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Free Great Circle Distance Calculator

Find the shortest-arc distance between two points on a sphere using the haversine formula.

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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.

  1. Enter point 1 latitude (°).
  2. Enter point 1 longitude (°).
  3. Enter point 2 latitude (°).
  4. Enter point 2 longitude (°).
  5. Enter sphere radius (default: Earth, 6371 km).
  6. 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.

Frequently asked questions

The sphere's radius is a configurable input rather than a hardcoded constant, so the same haversine formula works for any roughly spherical body — the Moon, another planet, or a purely abstract mathematical sphere — just by changing the radius value.
Because a flat map necessarily distorts the curved surface of the Earth. The great-circle route — the genuinely shortest path along the sphere — often appears as a curve on standard flat map projections, even though it's the straightest possible path when actually flown along the globe's surface.
A rhumb line (or loxodrome) is a path that crosses every meridian at the same constant compass bearing, making it easier to navigate by a fixed heading, but it's always equal to or longer than the true great-circle distance between the same two points, except along the equator or a meridian, where they coincide.
The spherical law of cosines is mathematically equivalent but can suffer from serious floating-point rounding errors for points that are very close together, since it involves taking the arccosine of a value extremely close to 1. The haversine formula avoids this numerical instability, making it the more commonly recommended approach in software.
No — the great-circle (surface arc) distance is always equal to or greater than the straight-line chord distance through the sphere's interior, since the arc must curve around the outside while the chord cuts directly through.
About half of Earth's circumference, roughly 20,000 km, which occurs between antipodal points — any two locations exactly opposite each other on the globe.

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