\right) \bmod 360$$

The +360 before mod 360 handles negative angles from arctan2 — it shifts the range from [-180, 180] to [0, 360) without changing positive values.

function bearing(lat1, lon1, lat2, lon2) {
  const toRad = d => d * Math.PI / 180;
  const φ1 = toRad(lat1), φ2 = toRad(lat2);
  const Δλ = toRad(lon2 - lon1);

  const y = Math.sin(Δλ) * Math.cos(φ2);
  const x = Math.cos(φ1) * Math.sin(φ2) -
            Math.sin(φ1) * Math.cos(φ2) * Math.cos(Δλ);

  return (Math.atan2(y, x) * 180 / Math.PI + 360) % 360;
}