Slope Degrees Gradient Grade

Overview

Engineering reference data for Slope Degrees Gradient Grade in miscellaneous.

Key Formulas

Unit Conversion

$y = x \cdot k$

Multiply by conversion factor.

Linear Interpolation

$y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}$

Estimate between two known points.

Percentage

$p = \frac{\text{part}}{\text{whole}} \times 100\%$

Part as fraction of whole.

Variables

Roof Pitch Formulas

Slope for roof pitch is commonly expressed in the form x:12 (like 4/12 or 9/12). The following formulas convert this pitch to grade and angle.

Roof pitch to grade: $S_{grade}(\%) = \frac{100 \cdot x}{12}$

Example - Roof Pitch 4/12 as Grade: $S_{grade}(\%) = \frac{100 \cdot 4}{12} = 33.3\%$

Roof pitch to angle: $S_{angle} = \tan^{-1}\left(\frac{x}{12}\right)$

Example - Roof Pitch 4/12 as Angle: $S_{angle} = \tan^{-1}\left(\frac{4}{12}\right) \approx 18.4°$

Slope Conversion Table

This table provides a reference for converting between common slope representations.

Common Equivalents

• 1% grade = 0.57 degrees
• 1% grade = 1 cm rise per 100 cm horizontal
• 1% grade = 1 inch rise per 100 inches horizontal
• 1% grade = 0.125 inch rise per foot horizontal

Interactive Charts

References

• Original Source