Great circle distance and the Haversine formula
Because the Earth is approximately spherical, the shortest distance between two points on its surface is along the arc of a great circle, often called "as the crow flies".
The Haversine formula calculates this spherical distance: a = sin²(Δlat/2) + cos(lat1) × cos(lat2) × sin²(Δlon/2), with angular distance c = 2 × atan2(√a, √(1−a)), and distance d = R × c, where Earth mean radius R ≈ 6,371.0 km (3,958.8 miles).
The calculator also determines the initial compass bearing (azimuth in degrees) pointing from the origin directly toward the destination.
Worked example: Paris to Berlin
Paris (48.8566° N, 2.3522° E) to Berlin (52.5200° N, 13.4050° E):
Great Circle distance is approximately 878 kilometres (546 miles, 474 nautical miles).
The initial compass bearing is 55.4° (East-North-East).
Inputs for the distance calculator
Coordinates (Latitude and Longitude)
Enter decimal degrees (-90 to +90 for latitude, -180 to +180 for longitude). Use negative values for South and West.
CALCULATOR QUESTIONS
Distance between coordinates calculator questions
What is "as the crow flies" distance?
It is the shortest straight-line or great-circle distance between two geographic points, ignoring roads, terrain elevation, and obstacles.
Why does flight distance differ from road distance?
Flights follow great circle arcs across the globe, whereas road routes must wind around topography, rivers, cities, and road networks.