Latitude Longitude Distance Calculator

This calculator relies on the Haversine formula, which computes the great-circle distance between two points on a sphere given their longitudes and latitudes. The formula accounts for the curvature of the Earth rather than assuming a flat surface. Mathematically, it evaluates the central angle between two points using trigonometric functions. The core formula is expressed as:

a = sin²(Δφ/2) + cos(φ1) · cos(φ2) · sin²(Δλ/2)

c = 2 · atan2(√a, √(1−a))

d = R · c

Where φ represents latitude, λ represents longitude, R is the Earth's mean radius (approximately 6,371,000 meters), and d is the resulting distance along the Earth's surface.

Let us calculate the distance between New York City (Point 1: 40.7128° N, 74.0060° W) and London (Point 2: 51.5074° N, 0.1278° W).

Step 1: Convert coordinates to radians.
Latitudes: φ1 = 0.7104 rad, φ2 = 0.8990 rad.
Longitudes: λ1 = -1.2916 rad, λ2 = -0.0022 rad.

Step 2: Find coordinate differences.
Δφ = 0.8990 - 0.7104 = 0.1886 rad.
Δλ = -0.0022 - (-1.2916) = 1.2894 rad.

Step 3: Apply the Haversine equation.
Compute the intermediate variable 'a' using the sine and cosine of the radian values. Then solve for 'c' and multiply by the Earth's radius (6,371 km). The resulting surface distance is approximately 5,570 kilometers.

Keep these best practices in mind when measuring distances across coordinates:

• Watch your signs: North latitudes and East longitudes are positive, while South latitudes and West longitudes are negative. Entering a wrong sign will skew your results dramatically.
• Understand surface vs. air distance: Great-circle distance measures the arc along the globe's surface, which is ideal for flight planning and maritime navigation.
• Decimal degrees vs. DMS: Ensure your inputs match the chosen calculation mode. Converting Degrees, Minutes, Seconds (DMS) to decimal degrees requires dividing minutes by 60 and seconds by 3,600.