Lat Long Distance Calculator Decimal Degrees

This calculator helps you determine the distance between two points on Earth using their latitude and longitude coordinates in decimal degrees. Whether you're a navigator, geographer, or just curious about the distance between two locations, this tool provides accurate results quickly.

How to Use This Calculator

Using the latitude and longitude distance calculator is straightforward:

Enter the latitude and longitude of the first location in decimal degrees.
Enter the latitude and longitude of the second location in decimal degrees.
Select the unit of measurement (kilometers or miles).
Click the "Calculate" button to get the distance between the two points.

The calculator will display the distance between the two points in the selected unit, along with a visual representation of the calculation.

Formula Used

The distance between two points on the surface of a sphere (like Earth) can be 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:

φ1, φ2 are the latitudes of the two points in radians
Δφ is the difference in latitudes (φ2 - φ1) in radians
Δλ is the difference in longitudes (λ2 - λ1) in radians
R is the Earth's radius (mean radius = 6,371 km)

This formula accounts for the curvature of the Earth and provides accurate distance measurements between any two points on the planet.

Worked Example

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 all coordinates to radians:
- New York: φ1 = 0.7106 rad, λ1 = -1.2915 rad
- Los Angeles: φ2 = 0.5936 rad, λ2 = -2.0632 rad
Calculate the differences:
- Δφ = φ2 - φ1 = -0.1170 rad
- Δλ = λ2 - λ1 = 0.7717 rad
Apply the Haversine formula:
- a = sin²(-0.1170/2) + cos(0.7106) ⋅ cos(0.5936) ⋅ sin²(0.7717/2)
- c = 2 ⋅ atan2(√a, √(1−a))
- d = 6,371 km ⋅ c ≈ 3,935 km

The calculated distance between New York City and Los Angeles is approximately 3,935 kilometers.

Frequently Asked Questions

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

Decimal degrees represent latitude and longitude as a single decimal number, while degrees, minutes, seconds break them into degrees, minutes, and seconds. This calculator uses decimal degrees for simplicity and precision.

Why does the Earth's curvature affect distance calculations?

The Earth is not flat, so straight-line distance (as the crow flies) is different from the actual path you'd take on roads or water. The Haversine formula accounts for this curvature to provide accurate results.

Can I use this calculator for points on other planets?

This calculator is designed for Earth. For other celestial bodies, you would need to adjust the radius value in the formula to match the planet's mean radius.