1. What is the Gradient To Angle Conversion?

The gradient to angle conversion calculates the angle (in degrees) from a given gradient (slope) value using the inverse tangent (arctan) function. This is particularly useful in mathematics, engineering, and physics applications.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \theta \) — Angle in degrees
• \( m \) — Gradient (slope) value
• \( \pi \) — Mathematical constant pi (approximately 3.14159)

Explanation: The arctangent function returns the angle in radians, which is then converted to degrees by multiplying by 180/π.

3. Importance of Angle Calculation

Details: Converting gradient to angle is essential in various fields including trigonometry, calculus, engineering design, slope analysis, and computer graphics applications.

4. Using the Calculator

Tips: Enter the gradient value (slope) in the input field. The calculator will compute the corresponding angle in degrees. Positive gradients result in positive angles, negative gradients result in negative angles.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of angles this calculator can produce?
A: The arctan function produces angles between -90° and +90° (-π/2 to +π/2 radians).

Q2: How does this relate to Desmos graphing?
A: In Desmos, you can use this conversion to find angles of lines, slopes of functions at specific points, or analyze trigonometric relationships.

Q3: What's the difference between gradient and angle?
A: Gradient represents the ratio of vertical change to horizontal change (rise/run), while angle represents the inclination measured in degrees from the horizontal.

Q4: Can I calculate the angle for vertical lines?
A: For vertical lines (undefined gradient), the angle is 90° but this calculator cannot process infinite gradients.

Q5: How accurate is this calculation?
A: The calculation uses PHP's built-in mathematical functions which provide high precision results suitable for most applications.