Math

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Great Circle Calculator.

Calculate spherical great-circle distance with the haversine formula.

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Set your values

Results update as you type.

Result: distance: 5570.222180 · centralAngleDegrees: 50.094212

Result

distance: 5570.222180 · centralAngleDegrees: 50.094212

Use Cases

Navigation and Travel Planning

Determine the shortest flight path or sailing route between two cities, useful for estimating travel time and fuel consumption.

Example: Calculate the distance between New York (40.7128° N, 74.0060° W) and London (51.5074° N, 0.1278° W).

Geographic Research and Education

Help students and researchers understand spherical geometry and the concept of great circles, which are the basis for many map projections.

Example: Find the distance between the North Pole (90° N, 0° E) and the equator (0° N, 0° E).

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. It is calculated using the haversine formula, which accounts for the spherical shape of the Earth.
How do I use this calculator?
Enter the latitude and longitude of the two points in degrees, and the sphere radius in kilometers. The calculator will output the great-circle distance in kilometers.
What is the haversine formula?
The haversine formula is an equation that calculates the great-circle distance between two points on a sphere given their longitudes and latitudes. It is accurate for small distances and widely used in navigation.

Tips & Common Mistakes

Tips

  • Ensure latitudes are between -90 and 90, and longitudes between -180 and 180. Use negative values for south and west coordinates.
  • For Earth, use a sphere radius of approximately 6371 km for a good average. For more precise results, consider the Earth's ellipsoidal shape.
  • The haversine formula assumes a perfect sphere, so results may differ slightly from actual distances on Earth's irregular surface.
  • Double-check that both points use the same coordinate system (e.g., decimal degrees) before entering them.

Common Mistakes to Avoid

  • Entering latitude and longitude in the wrong order. Latitude is the first field, longitude is the second.
  • Using degrees instead of radians. This calculator expects degrees, so do not convert to radians manually.
  • Forgetting to use negative signs for southern latitudes or western longitudes, which can lead to incorrect distances.

Last updated: August 13, 2026