Distance Calculator Latitude Longitude Decimal Degrees

This distance calculator helps you find the distance between two points on Earth when you know their latitude and longitude in decimal degrees. The calculation uses the Haversine formula, which accounts for the Earth's curvature.

How to Use This Calculator

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

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 will display the distance between the two points in the selected unit.

Formula Used

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

Haversine Formula:

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

c = 2 ⋅ atan2(√a, √(1−a))

d = R ⋅ c

Where:

φ1, λ1 = latitude and longitude of point 1
φ2, λ2 = latitude and longitude of point 2
Δφ = φ2 − φ1
Δλ = λ2 − λ1
R = Earth's radius (6,371 km or 3,959 miles)

This formula accounts for the Earth's curvature and provides an accurate distance measurement.

Worked Examples

Example 1: Distance Between New York and London

New York City: 40.7128° N, 74.0060° W

London: 51.5074° N, 0.1278° W

Using the Haversine formula:

Δφ = 51.5074° - 40.7128° = 10.7946°

Δλ = 0.1278° - (-74.0060°) = 74.1338°

a = sin²(10.7946°/2) + cos(40.7128°) ⋅ cos(51.5074°) ⋅ sin²(74.1338°/2)

c = 2 ⋅ atan2(√a, √(1−a))

d = 6,371 km ⋅ c ≈ 5,570 km (3,461 miles)

The distance between New York and London is approximately 5,570 kilometers or 3,461 miles.

Example 2: Distance Between Sydney and Tokyo

Sydney: 33.8688° S, 151.2093° E

Tokyo: 35.6762° N, 139.6503° E

Using the Haversine formula:

Δφ = 35.6762° - (-33.8688°) = 69.5450°

Δλ = 139.6503° - 151.2093° = -11.5590°

a = sin²(69.5450°/2) + cos(-33.8688°) ⋅ cos(35.6762°) ⋅ sin²(-11.5590°/2)

c = 2 ⋅ atan2(√a, √(1−a))

d = 6,371 km ⋅ c ≈ 7,770 km (4,830 miles)

The distance between Sydney and Tokyo is approximately 7,770 kilometers or 4,830 miles.

Frequently Asked Questions

What is the Haversine formula?: The Haversine formula is an equation important in navigation, giving great-circle distances between two points on a sphere from their longitudes and latitudes.
How accurate is this distance calculator?: This calculator provides accurate results based on the Haversine formula, which accounts for the Earth's curvature. The accuracy depends on the precision of the input values.
Can I use this calculator for air travel distances?: Yes, this calculator can be used to estimate air travel distances between two points. However, actual flight paths may vary due to air traffic control and other factors.
What is the difference between latitude and longitude?: Latitude measures how far north or south a point is from the Equator, while longitude measures how far east or west a point is from the Prime Meridian.
How do I convert degrees, minutes, seconds to decimal degrees?: To convert degrees, minutes, seconds to decimal degrees, use the formula: Decimal Degrees = Degrees + (Minutes/60) + (Seconds/3600).