Driving Miles Between Cities Calculator

Great-Circle Distance Formula:

\[ \text{Distance (miles)} = 3959 \times \arccos(\sin(lat1) \times \sin(lat2) + \cos(lat1) \times \cos(lat2) \times \cos(lon1 - lon2)) \]

Latitude 1:

degrees

Longitude 1:

degrees

Latitude 2:

degrees

Longitude 2:

degrees

Distance:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Great-Circle Distance?

The great-circle distance is the shortest distance between two points on the surface of a sphere, measured along the surface. For Earth, this represents the shortest path between two locations, commonly used for air and sea navigation.

2. How Does the Calculator Work?

The calculator uses the Haversine formula:

\[ \text{Distance (miles)} = 3959 \times \arccos(\sin(lat1) \times \sin(lat2) + \cos(lat1) \times \cos(lat2) \times \cos(lon1 - lon2)) \]

Where:

\( lat1, lon1 \) — Latitude and longitude of first location (degrees)
\( lat2, lon2 \) — Latitude and longitude of second location (degrees)
\( 3959 \) — Earth's radius in miles
All trigonometric functions use radians

Explanation: The formula calculates the central angle between two points and multiplies by Earth's radius to get the distance.

3. Importance of Distance Calculation

Details: Accurate distance calculation is essential for travel planning, logistics, navigation systems, and geographical analysis. Great-circle distance provides the most direct route between locations.

4. Using the Calculator

Tips: Enter latitude values between -90° and 90°, longitude values between -180° and 180°. Use decimal degrees format for precise calculations. Positive values for north/east, negative for south/west.

5. Frequently Asked Questions (FAQ)

Q1: Is this driving distance or straight-line distance?
A: This calculates great-circle (straight-line) distance. Actual driving distance may be longer due to roads and terrain.

Q2: Why 3959 miles for Earth's radius?
A: This is the mean radius of Earth in miles. More precise calculations might use 3958.8 miles.

Q3: How accurate is this calculation?
A: Very accurate for most purposes. Assumes Earth is a perfect sphere, while it's actually an oblate spheroid.

Q4: Can I use this for international locations?
A: Yes, the formula works globally. Just ensure coordinates are in decimal degrees format.

Q5: What's the difference from Euclidean distance?
A: Great-circle accounts for Earth's curvature, while Euclidean treats Earth as flat - only accurate for very short distances.