Great Circle Bearing Decimal Degrees Calculator

What is Great Circle Bearing?

A great circle is the largest possible circle that can be drawn on a sphere, such as Earth. The shortest path between two points on a sphere lies along a great circle. The bearing is the angle measured clockwise from a reference direction (typically north) to the direction of travel along this great circle path.

Great circle bearings are measured in decimal degrees (0-360) and are crucial for accurate navigation, especially for long-distance travel where the curvature of the Earth becomes significant.

How to Calculate Great Circle Bearing

To calculate the great circle bearing between two points on Earth's surface, you need the latitude and longitude of both points. The calculation involves spherical trigonometry and requires converting degrees to radians for the trigonometric functions.

The formula involves several steps:

1. Convert all coordinates from decimal degrees to radians
2. Calculate the difference in longitudes
3. Use spherical trigonometry to compute the bearing
4. Convert the result back to decimal degrees

Formula

The formula for great circle bearing (θ) between two points (lat1, lon1) and (lat2, lon2) is:

After calculating θ in radians, convert to degrees and adjust to the standard bearing range (0-360°).

Example Calculation

Let's calculate the bearing from New York (40.7128° N, 74.0060° W) to London (51.5074° N, 0.1278° W):

1. Convert coordinates to radians
2. Calculate Δlon = -74.0060° - (-0.1278°) = -73.8782°
3. Apply the formula to get θ ≈ 53.13°
4. Convert to standard bearing: 53.13°

The bearing from New York to London is approximately 53.13°.