# Bearing Between Coordinates Calculator

> Find the initial and final great-circle bearing from one latitude/longitude to another, in degrees from true north, with the compass point.

Category: Algebra, geometry & advanced math · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/bearing-between-coordinates-calculator

The initial bearing is the direction to set off along the great circle, measured clockwise from true north. On a sphere the bearing changes along the way, so the final bearing usually differs.

Also called: Azimuth calculator, Forward azimuth calculator.

## Inputs
- Start latitude (unit °; default 35)
- Start longitude (unit °; default 45)
- Destination latitude (unit °; default 35)
- Destination longitude (unit °; default 135)

## Results
- Initial bearing
- Compass point (16-wind)
- Initial bearing in DMS
- Final bearing on arrival
- Reverse of initial bearing
- Great-circle distance

## Formula

```
θ = atan2(sin Δλ · cos φ₂, cos φ₁ · sin φ₂ − sin φ₁ · cos φ₂ · cos Δλ), normalised to 0–360°;  final bearing = (bearing from 2 to 1 + 180°) mod 360°
```

Where:
- φ₁, φ₂: start and destination latitudes
- Δλ: difference in longitude
- θ: bearing clockwise from true north

## Worked example
1. Δλ = 90°, so sin Δλ = 1 and cos Δλ = 0.
2. θ = atan2(cos 35°, cos 35° × sin 35°) = atan(1 ÷ sin 35°) = atan(1.743447) ≈ 60.1624°.
3. Both points share a latitude, so by symmetry the final bearing is 180° − 60.1624° = 119.8376°.

**Result:** From 35°N 45°E to 35°N 135°E you set off on 60.16° (ENE) and arrive heading 119.84° (ESE).

## What the result means

A great-circle route changes heading continuously. A constant compass heading (a rhumb line) is easier to steer but longer, except along the equator or a meridian.

## Assumptions and limits
- Spherical Earth (mean radius 6,371.0088 km for the distance).
- Bearings are from true north, not magnetic north; add or subtract the local magnetic declination for a compass.
- Undefined at a pole and for identical or antipodal points.
- Ellipsoidal (WGS-84) azimuths can differ by a fraction of a degree.

## Questions

### Why is the final bearing different from the initial one?

Meridians converge towards the poles, so a great circle crosses each one at a different angle. Only routes along the equator or a meridian keep a constant bearing.

### Is the return bearing just the initial bearing plus 180°?

Only on a flat map. On the sphere the bearing for the return trip is the final bearing plus 180°, which generally differs.

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- [Great Circle Distance Calculator](https://calculators.geekmidst.com/calculators/great-circle-distance-calculator)
- [Coordinate Midpoint Calculator](https://calculators.geekmidst.com/calculators/coordinate-midpoint-calculator)
- [Degrees Minutes Seconds Converter](https://calculators.geekmidst.com/calculators/degrees-minutes-seconds-conversion-calculator)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/bearing-between-coordinates-calculator