1. What is the Axis Lens Calculation?

The Axis Lens calculation determines the angular direction of a vector from its X and Y coordinates using the atan2 function. This is particularly useful in optics for determining lens orientation and in various engineering applications.

2. How Does the Calculator Work?

The calculator uses the atan2 formula:

Where:

• \( y \) — Y coordinate value
• \( x \) — X coordinate value
• \( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The atan2 function computes the angle between the positive x-axis and the point (x, y), returning a value in radians which is then converted to degrees.

3. Importance of Axis Calculation

Details: Accurate axis calculation is essential in optics for proper lens alignment, in navigation systems for direction determination, and in various scientific and engineering applications where angular orientation matters.

4. Using the Calculator

Tips: Enter both X and Y coordinate values. The calculator will compute the axis angle in degrees, normalized to the 0-360° range. Both values cannot be zero simultaneously.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between atan and atan2?
A: atan2 takes both x and y coordinates as parameters and returns the angle in the correct quadrant, while atan only takes a single ratio (y/x) and may return results in the wrong quadrant.

Q2: What is the range of values returned?
A: The calculator returns values between 0° and 360°, with 0° pointing east, 90° north, 180° west, and 270° south.

Q3: Can both X and Y be zero?
A: No, if both X and Y are zero, the angle is undefined as there is no direction from the origin.

Q4: How precise is the calculation?
A: The calculation is mathematically precise based on the input values, with the result rounded to one decimal place.

Q5: What applications use this calculation?
A: This calculation is used in optics, computer graphics, robotics, navigation systems, and many other fields where directional information is needed.