Great Circle
Calculate the great circle distance and initial bearing between two points on Earth using latitude and longitude. Free online Haversine formula distance calculator with instant results.
Point 1
Point 2
About This Calculator
About the Great Circle Distance Calculator
The Great Circle Distance Calculator computes the shortest path between any two points on Earth's surface using the Haversine formula. By entering the latitude and longitude coordinates of two locations in decimal degrees, the calculator instantly returns the great circle distance in both kilometers and miles, along with the initial bearing (azimuth) from the starting point to the destination.
This calculator is designed for travelers, pilots, sailors, geographers, students, and anyone who needs to measure distances across the globe. Unlike straight-line distances through the Earth, the great circle distance follows the curvature of the planet and represents the actual distance a plane or ship would travel along the most efficient route.
The Haversine Formula
The Haversine formula calculates the great circle distance between two points on a sphere given their latitude and longitude. The formula is: a = sin^2(Deltaφ/2) + cos(φ1) · cos(φ2) · sin^2(Deltalambda/2), where φ1 and φ2 are the latitudes, Deltaφ is the latitude difference, and Deltalambda is the longitude difference. The central angle c = 2 · atan2(sqrta, sqrt(1-a)), and the distance d = R · c, where R is Earth's mean radius of 6,371 kilometers.
Initial Bearing
The initial bearing (or forward azimuth) tells you the direction you need to head from Point 1 to reach Point 2 along the great circle path. It is measured in degrees clockwise from true north. For example, traveling from New York to London has an initial bearing of approximately 46 deg, meaning you would head northeast from New York. Note that the bearing changes along the route since great circles are not straight lines on a flat map.
How to Use the Calculator
Enter the latitude and longitude of your first and second points in decimal degrees. Use positive values for north latitudes and east longitudes, and negative values for south latitudes and west longitudes. For example, New York City is approximately latitude 40.71 and longitude -74.01 (negative because it is west of the prime meridian). Click Calculate Distance to see the great circle distance in both kilometers and miles, plus the initial bearing. The URL updates automatically, so you can share your calculation with others.
Practical Applications
Great circle calculations are essential for aviation route planning, maritime navigation, satellite orbit tracking, and telecommunications (calculating the shortest path for undersea cables). Understanding great circles also helps explain why international flight paths appear curved on standard world maps -- they are actually the straightest possible routes on a spherical Earth.
Frequently Asked Questions
What is a great circle?
A great circle is the largest possible circle that can be drawn on a sphere, formed by the intersection of the sphere and a plane passing through its center. On Earth, the equator is a great circle, and lines of longitude are halves of great circles. The shortest path between any two points on a sphere always follows a great circle arc.
How does the great circle distance formula work?
The Great Circle Calculator uses the Haversine formula: a = sin^2(Deltalat/2) + cos(lat1) x cos(lat2) x sin^2(Deltalon/2), then c = 2 x atan2(sqrta, sqrt(1-a)), and finally d = R x c, where R is Earth's mean radius of 6,371 km. The initial bearing is calculated separately using the four-quadrant arctangent function.
Why do flight routes look curved on a map?
Flight routes follow great circle paths, which are the shortest distance between two points on Earth. When projected onto flat maps (especially the Mercator projection), these straight three-dimensional arcs appear curved because it is impossible to represent a sphere on a flat surface without distortion. This is why a flight from Los Angeles to London appears to pass over Greenland, even though it is the shortest route.
How accurate is the Haversine formula?
The Haversine formula is highly accurate for most practical purposes, with errors typically less than 0.5% compared to more complex ellipsoidal models like Vincenty's formula. It assumes Earth is a perfect sphere with a mean radius of 6,371 km. For high-precision applications requiring centimeter accuracy, ellipsoidal models such as WGS-84 are preferred.
What is initial bearing?
Initial bearing (also called forward azimuth) is the direction you would start traveling from Point 1 to follow the great circle path to Point 2. It is measured in degrees clockwise from true north, ranging from 0 deg (north) through 90 deg (east), 180 deg (south), and 270 deg (west). The bearing changes continuously along the great circle path, so the final bearing at the destination is different from the initial bearing.
Can this calculator be used for any two points on Earth?
Yes, the calculator works for any two points on Earth given their latitude and longitude coordinates in decimal degrees. Use positive values for north latitudes and east longitudes, and negative values for south latitudes and west longitudes. The calculator also handles antipodal points (opposite sides of the Earth) correctly.
What is the difference between great circle distance and straight-line distance?
Great circle distance is the shortest path along the surface of a sphere (Earth), following the curvature of the planet. Straight-line distance (or Euclidean distance) is the straight path through the Earth between two points and is always shorter than the great circle distance. For aviation, shipping, and overland navigation, the great circle distance is the relevant measure.
Is the great circle distance calculator free to use?
Yes, all calculators on Calculy, including the Great Circle Distance Calculator, are completely free to use with no registration or subscription required. You can also share your calculations via the shareable URL that saves all input values.