Calculate Distance Between Lat Lon Points in Degrees

Calculating the distance between two points on Earth's surface using latitude and longitude coordinates is essential for navigation, logistics, and geographic analysis. This guide explains how to perform the calculation accurately and interpret the results.

How to Use This Calculator

To calculate the distance between two points using latitude and longitude coordinates:

Enter the latitude and longitude of the first point in decimal degrees
Enter the latitude and longitude of the second point in decimal degrees
Select the unit of measurement (kilometers or miles)
Click "Calculate Distance" to see the result

The calculator uses the Haversine formula, which provides accurate results for most practical applications. The formula accounts for the Earth's curvature and provides distances in either kilometers or miles.

The Haversine Formula

The Haversine formula calculates the great-circle distance between two points on a sphere given their longitudes and latitudes. The formula is:

Haversine Formula

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

c = 2 ⋅ atan2(√a, √(1−a))

d = R ⋅ c

Where:

φ₁ is the latitude of point 1 in radians
φ₂ is the latitude of point 2 in radians
Δφ is the difference in latitude (φ₂ - φ₁) in radians
Δλ is the difference in longitude (λ₂ - λ₁) in radians
R is the Earth's radius (mean radius = 6,371 km)

The formula first calculates the haversine of half the central angle between the points, then converts this to the actual distance by multiplying by the Earth's radius. The result is the shortest distance between the two points along the surface of the Earth.

Worked Examples

Let's look at two practical examples of calculating distances between latitude and longitude points.

Example 1: Distance Between New York and Los Angeles

Coordinates:

New York: 40.7128° N, 74.0060° W
Los Angeles: 34.0522° N, 118.2437° W

Using the Haversine formula with these coordinates and converting to miles:

The calculated distance is approximately 2,445 miles.

Example 2: Distance Between London and Paris

Coordinates:

London: 51.5074° N, 0.1278° W
Paris: 48.8566° N, 2.3522° E

Using the Haversine formula with these coordinates and converting to kilometers:

The calculated distance is approximately 343 kilometers.

Note

These examples show how the Haversine formula provides accurate distances between major cities. The actual road distance may vary due to route choices and terrain.

Frequently Asked Questions

What is the difference between Haversine and Vincenty formulas?: The Haversine formula is simpler and slightly less accurate than the Vincenty formula, which accounts for the Earth's ellipsoidal shape. For most practical purposes, the Haversine formula is sufficient.
Can I use this calculator for points on Mars?: No, this calculator is designed for Earth coordinates only. Mars has a different radius and shape that would require a different calculation method.
Why does the distance calculation sometimes seem off?: Small calculation errors can occur due to rounding of coordinates or the Earth's imperfect spherical shape. For precise measurements, professional surveying tools should be used.
What units should I use for latitude and longitude?: Always use decimal degrees for latitude and longitude coordinates. The calculator will convert these to radians internally for the calculation.
Is the Earth's radius constant in the Haversine formula?: The formula uses a mean Earth radius of 6,371 km. For more precise calculations, you might use a different radius based on the specific location's elevation.