Great Circle Distance Calculator

Calculate the shortest distance between two points on Earth's surface using the Haversine formula.

Enter Coordinates

Point A
Point B

Result

Great Circle Distance
--
kilometers

Step-by-Step Solution

d = R * arccos(sin(lat1)*sin(lat2) + cos(lat1)*cos(lat2)*cos(dlon))

Understanding Great Circle Distance

The great circle distance is the shortest distance between two points on the surface of a sphere. On Earth, this represents the most direct route between two locations, following the curvature of the planet rather than a straight line on a flat map.

This distance is what airlines use to plan flight routes, and it is fundamental to navigation, geodesy, and geography.

Calculation Methods

Haversine Formula

The most commonly used formula for computing great circle distances. Numerically stable for small distances.

a = sin^2(dlat/2) + cos(lat1)*cos(lat2)*sin^2(dlon/2)

Spherical Law of Cosines

A simpler formula, but can suffer from rounding errors for very small distances.

d = acos(sin(p1)*sin(p2)+cos(p1)*cos(p2)*cos(dl))*R

Vincenty's Formula

More accurate for an oblate spheroid (ellipsoid) model of Earth. Used in high-precision geodesy.

Iterative solution on WGS-84 ellipsoid

Initial Bearing

The compass direction you would need to travel from point A to reach point B.

theta = atan2(sin(dl)*cos(p2), cos(p1)*sin(p2)-sin(p1)*cos(p2)*cos(dl))

The Haversine Formula Explained

The Haversine formula determines the great circle distance between two points on a sphere given their longitudes and latitudes. The name comes from the haversine function: hav(theta) = sin2(theta/2).

  1. Convert all coordinates from degrees to radians.
  2. Compute the differences in latitude and longitude.
  3. Apply the haversine formula: a = sin2(dlat/2) + cos(lat1) * cos(lat2) * sin2(dlon/2)
  4. Compute c = 2 * atan2(sqrt(a), sqrt(1-a))
  5. The distance is d = R * c, where R is Earth's radius.

Coordinate Systems

Latitude measures how far north or south a point is from the equator (-90 to +90 degrees). Longitude measures how far east or west a point is from the Prime Meridian (-180 to +180 degrees). Together, they uniquely identify any point on Earth's surface.

Applications

  • Aviation: flight path planning and fuel estimation
  • Maritime navigation: ship routing and distance calculations
  • Telecommunications: satellite coverage and signal path calculations
  • Logistics: shipping route optimization
  • Geospatial analysis: proximity queries and distance-based filtering
  • Seismology: measuring distances from epicenters