The shortest route between two airports follows a great circle, the curved path that looks longer on a flat map but is actually the most direct. This calculator returns the great-circle distance, the initial true course, and a set of en-route waypoints for any two coordinates.
How it works
Distance comes from the haversine formula and the course from the standard initial-bearing formula:
a = sin²(Δφ/2) + cos φ1 · cos φ2 · sin²(Δλ/2)
distance = 2R · atan2(√a, √(1−a)) R = 3440.065 nm
course = atan2( sinΔλ·cosφ2 ,
cosφ1·sinφ2 − sinφ1·cosφ2·cosΔλ )Waypoints are placed by spherical interpolation, so each one sits on the true great circle at an equal fraction of the total distance.
Example: London Heathrow to New York JFK
From London Heathrow (51.4775°N, 0.4614°W) to New York JFK (40.6413°N, 73.7781°W), the great-circle distance is about 3,000 nautical miles with an initial true course near 288 degrees — heading northwest even though JFK appears almost due west on a flat map. This is the polar-arc effect that makes transatlantic routes arc over or near Greenland. The course swings noticeably as you cross the Atlantic, which is why the generated waypoints matter: re-check the course at each one, and apply the local magnetic variation to fly the magnetic heading.
Why courses change along a great circle
A great circle cuts every meridian at a different angle, so the true course you are flying shifts continuously from the departure bearing. A flat-earth rhumb line keeps a constant heading but travels a longer distance. Oceanic ATC clearances therefore usually specify a series of lat/long waypoints — exactly what this tool generates — rather than a single heading, because the heading is not constant.
Practical use for flight planning
- Route verification: Compare a filed great-circle distance against what your FMS shows. Small discrepancies come from the FMS using a flattened ellipsoid (WGS-84) rather than a sphere; the haversine result is typically within 0.3% for intercontinental routes.
- Fuel planning baseline: Nautical miles from this tool feed directly into a specific range calculation. Divide by true airspeed to get approximate block time, then multiply by fuel flow for a planning burn.
- Oceanic entry/exit points: Generate 6 to 10 waypoints along the great circle to identify which organised track (NAT, PACOTS) most closely follows your optimum route.
- True vs magnetic courses: The tool outputs true courses. You must apply magnetic variation at each waypoint. Over the North Atlantic, variation can exceed 20 degrees west and changes several degrees between waypoints.
Common mistakes and edge cases
Entering coordinates as degrees-minutes-seconds (DMS) rather than decimal degrees is the most frequent input error. Convert first: for example 51°28’39”N is 51 + 28/60 + 39/3600 = 51.4775 decimal. West and south longitudes and latitudes are entered as negative values.
For antipodal points (exactly opposite sides of the Earth), the great-circle direction is undefined and any heading works — the tool handles this gracefully. For very short legs under about 10 nm, rhumb-line and great-circle distances are essentially identical and it makes no practical difference which you use.