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The Haversine formula calculates the great-circle distance between two points on a sphere (like Earth) from their latitude and longitude. It is used in navigation, mapping, and GPS applications.
Công thức
a = sin²(Δφ/2) + cos(φ₁)cos(φ₂)sin²(Δλ/2); d = 2R·arcsin(√a)
- φ₁, φ₂
- latitude of points 1 and 2 (radians)
- Δφ
- difference in latitude (radians)
- λ₁, λ₂
- longitude of points 1 and 2 (radians)
- Δλ
- difference in longitude (radians)
- R
- Earth radius (km (≈6371)) — or miles (≈3959)
- d
- great-circle distance (km or miles)
Hướng dẫn từng bước
- 1a = sin²(Δlat/2) + cos(lat₁)cos(lat₂)sin²(Δlon/2)
- 2c = 2×atan2(√a, √(1−a))
- 3d = R × c, where R = 6371 km (Earth radius)
- 4Gives shortest path along Earth's surface
Ví dụ có lời giải
đầu vào
London (51.5°N,0.1°W) to New York (40.7°N,74°W)
Kết quả
≈ 5,570 km / 3,461 miles
đầu vào
Paris to Berlin
Kết quả
≈ 878 km
Câu hỏi thường gặp
What is a great circle?
The shortest path between two points on a sphere. On Earth, that's the shortest route between two locations.
Why not use Euclidean distance for GPS?
Earth is curved (sphere). Euclidean distance (straight line) ignores the curvature and gives incorrect results.
Is haversine the only way to calculate geographic distance?
No, but it's accurate, numerically stable, and avoids singularity issues of other formulas.
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