How this calculation works
The Great Circle Distance Between Cities Calculator computes geodesic distances across Earth's curved oblate spheroid in kilometers, statute miles, and nautical miles using the Haversine spherical trigonometric formula.
Mathematical formula and logic
Haversine Formula: a = sin²(Δφ/2) + cos(φ₁)·cos(φ₂)·sin²(Δλ/2), d = 2·R·atan2(√a, √(1−a)), where Earth radius R = 6,371 km (3,959 mi).
Worked example
The great-circle air distance between New York (40.71° N, 74.00° W) and London (51.50° N, 0.12° W) is 3,459 statute miles (5,567 kilometers / 3,006 nautical miles).
Calculation assumptions
- WGS84 mean volumetric Earth radius R = 6,371.0088 kilometers (3,958.761 miles).
- Direct geodesic flight line across the spherical globe.
Frequently asked questions
What is the Haversine formula?
The Haversine formula calculates the shortest surface distance between two latitude and longitude coordinate points on a sphere, remaining numerically stable even for small distances.
Why do airplane routes curve toward the North Pole on flat maps?
The shortest path between two points on a 3D sphere is a straight arc called a Great Circle. When projected onto a flat 2D Mercator map, this straight arc appears as an upward curved line toward the polar regions.
What is the difference between a statute mile and a nautical mile?
A statute mile (land mile) equals 5,280 feet (1,609.34 meters). A nautical mile (NM) equals exactly 1 minute of arc of latitude = 1,852 meters (1.1508 statute miles), standard in aviation and maritime navigation.
What is the longest non-stop commercial flight in the world?
Singapore Airlines flight SQ23/SQ24 between Singapore (SIN) and New York (JFK) covers 9,537 miles (15,349 km) in approximately 18 hours and 45 minutes on an Airbus A350-900ULR.
What is the antipodal point of a city?
The antipodal point of any location on Earth is the exact point on the diametrically opposite side of the globe (e.g. the antipode of Madrid, Spain is in New Zealand).