Air Route Distance Calculator

Great-circle Distance Formula:

\[ Distance (km) = 6371 \times \arccos(\sin(lat1) \times \sin(lat2) + \cos(lat1) \times \cos(lat2) \times \cos(\Delta lon)) \]

Distance:

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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 of the sphere. For air travel, this represents the most efficient route between two locations on Earth.

2. How Does the Calculator Work?

The calculator uses the great-circle distance formula:

\[ Distance (km) = 6371 \times \arccos(\sin(lat1) \times \sin(lat2) + \cos(lat1) \times \cos(lat2) \times \cos(\Delta lon)) \]

Where:

\( lat1 \) — Latitude of first point in radians
\( lat2 \) — Latitude of second point in radians
\( \Delta lon \) — Difference in longitude between the two points in radians
6371 — Earth's mean radius in kilometers

Explanation: This formula calculates the central angle between two points on a sphere and multiplies by the Earth's radius to get the surface distance.

3. Importance of Air Route Distance Calculation

Details: Accurate distance calculation is crucial for flight planning, fuel estimation, flight time calculation, and optimizing air travel routes for efficiency and cost-effectiveness.

4. Using the Calculator

Tips: Enter latitudes and longitude difference in radians. Remember to convert degrees to radians if necessary (degrees × π/180). All values must be valid numerical inputs.

5. Frequently Asked Questions (FAQ)

Q1: Why use radians instead of degrees?
A: Trigonometric functions in mathematical calculations typically require radians. Convert degrees to radians by multiplying by π/180.

Q2: What is Earth's radius used in the calculation?
A: We use 6371 km, which is the mean radius of Earth. For more precise calculations, specific ellipsoidal models may be used.

Q3: How accurate is this calculation?
A: For most practical purposes, this provides excellent accuracy. For precise navigation, additional factors like Earth's oblateness may be considered.

Q4: Can I use this for any two points on Earth?
A: Yes, this formula works for any two points on Earth's surface, provided the coordinates are in radians.

Q5: What if my coordinates are in degrees?
A: Convert degrees to radians by multiplying each coordinate by π/180 before entering into the calculator.