1. What is the Slope Formula?

The slope formula calculates the steepness or gradient of a line from the angle of inclination. The mathematical relationship is expressed as m = tan(θ), where m represents the slope and θ represents the angle in degrees.

2. How Does the Calculator Work?

The calculator uses the slope formula:

Where:

• \( m \) — Slope (unitless)
• \( \theta \) — Angle in degrees
• \( \tan \) — Tangent trigonometric function

Explanation: The calculator converts the angle from degrees to radians, then applies the tangent function to determine the slope value.

3. Importance of Slope Calculation

Details: Slope calculation is essential in various fields including mathematics, engineering, construction, and physics for determining inclination, gradient, and rate of change.

4. Using the Calculator

Tips: Enter the angle in degrees (0-90°). The calculator will compute the corresponding slope value using the tangent function.

5. Frequently Asked Questions (FAQ)

Q1: What is the range of valid angle inputs?
A: The calculator accepts angles between 0 and 90 degrees. Angles outside this range may produce invalid or undefined results.

Q2: What does a slope of 1 mean?
A: A slope of 1 corresponds to a 45-degree angle, indicating a 1:1 ratio (rise equals run).

Q3: How is the tangent function calculated?
A: The tangent function is computed mathematically, typically using the PHP tan() function after converting degrees to radians.

Q4: Can this calculator handle decimal angles?
A: Yes, the calculator accepts decimal values for more precise slope calculations.

Q5: What are some practical applications of slope calculation?
A: Slope calculations are used in road construction, roof pitch determination, wheelchair ramp design, and various engineering applications.