What it is for
The "straight-line" distance between two far-apart cities is not a straight line on a flat map: because the Earth is (roughly) a sphere, the shortest path follows an arc of a great circle. This calculator gives that distance in kilometers, miles and nautical miles, plus a flight-time estimate. Pick two cities from the list or type the coordinates of any point on the planet.
The Haversine formula
We use the Haversine formula with a mean Earth radius of R = 6371.0088 km: a = sin²(Δφ/2) + cos φ1 · cos φ2 · sin²(Δλ/2) and d = 2R · arcsin(√a), where φ is latitude and λ is longitude, in radians. Conversions: 1 mi = 1.609344 km and 1 nautical mile = 1.852 km. Because the Earth is not a perfect sphere, the typical error is around 0.3% (a few dozen kilometers on intercontinental routes).
Flight-time estimate
Time = distance ÷ cruise speed (default 800 km/h, typical of commercial jets) + 30 minutes for takeoff, climb and landing. It is a rough estimate: real routes are longer than the ideal arc and winds aloft can add or subtract a lot of time. For the actual arrival clock time, use the flight arrival time calculator as well.
Examples
London to New York: about 5,570 km (3,461 mi, 3,008 nautical miles), which gives roughly 7 h 28 min with the default estimate. São Paulo to Lisbon: about 7,949 km (4,939 mi), roughly 10 h 26 min. City values use urban-center coordinates rounded to 0.01 degree.
Limits
The distance is that of the ideal arc on the surface, ignoring altitude, terrain, closed borders or airspace. It is not road distance, which is usually much longer. For custom coordinates use decimal degrees (for example −23.55 and −46.63 for São Paulo).
Frequently asked questions
What is the difference between straight-line and road distance?
Great-circle distance is the shortest distance over the Earth's surface. Road distance follows the road network and is almost always longer.
What is a nautical mile?
A nautical mile is 1.852 km, roughly 1 arc-minute of latitude. It is the standard unit in air and sea navigation.
How accurate is the Haversine formula?
It assumes a spherical Earth with a mean radius of 6371.0088 km, with a typical error of about 0.3% compared with fuller ellipsoidal models.
Why does the estimated flight time differ from my ticket?
Because it assumes constant speed plus a fixed 30-minute allowance. The real route, winds and each airport's procedures change the time.