Azimuth And Distance Calculator

Distance and Azimuth Formulas:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] \[ \text{Azimuth} = \arctan2(y_2 - y_1, x_2 - x_1) \]

X1 (m):

Y1 (m):

X2 (m):

Y2 (m):

Distance:

Azimuth:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is Distance and Azimuth Calculation?

Distance and azimuth calculations are fundamental in surveying, navigation, and GIS. Distance measures the straight-line separation between two points, while azimuth represents the direction from the first point to the second, measured in degrees clockwise from north.

2. How Does the Calculator Work?

The calculator uses these mathematical formulas:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] \[ \text{Azimuth} = \arctan2(y_2 - y_1, x_2 - x_1) \]

Where:

\( x_1, y_1 \) — Coordinates of the first point
\( x_2, y_2 \) — Coordinates of the second point
\( \arctan2 \) — The two-argument arctangent function that preserves quadrant information

Explanation: The distance formula calculates the Euclidean distance between two points, while the azimuth formula calculates the angle from the positive x-axis to the vector between the points.

3. Applications of Distance and Azimuth

Details: These calculations are essential in surveying, navigation systems, geographic information systems (GIS), robotics, computer graphics, and many engineering applications where spatial relationships between points need to be determined.

4. Using the Calculator

Tips: Enter the coordinates of both points in meters. The calculator will compute both the straight-line distance between the points and the azimuth angle measured in degrees clockwise from the positive x-axis.

5. Frequently Asked Questions (FAQ)

Q1: What coordinate system does this calculator use?
A: The calculator uses a Cartesian coordinate system with x and y coordinates measured in meters.

Q2: How is azimuth different from bearing?
A: Azimuth is measured clockwise from north (0-360°), while this calculator provides angle from the positive x-axis. For true azimuth, you may need to adjust based on your coordinate system orientation.

Q3: Can I use this for geographic coordinates?
A: For small areas, the calculations are approximately correct, but for large distances on the Earth's surface, you should use great circle distance formulas that account for Earth's curvature.

Q4: What is the precision of the calculations?
A: The calculator provides results with 4 decimal places, suitable for most engineering and surveying applications.

Q5: How does atan2 differ from regular arctangent?
A: atan2(y, x) preserves the quadrant information of the angle, providing results in the full 0-360° range, unlike atan(y/x) which only returns values between -90° and 90°.