everyday ToolUpdated 2026-09-20

Distance Calculator (Coordinates & Great-Circle)

Compute the true curvature-adjusted great-circle flight distance between any two geographical coordinates on Earth in miles, kilometers, and nautical miles.

Formula & Mathematical Methodology

d = 2R × arcsin(√(sin²(Δlat/2) + cos(lat1) × cos(lat2) × sin²(Δlon/2)))

The Haversine formula calculates the shortest distance over the Earth’s spherical surface (great-circle distance), accounting for spherical curvature.

Step-by-Step Worked Example

Scenario: Distance from New York City (40.7128°, -74.0060°) to Los Angeles (34.0522°, -118.2437°).

1. Convert coordinates to radians.

2. Compute angular differences: Δlat = -0.1162 rad, Δlon = -0.7721 rad.

3. Apply Haversine formula with Earth radius R = 3,958.8 miles.

4. Great-circle distance = 2,445.5 miles (3,935.7 kilometers).

5. Estimated commercial flight time: ~5 hours and 23 minutes.

Final Calculated Result: 2,445.55 miles (3,935.74 km)

Frequently Asked Questions

What is great-circle distance?

Great-circle distance is the shortest navigational distance between two points on the surface of a sphere, representing the path that commercial airliners fly.