Azimuth Calculator Between Two Points

Azimuth Formula:

\[ \text{azimuth} = \arctan2(\sin(\Delta\lambda) \cdot \cos(\phi_2), \cos(\phi_1) \cdot \sin(\phi_2) - \sin(\phi_1) \cdot \cos(\phi_2) \cdot \cos(\Delta\lambda)) \]

Longitude Difference (Δλ):

radians

Latitude Point 1 (φ₁):

radians

Latitude Point 2 (φ₂):

radians

Azimuth:

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1. What is Azimuth?

Azimuth is the angle between a reference direction (typically north) and the direction to a point of interest, measured clockwise in degrees. In navigation and geodesy, it's used to describe the direction from one point to another on the Earth's surface.

2. How Does the Calculator Work?

The calculator uses the azimuth formula:

\[ \text{azimuth} = \arctan2(\sin(\Delta\lambda) \cdot \cos(\phi_2), \cos(\phi_1) \cdot \sin(\phi_2) - \sin(\phi_1) \cdot \cos(\phi_2) \cdot \cos(\Delta\lambda)) \]

Where:

\( \Delta\lambda \) — Difference in longitude between two points (radians)
\( \phi_1 \) — Latitude of first point (radians)
\( \phi_2 \) — Latitude of second point (radians)
\( \arctan2 \) — Two-argument arctangent function

Explanation: The formula calculates the initial bearing (forward azimuth) from point 1 to point 2 using spherical trigonometry.

3. Importance of Azimuth Calculation

Details: Azimuth is crucial in navigation, surveying, astronomy, and various engineering applications. It helps determine direction between points on a sphere (like Earth) and is fundamental for route planning and orientation.

4. Using the Calculator

Tips: Enter all angles in radians. For degrees to radians conversion: radians = degrees × (π/180). The result is given in degrees from North (0°), increasing clockwise (East = 90°, South = 180°, West = 270°).

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between azimuth and bearing?
A: Azimuth is typically measured clockwise from North (0° to 360°), while bearing might use different reference systems (like North/South with East/West components).

Q2: How accurate is this calculation?
A: This provides the initial azimuth on a perfect sphere. For precise geodesy work, ellipsoidal models are more accurate.

Q3: Can I use degrees instead of radians?
A: The formula requires radians. Convert degrees to radians first (multiply by π/180).

Q4: What's the reverse azimuth?
A: The reverse azimuth (from point 2 to point 1) is typically ±180° from the forward azimuth.

Q5: Does this work for any two points on Earth?
A: Yes, but for antipodal points (exactly opposite each other), the azimuth is undefined.