Bearing & Distance Calculator (Latitude/Longitude)
Enter the latitude and longitude of two points to calculate the great-circle distance (via the Haversine formula) and the initial bearing (angle from true north) from the first point to the second.
What are bearing and great-circle distance
The shortest path between two points on Earth is not a straight line on a flat map, but a curve that follows the surface of the sphere. This is called a great-circle route, and its length is the great-circle distance. The bearing tells you which direction the destination lies in when you stand at the starting point, measured as an angle from true north. By simply entering the latitude and longitude of two points, this tool calculates both of these values, plus the back bearing — the direction you would need to look from the destination to see the starting point.
On long routes, the heading gradually changes as you travel along the great-circle path, so the bearing shown here is only the value at departure — it will not match the direction you are actually facing on arrival. For the same reason, the back bearing is not exactly 180 degrees opposite the forward bearing; this gap grows larger the more the two points differ in longitude.
How to calculate bearing and great-circle distance
- Enter the latitude and longitude of your starting point Use decimal degree format. Use a negative value for latitude in the Southern Hemisphere, and a negative value for longitude west of the prime meridian.
- Enter the latitude and longitude of your destination Enter the destination coordinates in the same format. You can find coordinates by right-clicking a location in most map services.
- Read the results The bearing, great-circle distance, and back bearing are displayed. The bearing also comes with a compass direction name, such as north-northeast.
Tips for getting more out of it
- The bearing shown is the initial bearing — the direction a compass would point at the starting location. On long routes, the heading gradually changes along the great-circle path, so it differs from the bearing on arrival.
- The back bearing (from the destination toward the starting point) is not simply 180° opposite the forward bearing. Because the Earth is a sphere, this difference grows larger the more the two points differ in longitude.
- Enter coordinates in decimal degrees (for example, Tokyo Station is 35.6812, 139.7671). Convert degrees/minutes/seconds to decimal first if needed.
- Use a negative latitude for the Southern Hemisphere and a negative longitude for locations west of the prime meridian.
Ways to use bearing and distance calculations
Check the distance between two cities
Get a feel for the scale of a flight or understand why time zones differ the way they do. The real shortest distance often looks quite different from what a flat map suggests.
Determine the direction to point an antenna
Enter the coordinates of a target station or satellite to find the bearing from your installation site. Useful when aiming a directional antenna.
Support geography lessons
See with real numbers why a great-circle route looks curved on a map. Helps build an intuitive sense of distance on a sphere rather than a flat plane.
Find your heading during outdoor activities
Work out which direction to head based on your current location and destination coordinates. A useful reference when combining a map with a compass.
Bearing and geodesy terms
- Bearing
- The angle of a direction measured clockwise from true north. 90 degrees is east, 180 degrees is south, and 270 degrees is west.
- Great-circle distance
- The length of the shortest path between two points on a sphere's surface. It does not match the straight-line distance measured on a flat map.
- Back bearing
- The bearing from the destination looking back toward the starting point. Because the Earth is a sphere, this is not necessarily 180 degrees opposite the forward bearing.
- Haversine formula
- A formula that calculates the distance between two points by treating the Earth as a sphere. It is computationally light while still offering practically useful accuracy.
- True north
- The direction pointed to by the Earth's axis of rotation. It differs from magnetic north, the direction a compass needle points, by an amount that varies by location.
Frequently Asked Questions
Side Note — Why the "shortest path" doesn't look like a straight line
Draw a straight line between Tokyo and New York on a Mercator world map, and it looks almost due east. But the actual shortest route (the great-circle path) arcs far to the north, passing over Alaska and northern Canada. That's a direct consequence of map projection: squashing a sphere onto a flat map always distorts area, angle, or distance somewhere — you can't have all three at once.
Airlines flying from Tokyo to New York sometimes fly close to this great-circle route, since the shortest path on a sphere is often shorter than the straight line on a flat map — a meaningful fuel saving. In practice, though, strong westerly jet streams over the North Atlantic and airspace or air-traffic-control constraints mean the actual flight path never matches the textbook great circle exactly.
The concept of bearing was especially critical to navigation and surveying before GPS existed. "Celestial navigation" — measuring the altitude of stars like Polaris or the sun with a sextant, checking direction with a magnetic compass, and calculating the bearing and distance to a destination — was the basic method ships used to determine their position from the Age of Exploration all the way until GPS became practical in the late 20th century.