Azimuth Calculator From Coordinates

Azimuth Formula:

\[ \text{Azimuth} = \left( \text{atan2}(y2 - y1, x2 - x1) \times \frac{180}{\pi} \right) \mod 360 \]

Point 1 X-coordinate:

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Point 1 Y-coordinate:

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Point 2 X-coordinate:

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Point 2 Y-coordinate:

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Azimuth:

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1. What is Azimuth?

Azimuth is the angular measurement in a spherical coordinate system, representing the angle between a reference direction (typically north) and the line from the observer to a point of interest. It's commonly used in navigation, astronomy, and geosciences.

2. How Does the Calculator Work?

The calculator uses the mathematical formula:

\[ \text{Azimuth} = \left( \text{atan2}(y2 - y1, x2 - x1) \times \frac{180}{\pi} \right) \mod 360 \]

Where:

\( x1, y1 \) — Coordinates of the starting point
\( x2, y2 \) — Coordinates of the target point
\( \text{atan2} \) — The two-argument arctangent function
\( \mod 360 \) — Ensures result is between 0-360 degrees

Explanation: The atan2 function calculates the angle between the positive x-axis and the point (x2-x1, y2-y1), which is then converted to degrees and normalized to 0-360 range.

3. Applications of Azimuth Calculation

Details: Azimuth is used in navigation (compass bearings), astronomy (celestial coordinates), surveying, antenna alignment, and various geospatial applications.

4. Using the Calculator

Tips: Enter coordinates of two points in the same coordinate system. The calculator works with any consistent units (meters, feet, etc.) as long as both points use the same units.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between azimuth and bearing?
A: Azimuth is measured clockwise from north (0-360°), while bearing uses north/south reference with east/west deflection (e.g., N45°E).

Q2: How does this relate to compass directions?
A: 0°=North, 90°=East, 180°=South, 270°=West. Intermediate values represent directions between these cardinal points.

Q3: Does the coordinate system matter?
A: Yes, the result assumes standard mathematical convention where positive X is right and positive Y is up. For GIS systems, you may need to adjust.

Q4: What about elevation/distance?
A: This calculates only the horizontal angle. For 3D direction, you'd need to calculate both azimuth and elevation.

Q5: How accurate is this calculation?
A: Mathematically precise, but real-world accuracy depends on coordinate precision and the flatness of the projection used.