Calculate Distance with Decimal Degrees

Calculating distances between geographic coordinates is essential for navigation, mapping, and geographic analysis. This calculator uses decimal degrees to determine the shortest distance between two points on Earth's surface, accounting for the planet's curvature.

How to Use This Calculator

To calculate the distance between two points using decimal degrees:

Enter the latitude and longitude of the first point in decimal degrees (e.g., 40.7128 for latitude, -74.0060 for longitude)
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 will display the distance between the two points, rounded to two decimal places. You can also view a visualization of the points on a map.

The Haversine Formula

The distance between two points on a sphere (like Earth) is calculated using the Haversine formula, which accounts for the curvature of the planet. The formula is:

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

c = 2 ⋅ atan2(√a, √(1−a))

d = R ⋅ c

Where:

φ₁, φ₂ are the latitudes of points 1 and 2 in radians
Δφ is the difference in latitudes (φ₂ - φ₁)
Δλ is the difference in longitudes (λ₂ - λ₁)
R is the Earth's radius (6,371 km or 3,959 miles)

This formula provides an accurate approximation of the shortest distance between two points on Earth's surface.

Worked Examples

Let's calculate the distance between New York City (40.7128° N, 74.0060° W) and Los Angeles (34.0522° N, 118.2437° W) in kilometers:

Convert degrees to radians:
- φ₁ = 40.7128° × π/180 ≈ 0.7102 radians
- φ₂ = 34.0522° × π/180 ≈ 0.5946 radians
- Δφ = φ₂ - φ₁ ≈ -0.1156 radians
- Δλ = (118.2437° - 74.0060°) × π/180 ≈ 1.3718 radians
Calculate a:
- a = sin²(-0.1156/2) + cos(0.7102) ⋅ cos(0.5946) ⋅ sin²(1.3718/2)
- a ≈ 0.0033 + 0.7547 ⋅ 0.8439 ⋅ 0.3333 ≈ 0.2006
Calculate c:
- c = 2 ⋅ atan2(√0.2006, √(1-0.2006)) ≈ 2 ⋅ atan2(0.4479, 0.9296) ≈ 0.4887 radians
Calculate distance:
- d = 6,371 km ⋅ 0.4887 ≈ 3,125.6 km

The distance between New York City and Los Angeles is approximately 3,125.6 kilometers.

Frequently Asked Questions

What are decimal degrees?: Decimal degrees represent geographic coordinates where latitude and longitude are expressed as decimal numbers rather than degrees, minutes, and seconds. For example, 40.7128° N, 74.0060° W.
Why use the Haversine formula instead of Euclidean distance?: The Haversine formula accounts for the Earth's curvature, providing more accurate distance measurements between geographic coordinates than the simpler Euclidean distance formula.
What is the Earth's radius used in the calculation?: The calculator uses the mean Earth radius of 6,371 kilometers (3,959 miles) for distance calculations. This value is an average and may vary slightly depending on the specific location.
Can I calculate distances between points in different hemispheres?: Yes, the Haversine formula works for all pairs of geographic coordinates, regardless of whether they are in the same or different hemispheres.
How accurate are the distance calculations?: The calculations are accurate to within about 0.5% of the actual distance between two points on Earth's surface, which is sufficient for most practical applications.