In Guess The Distance every answer is a great-circle distance: the length of the shortest path between two cities over the surface of the Earth. It sounds technical, but the idea is simple, and understanding it explains a few things that look strange on a map, like why a flight from Madrid to Tokyo heads north over Russia instead of flying straight east.
Picture slicing an orange exactly through its centre. The edge of that cut is a great circle, the largest circle you can draw on a sphere. The equator is a great circle, and so is every line of longitude when joined with the one opposite it. Lines of latitude other than the equator are not great circles. They are smaller rings.
For any two points on a sphere there is exactly one great circle passing through both of them (unless they are exact opposites). The shorter arc of that circle is the shortest route between the points. That arc length is the great-circle distance.
Most world maps use the Mercator projection, which stretches the globe into a rectangle. Straight lines on that map are lines of constant compass bearing, which are useful for sailing but are not the shortest path. A great-circle route, drawn on the same map, bends toward the nearest pole.
That is why flights between Europe and East Asia pass over Scandinavia, Russia or the Arctic, and why flights from North America to Europe arc up past Newfoundland, Greenland and Iceland. On a globe these routes are perfectly straight. It is the flat map that makes them look curved. You can check this yourself by stretching a piece of string between two cities on a desk globe.
Given the latitude and longitude of two places, the distance is usually computed with the haversine formula. With latitudes φ1, φ2, the difference in latitude Δφ and the difference in longitude Δλ (all in radians):
a = sin²(Δφ/2) + cos φ1 · cos φ2 · sin²(Δλ/2)
distance = 2 · R · atan2(√a, √(1−a))
Here R is the Earth's mean radius, about 6,371 km. The formula treats the Earth as a perfect sphere. The real planet is slightly flattened at the poles, so precise surveying tools use an ellipsoid model instead, but the difference is small, typically well under one percent, which is far more precise than anyone's guess.
| Route | Great-circle distance |
|---|---|
| Berlin – Paris | ≈ 880 km |
| Rome – Istanbul | ≈ 1,370 km |
| Dublin – New York | ≈ 5,100 km |
| Beijing – Berlin | ≈ 7,350 km |
| Sydney – Los Angeles | ≈ 12,000 km |
| Half the Earth's circumference (the maximum) | ≈ 20,000 km |
The last line is the upper limit: two points on exactly opposite sides of the Earth (called antipodes) are about 20,000 km apart, and nothing can be farther. Some of the longest pairs in the game, like Wellington to London or São Paulo to Tokyo, come within a couple of thousand kilometres of that limit.
Real journeys are almost always longer than the great-circle distance. Roads follow terrain and borders, and railways bend around mountains. Even aircraft rarely fly the perfect great circle: they follow air corridors, avoid restricted airspace and ride favourable jet-stream winds, which can add a few percent. When you play Guess The Distance, think “as the crow flies”, not “as the car drives”.
Want more ways to sharpen your guesses? Read How to Get Better at Estimation Games, or jump straight into Guess The Distance.