Great Circle Distance Calculator
Free Great circle distance Converter for geography & distance units. Enter a value to see equivalent measurements across systems.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
d = 2R * arcsin(sqrt(sin((lat2-lat1)/2)^2 + cos(lat1)*cos(lat2)*sin((lon2-lon1)/2)^2))
The Haversine formula calculates the great circle distance by first computing the haversine of the central angle between two points. It uses latitude and longitude in radians, with R being Earth's mean radius of 6,371 km. The formula handles antipodal points correctly and avoids numerical issues at small distances.
Worked Examples
Example 1: New York to London Flight Distance
Problem:Calculate the great circle distance from New York (40.7128 N, 74.006 W) to London (51.5074 N, 0.1278 W).
Solution:Using Haversine formula with R = 6,371 km:\ndLat = 10.7946 deg, dLon = 73.8782 deg\na = sin(5.3973)^2 + cos(40.7128) * cos(51.5074) * sin(36.9391)^2\nc = 2 * atan2(sqrt(a), sqrt(1-a))\nDistance = 6371 * c
Result:Distance: 5,570.25 km | 3,461.05 miles | 3,007.69 nautical miles | Bearing: 51.37 degrees
Example 2: Sydney to Tokyo
Problem:Find the distance from Sydney (-33.8688, 151.2093) to Tokyo (35.6762, 139.6503).
Solution:dLat = 69.545 deg, dLon = -11.559 deg\nApply Haversine formula with Earth radius 6,371 km.\nCompute intermediate value a, then angular distance c.
Result:Distance: approximately 7,823 km | 4,861 miles | Initial bearing: 338.68 degrees
Frequently Asked Questions
What is the great circle distance?
The great circle distance is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere rather than through it. On Earth, this represents the shortest flight path between two locations. The concept comes from the fact that the shortest path on a sphere always lies along a great circle, which is a circle whose center coincides with the center of the sphere. Airlines use great circle routes to minimize fuel consumption and flight time.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy