Great-Circle (Orthodromic) Distance Tool
Enter two points on Earth using decimal latitude and longitude. This calculator returns the shortest surface path between them (the orthodromic distance).
Latitude range: -90 to 90, Longitude range: -180 to 180.
What is orthodromic distance?
Orthodromic distance is the shortest distance between two points on the surface of a sphere. On Earth, this path is called a great-circle route. If you have ever noticed airline routes curving on a world map, that curve often represents an orthodrome rather than a straight line on a flat projection.
Because Earth is curved, straight lines on a 2D map can be misleading. Orthodromic distance gives a more realistic measure for long-range travel, aviation planning, marine navigation, and geospatial analysis.
How this orthodromic distance calculator works
This calculator uses the haversine formula, a standard trigonometric method for computing great-circle distance between two latitude/longitude coordinates. It treats Earth as a sphere with mean radius 6,371.0088 km.
- Step 1: Convert latitude and longitude from degrees to radians.
- Step 2: Compute angular separation between the two points.
- Step 3: Multiply central angle by Earth’s radius.
- Step 4: Convert the result to kilometers, miles, or nautical miles.
In addition to distance, the calculator also shows the central angle and initial bearing from Point A to Point B.
Orthodromic vs. rhumb line distance
Orthodromic (great-circle) route
Shortest path on a sphere. Preferred when minimizing distance and fuel over long routes.
Rhumb line (loxodrome) route
Maintains constant compass bearing. Easier for manual navigation but usually longer than the great-circle path except along meridians and the equator.
Practical uses
- Aviation: Optimize routes and estimate flight path length.
- Shipping: Evaluate shortest marine paths between ports.
- GIS and mapping: Measure realistic point-to-point distances globally.
- Logistics: Build accurate long-haul estimates for transport cost and time.
- Education: Understand spherical geometry and Earth coordinate systems.
Input tips for better accuracy
Use decimal degrees
Format coordinates as decimal values (for example, 34.0522 and -118.2437). Negative values indicate south latitudes and west longitudes.
Validate coordinate ranges
Latitudes must be between -90 and 90. Longitudes must be between -180 and 180. Out-of-range values are invalid.
Know model limitations
This calculator assumes a spherical Earth. For survey-grade precision, ellipsoidal geodesic models (such as WGS84 inverse formulas) are more accurate, especially over very long distances.
Example route
Try these points:
- Point A: New York (40.7128, -74.0060)
- Point B: London (51.5074, -0.1278)
You should see an orthodromic distance of roughly 5,570 km (depending on Earth radius assumptions and rounding).
Frequently asked questions
Is orthodromic distance always the shortest?
Yes, on a sphere, the great-circle path is the shortest path between two surface points.
Why is the route curved on many maps?
Map projections flatten Earth to 2D, which distorts geometry. A great-circle path can look curved even though it is the shortest surface route.
What unit should I choose?
Use kilometers for most scientific and international contexts, miles for common U.S. use, and nautical miles for marine and aviation workflows.