Haversine Formula Distance Calculator

Haversine Formula:

\[ d = 2 \times R \times \arcsin\left(\sqrt{\sin^2\left(\frac{lat2 - lat1}{2}\right) + \cos(lat1) \times \cos(lat2) \times \sin^2\left(\frac{lon2 - lon1}{2}\right)}\right) \]

Latitude 1 (radians):

rad

Longitude 1 (radians):

rad

Latitude 2 (radians):

rad

Longitude 2 (radians):

rad

Earth Radius:

Great-Circle Distance:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Haversine Formula?

The Haversine formula calculates the great-circle distance between two points on a sphere given their longitudes and latitudes. It's particularly useful for calculating distances between locations on Earth, accounting for the Earth's spherical shape.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

\[ d = 2 \times R \times \arcsin\left(\sqrt{\sin^2\left(\frac{lat2 - lat1}{2}\right) + \cos(lat1) \times \cos(lat2) \times \sin^2\left(\frac{lon2 - lon1}{2}\right)}\right) \]

Where:

\( lat1, lat2 \) — Latitude coordinates in radians
\( lon1, lon2 \) — Longitude coordinates in radians
\( R \) — Earth's radius (6371 km or 3959 miles)

Explanation: The formula calculates the shortest distance between two points on the surface of a sphere, following the curvature of the sphere rather than a straight line through the sphere.

3. Importance of Great-Circle Distance Calculation

Details: Great-circle distance calculation is essential for navigation, aviation, maritime travel, and geographic information systems. It provides the most accurate measurement of distance between two points on a spherical surface.

4. Using the Calculator

Tips: Enter latitude and longitude coordinates in radians. The default Earth radius is set to 6371 km (mean Earth radius). For miles, use 3959. Ensure all angular measurements are in radians.

5. Frequently Asked Questions (FAQ)

Q1: Why use radians instead of degrees?
A: The trigonometric functions in the formula require angles in radians. Convert degrees to radians by multiplying by π/180.

Q2: How accurate is the Haversine formula?
A: The formula provides good accuracy for most practical purposes, though it assumes a perfect sphere. For extreme precision, more complex ellipsoidal models may be used.

Q3: What's the difference between great-circle distance and rhumb line?
A: Great-circle distance is the shortest path between two points, while a rhumb line maintains a constant bearing. Great-circle is shorter but requires constant course adjustments.

Q4: Can I use this for other celestial bodies?
A: Yes, the formula works for any sphere. Just replace the Earth's radius with the radius of the celestial body you're calculating for.

Q5: What are typical applications of this formula?
A: Navigation systems, flight planning, maritime routing, geographic analysis, and location-based services all use great-circle distance calculations.