Geodesy & Distance CalcyZone Calculator

Haversine Distance Calculator

Compute exact great-circle distance between two latitude and longitude coordinates using the Haversine trigonometric formula.

📍 Select World Location Presets or Custom Coordinates

WGS-84 Ellipsoid

Origin Location Preset

Destination Location Preset

Point 1 Coordinates (Origin)

Latitude (°N/S)

Longitude (°E/W)

Point 2 Coordinates (Destination)

Latitude (°N/S)

Longitude (°E/W)

Calculated Geodetic Solution

5,570.23 km (3,461.179 miles)

Kilometers (km)5570.23 km

Miles (mi)3461.179 mi

Nautical Miles (NM)3007.685 NM

Meters (m)5570229.9 m

🗺️ Interactive Geographic Map & Geodesic Trajectory

Click anywhere on the map or drag pins to update coordinates live.

Map Data: © OpenStreetMap ContributorsWGS-84 Precision Geodesic Curve

Step-by-Step Mathematical Derivation

1. Given Input Coordinates:

Origin P1: (40.7128°, -74.006°)
Destination P2: (51.5074°, -0.1278°)

2. Model & Ellipsoid Reference:WGS-84 / Earth Sphere R = 6,371 km

3. Governing Geodesic Formula:d = 2R × arcsin(sqrt(sin²(Δφ/2) + cos(φ1)cos(φ2)sin²(Δλ/2)))

4. Variable Substitution:R = 6,371 km, Δφ = 10.7946°, Δλ = 73.8782°

5. Interpretation & Practical Application:

The great-circle flight distance between (40.7128, -74.006) and (51.5074, -0.1278) is 5570.23 km.

Mathematical Formula

d = 2R * asin( sqrt( sin²(Δlat/2) + cos(lat1)*cos(lat2)*sin²(Δlng/2) ) )

Overview & Explanation

Standard spherical distance formula accounting for Earth curvature.

How It Works

Uses sine half-angles to maintain precision over both short and long distances.

Practical Applications

Geolocation search radius.
Spatial database queries.

How the haversine formula works

The haversine formula gives the great-circle distance between two points on a sphere from their latitudes and longitudes. With latitudes φ₁, φ₂ and longitudes λ₁, λ₂ in radians: a = sin²(Δφ/2) + cos φ₁ × cos φ₂ × sin²(Δλ/2), c = 2 × atan2(√a, √(1 − a)), and distance = R × c, where R is Earth's mean radius of about 6,371 km.

The great-circle route is the shortest path over the surface, which is why long-haul flights look curved on a flat map.

Worked example

Mumbai (19.076° N, 72.878° E) to Delhi (28.704° N, 77.102° E): Δφ = 9.628° and Δλ = 4.224°. Working through the formula gives c ≈ 0.1810 radians, so the distance is about 6,371 × 0.1810 ≈ 1,153 km in a straight line. Road distance is longer, about 1,400 km, because roads do not follow the great circle.

Accuracy

Earth is slightly flattened at the poles, so treating it as a sphere introduces an error of up to about 0.5 percent. For surveying or long distances where that matters, use the Vincenty distance calculator, which models the WGS-84 ellipsoid.