Distance Between Cities

Have you ever wondered exactly how far Tokyo is from New York, or what the straight-line distance between London and Sydney really is? The distance between two cities is not as simple as it first appears. Because the Earth is a sphere — or more precisely an oblate spheroid — the shortest path between two surface points follows a curve called a great circle, not a flat straight line. This calculator uses the Haversine formula to compute that great-circle distance accurately for any pair of latitude/longitude coordinates.

What Is Great-Circle Distance?

A great circle is any circle on the surface of a sphere whose centre coincides with the centre of the sphere. The equator and all lines of longitude are great circles; lines of latitude other than the equator are not. The shortest path between any two points on a sphere lies along the arc of the great circle that passes through both points.

For terrestrial navigation this matters a great deal. If you look at a flat map (Mercator projection), a flight from Los Angeles to London appears to curve northward — because the flat map distorts the shape of great-circle routes. In reality, that curved path on the map is the geometrically shortest route over the globe. Airlines and transoceanic shipping routes are planned along great circles to minimise fuel consumption and travel time.

The Haversine Formula Explained

The Haversine formula is a trigonometric equation derived from the spherical law of cosines, optimised to remain numerically stable even for very short distances (where floating-point rounding would otherwise cause errors). The name comes from the 'haversine' function: hav(theta) = sin squared(theta/2).

The computation proceeds in three steps. First, convert both latitude and longitude values from degrees to radians. Second, compute the intermediate value: a = sin squared(delta lat/2) + cos(lat1) times cos(lat2) times sin squared(delta lon/2). Third, compute the central angle: c = 2 times atan2(sqrt(a), sqrt(1-a)). Finally, multiply by Earth's mean radius (6,371 km) to obtain the distance. The formula is accurate to within about 0.5% of the true geodetic distance for most practical purposes.

Straight-Line vs. Road Distance

It is important to understand that great-circle distance is the straight-line distance over the Earth's surface — it is not road distance. Actual driving routes follow roads, highways, and the physical topology of the terrain. For adjacent cities connected by a direct highway, the road distance may be only 5-10% longer than the straight-line figure. For cities separated by mountains, rivers, or bodies of water, the road distance can be dramatically longer.

Straight-line distance has practical uses, however. It is the starting point for flight planning, as commercial aircraft follow great-circle routes (adjusted for winds and airspace restrictions). It is also used in logistics to assess whether a direct flight is feasible, in telecommunications to calculate signal delay, and in geographic information systems for spatial analysis.

Interpreting the Flight Time Estimate

This calculator estimates flight time by dividing the great-circle distance by 900 km/h, a typical cruise speed for modern narrow-body and wide-body jet aircraft. This figure is a rough approximation. Actual flight times depend on several factors: the specific aircraft type, payload, altitude, jet-stream winds (which can add or subtract hours on long-haul routes), departure and arrival taxi time, and the fact that aircraft must climb and descend rather than cruising at maximum speed for the entire journey.

On short-haul flights (under 1,000 km), the estimate will be optimistic because climb and descent phases represent a larger fraction of the journey. On ultra-long-haul routes (10,000+ km), tailwinds can make the estimate pessimistic in one direction and optimistic in the other. Use the flight time as an order-of-magnitude guide rather than a schedule.

Interpreting the Driving Time Estimate

The driving time estimate divides the straight-line distance by 80 km/h. Because road distance is always longer than straight-line distance and because actual driving speed is influenced by speed limits, traffic, stops, and terrain, this figure is best interpreted as a theoretical minimum — the actual drive will almost always take longer.

For cities separated by water (for example, London to New York), the driving time figure has no practical meaning because no road connection exists. In those cases, the estimate serves as a reference for the sheer scale of the distance rather than actionable travel information.

Notable City Pair Distances

A few famous great-circle distances illustrate the scale of global geography. New York to London spans approximately 5,570 km, a journey that takes roughly 7 hours by modern jetliner. Tokyo to Los Angeles is about 8,815 km across the Pacific, typically a 10-11 hour flight. Sydney to London, one of the longest commercial routes in the world, covers around 16,990 km and can take 20+ hours nonstop.

Even within a single continent, distances can be surprisingly large. Moscow to Vladivostok spans about 6,400 km across Russia — farther than London to New York. Sao Paulo to Buenos Aires, which may feel like neighbouring cities, are still about 1,700 km apart as the crow flies.

Coordinate Systems and Accuracy

This calculator uses the WGS84 geographic coordinate system, the same standard used by GPS and most modern mapping applications. Latitude is measured in degrees north (+) or south (-) of the equator, ranging from -90 to +90. Longitude is measured east (+) or west (-) of the prime meridian through Greenwich, ranging from -180 to +180.

The Haversine formula models Earth as a perfect sphere with a radius of 6,371 km. Earth is actually an oblate spheroid slightly flattened at the poles — its equatorial radius is about 6,378 km and polar radius about 6,357 km. For most purposes this spherical approximation introduces an error of less than 0.5%, which is negligible when planning travel. For geodetic surveying requiring millimetre precision, more sophisticated formulae such as Vincenty's method are used.