GPS Distance Calculator
Calculate the great-circle distance between two coordinates.
About the GPS Distance Calculator
Calculates the great-circle (as-the-crow-flies) distance between two latitude/longitude points using the haversine formula on a spherical Earth.
$$ d = 2R\,\arcsin\sqrt{\sin^2\frac{\Delta\phi}{2}+\cos\phi_1\cos\phi_2\sin^2\frac{\Delta\lambda}{2}} $$
How to use
Enter the latitude and longitude of both points in decimal degrees, then click Calculate.
Worked example
New York (40.71, −74.01) to London (51.51, −0.13) → about 5,570 km.
How to use this calculator
- Enter the latitude and longitude of the first location.
- Enter the latitude and longitude of the second location.
- Choose the distance units if the calculator offers them.
- Calculate the result to get the great-circle distance.
The formula explained
$$ d = R \arccos\left(\sin\varphi_1\sin\varphi_2 + \cos\varphi_1\cos\varphi_2\cos\left(\lambda_2 - \lambda_1\right)\right) $$
- \(d\) = great-circle distance between the two points
- \(R\) = radius of the Earth
- \(\varphi_1\) = latitude of the first point in radians
- \(\varphi_2\) = latitude of the second point in radians
- \(\lambda_1\) = longitude of the first point in radians
- \(\lambda_2\) = longitude of the second point in radians
Step by step method
- The tool takes two geographic coordinates, usually written as latitude and longitude.
- It converts the angle values into a spherical distance along the Earth's surface.
- It applies the great-circle formula using the Earth as a sphere.
- It returns the shortest surface distance between the two points.
Worked example
Suppose you want the distance between New York City and Los Angeles using their coordinates.
- Use New York City as the first point: approximately 40.7128, -74.0060.
- Use Los Angeles as the second point: approximately 34.0522, -118.2437.
- Enter both coordinate pairs into the calculator and compute the great-circle distance.
- The result is about 3,945 kilometers, or about 2,451 miles.
Answer. The great-circle distance is about 3,945 kilometers, or about 2,451 miles.
Tips and common mistakes
- Make sure latitude and longitude are entered in the correct order.
- Use decimal degrees if the calculator expects them.
- Do not confuse the great-circle distance with road distance, which is usually longer.
- Check the sign of each coordinate, since north and east are positive while south and west are negative.
Frequently asked questions
What is the great-circle distance?+
The shortest distance over the Earth's curved surface between two points.
How accurate is it?+
Within ~0.5%, it assumes a perfect sphere, not the slightly flattened real Earth.
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