Home
Back
Inclination Angle Formula:
| From: | To: |
The inclination angle formula calculates the angle of inclination from the vertical and horizontal components of a slope. It is derived from the trigonometric relationship in a right triangle where the tangent of the angle equals the ratio of the opposite side (dy) to the adjacent side (dx).
The calculator uses the inclination angle formula:
Where:
Explanation: The arctangent function converts the ratio of vertical to horizontal change into an angle measurement, providing the slope's inclination in degrees.
Details: Calculating inclination angles is essential in various fields including engineering, construction, geography, and physics. It helps determine slope stability, design appropriate gradients for roads and ramps, and analyze terrain features.
Tips: Enter both vertical change (dy) and horizontal change (dx) as unitless values. The horizontal change (dx) must be a positive non-zero value to avoid division by zero.
Q1: What units should I use for dy and dx?
A: The values should be in the same units (both in meters, both in feet, etc.), but the calculator treats them as unitless since the ratio is what matters for the angle calculation.
Q2: What is the range of possible inclination angles?
A: The inclination angle can range from -90° to 90°, representing downward and upward slopes respectively.
Q3: How does this relate to slope percentage?
A: Slope percentage = (dy/dx) × 100%. The inclination angle is the arctangent of this ratio.
Q4: What if dx is zero?
A: If dx is zero, you have a vertical line and the inclination angle is 90° (undefined in the formula). The calculator requires dx > 0.
Q5: Can I use this for three-dimensional slopes?
A: This formula calculates the inclination in a two-dimensional plane. For 3D slopes, additional calculations involving azimuth angles are needed.