Elevation Grade / Slope Calculator
The Elevation Grade / Slope Calculator calculates the height difference, percent grade, slope ratio, and slope angle based on a given slope per foot. This tool is useful for construction, landscaping, and grading projects requiring precise slope measurements.
Elevation Grade / Slope of Inches per Foot
Calculator
- the slope length in feet and inches
- required slope in inches per foot
Results
- the total elevation change in decimal inches
- elevation change in inches
- elevation change in feet and inches
- the change of elevation as a percentage
- the slope expressed as a ratio
- the angle of the slope in degrees
This calculator provides accurate slope measurements for grading, construction, and engineering applications.
Elevation Grade / Slope Calculator - Formulas & Example
Formulas Used
The total height difference is calculated using the formula:
\[ \text{Height Difference} = \left( \frac{\text{Length (ft)} \times 12 + \text{Length (in)}}{12} \right) \times \text{Slope per Foot} \]The percent grade is determined as:
\[ \text{Percent Grade} = \left( \frac{\text{Slope per Foot}}{12} \right) \times 100 \]The slope ratio (1:X format) is calculated as:
\[ \text{Slope Ratio} = \frac{12}{\text{Slope per Foot}} \]The angle of the slope in degrees is found using the inverse tangent function:
\[ \theta = \tan^{-1} \left(\frac{\text{Slope per Foot}}{12}\right) \]Example Calculation
Given the following inputs:
- Length: 24 ft 6 in
- Slope per Foot: 1 3/8 in
Step 1: Convert Length to Feet
\[ \text{Total Length} = 24 + \frac{6}{12} = 24.5 \text{ ft} \]Step 2: Convert Slope to Decimal
\[ 1 \frac{3}{8} = 1 + \frac{3}{8} = 1.375 \text{ inches per foot} \]Step 3: Calculate Total Height Difference
\[ \text{Height Difference} = 24.5 \times 1.375 \] \[ = 30.9375 \text{ inches} \]Step 4: Convert to Feet & Inches
\[ 30.9375 \div 12 = 2 \text{ full feet} \quad \text{with remainder} \quad 30.9375 - 24 = 6.9375 \text{ inches} \] Convert 6.9375 inches to a proper fraction with denominator 16: \[ 0.9375 \times 16 = 15 \quad \Rightarrow \quad \frac{15}{16} \] Final result in feet and inches: \[ 2 \text{ ft } 6 \frac{15}{16} \text{ in} \]Step 5: Convert Height Difference to Inches + Proper Fraction
\[ 30.9375 \text{ in} = 30 + 0.9375 \text{ in} \] \[ 0.9375 \times 16 = 15 \quad \Rightarrow \quad \frac{15}{16} \] Final result in inches plus fraction: \[ 30 \frac{15}{16} \text{ in} \]Step 6: Calculate Percent Grade
\[ \text{Percent Grade} = \left( \frac{1.375}{12} \right) \times 100 \] \[ = 11.46\% \]Step 7: Calculate Slope Ratio
\[ \text{Slope Ratio} = \frac{12}{1.375} = 1:8.73 \]Step 8: Calculate Angle of Slope
\[ \theta = \tan^{-1} \left(\frac{1.375}{12}\right) \] \[ = 6.54^\circ \]Final Results
- Height Difference: 30.9375 inches
- Height Difference in Feet & Inches: 2 ft 6 15/16 in
- Height Difference in Inches + Proper Fraction: 30 15/16 in
- Percent Grade: 11.46%
- Slope Ratio: 1:8.73
- Angle of Slope: 6.54°
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Equipment
Factors, Grades, Percentages
- Elevation Grade Slope in a Percentage, Millimetres
- Elevation Grade from Inches per Foot
- Elevation Grade from a Percentage
- Grade Percentage to Angle in Degrees
- Horizontal Length from Angle and Slope Length
- Spike's Compaction Factor Calculator
- Shrink and Load Factor Calculator
- Slope Percent and Angle of the Slope - Metric
- Swell and Load Factor Calculator
- Vertical Depth from a Slope Percentage and Horizontal Length