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Instant Calculation
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The great-circle distance is the shortest possible path between two points along the surface of a sphere — a curved arc rather than a straight line, since a straight "as the crow flies" tunnel would have to cut through the sphere's interior. This curved path is exactly what an airplane, ship, or ocean cable actually follows, because it minimizes real travel distance across a curved surface. The name comes from the fact that this shortest path is always part of a "great circle" — any circle drawn on a sphere's surface that shares the sphere's exact center and radius, such as the Earth's equator or any line of longitude. This calculation underpins commercial and military flight-path planning (long international flights often look curved on a flat map precisely because they're following a great-circle route, the true shortest path), maritime navigation, submarine cable route planning, and any GPS or mapping application that needs an accurate "as the crow flies" distance between two latitude/longitude points on Earth or another roughly spherical body.
How it works
Enter both points' latitude and longitude in degrees, plus the sphere's radius (defaulting to Earth's mean radius of 6371 km). The calculator applies the haversine formula, which converts both points' coordinates to radians, computes the differences in latitude and longitude, and combines them through a specific chain of sine and cosine terms designed to remain numerically accurate even for points that are very close together (unlike some simpler spherical-distance formulas, which can lose precision at short distances due to floating-point rounding). The final central angle between the two points is then multiplied by the sphere's radius to convert it into an actual arc-length distance.
- Enter point 1 latitude (°).
- Enter point 1 longitude (°).
- Enter point 2 latitude (°).
- Enter point 2 longitude (°).
- Enter sphere radius (default: Earth, 6371 km).
- Click Calculate to see your results.
Examples
New York to London
Using Earth's mean radius, the great-circle distance between (40.71°N, 74.01°W) and (51.51°N, 0.13°W) works out to roughly 5,570 km — noticeably shorter than the distance you'd get by naively treating latitude and longitude differences as if they were flat x-y coordinates.
Quarter of the way around the equator
Between (0°, 0°) and (0°, 90°), both on the equator, the central angle is exactly 90° (π/2 radians). Distance = 6371 × (π/2) ≈ 10,007 km — almost exactly one quarter of Earth's roughly 40,030 km circumference, as expected for a 90° arc along the equator.
Antipodal points
Between (0°, 0°) and (0°, 180°) — exact opposite sides of the globe — the central angle is a full 180° (π radians). Distance = 6371 × π ≈ 20,015 km, essentially half of Earth's circumference, the maximum possible great-circle distance between any two points on the sphere.
Common mistakes to avoid
- Mixing up latitude and longitude, or entering longitude values outside the standard -180° to 180° range.
- Forgetting to convert degrees to radians before applying the trigonometric terms in the haversine formula, if computing this by hand rather than using the tool.
- Assuming the great-circle distance equals the straight-line (chord) distance through the Earth — the great-circle distance is always somewhat longer, since it follows the curved surface.
- Using the wrong sphere radius for a non-Earth calculation, such as accidentally leaving Earth's default radius in place when modeling the Moon or another planet.