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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.
الصيغة
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)
دليل خطوة بخطوة
- 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
أمثلة محلولة
الإدخال
London (51.5°N,0.1°W) to New York (40.7°N,74°W)
النتيجة
≈ 5,570 km / 3,461 miles
الإدخال
Paris to Berlin
النتيجة
≈ 878 km
أسئلة شائعة
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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