Decimal Degrees to Miles Calculator

This calculator converts decimal degrees of latitude and longitude into miles, showing the distance between two points on Earth's surface. It's useful for navigation, mapping, and geographic calculations.

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
Enter the latitude and longitude of the second point in decimal degrees
Click "Calculate" to see the distance in miles
Review the result and chart visualization

The calculator uses the Haversine formula to account for Earth's curvature, providing accurate distance measurements.

Formula Explained

The distance between two points on Earth's surface is calculated using the Haversine formula:

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

c = 2 ⋅ atan2(√a, √(1−a))

d = R ⋅ c

Where:

φ is latitude, λ is longitude
R is Earth's radius (3958.8 miles)
Δφ and Δλ are differences in coordinates

This formula accounts for Earth's curvature and provides accurate distance measurements between geographic coordinates.

Worked Examples

Example 1: New York to Los Angeles

Coordinates:

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

Calculation:

Δφ = 40.7128° - 34.0522° = 6.6606°

Δλ = 74.0060° - (-118.2437°) = 192.2497°

a = sin²(3.6303°) + cos(40.7128°) ⋅ cos(34.0522°) ⋅ sin²(96.1249°)

c = 2 ⋅ atan2(√a, √(1−a))

d = 3958.8 ⋅ c ≈ 2443 miles

The distance between New York and Los Angeles is approximately 2443 miles.

Example 2: London to Paris

Coordinates:

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

Calculation:

Δφ = 51.5074° - 48.8566° = 2.6508°

Δλ = 0.1278° - 2.3522° = -2.2244°

a = sin²(1.3254°) + cos(51.5074°) ⋅ cos(48.8566°) ⋅ sin²(-1.1122°)

c = 2 ⋅ atan2(√a, √(1−a))

d = 3958.8 ⋅ c ≈ 205 miles

The distance between London and Paris is approximately 205 miles.

Frequently Asked Questions

What is the difference between decimal degrees and degrees, minutes, seconds?

Decimal degrees represent latitude and longitude as single decimal numbers (e.g., 40.7128°). Degrees, minutes, seconds break coordinates into degrees, minutes, and seconds (e.g., 40°42'46"N). This calculator uses decimal degrees for simplicity and precision.

Why does the calculator use the Haversine formula?

The Haversine formula is the most accurate method for calculating distances between two points on a sphere, accounting for Earth's curvature. It provides more precise results than simple Euclidean distance calculations.

Can I use this calculator for air travel distances?

Yes, this calculator provides a good approximation for air travel distances between cities. However, actual flight paths may vary due to air traffic control, weather, and other factors.