Driveway Grade Calculator - Slope, Ratio, and Angle

Driveway Grade Calculator - Formulas and Example

Formulas Used

Grade Percentage - This expresses the slope as a percentage of the horizontal length: \[ \text{Grade} = \frac{\text{Height}}{\text{Length}} \times 100 \]

Grade per mill - This expresses the slope as parts per thousand: \[ \text{Grade (per mill)} = \frac{\text{Height}}{\text{Length}} \times 1000 \]

Slope Ratio - This compares the horizontal length to the vertical rise: \[ \text{Slope Ratio} = \frac{\text{Length}}{\text{Height}} \] The result is shown as: \[ 1 : x \] This means for every **1 unit of rise**, the driveway runs horizontally **x units**.

Slope Angle - This is the angle between the driveway surface and the horizontal ground: \[ \theta = \arctan\left(\frac{\text{Height}}{\text{Length}}\right) \]

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Example Calculation - Imperial

Given:

• Height = 5 feet 6 inches
• Length = 50 feet 0 inches

Step 1: Convert to Decimal Feet

\[ \text{Height} = 5 + \frac{6}{12} = 5.5 \ \text{feet} \] \[ \text{Length} = 50 + \frac{0}{12} = 50 \ \text{feet} \]

Step 2: Calculate Grade Percentage

\[ \text{Grade} = \frac{5.5}{50} \times 100 = 11.0\% \]

Step 3: Calculate Grade per mill

\[ \text{Grade (per mill)} = \frac{5.5}{50} \times 1000 = 110.0 \ \text{‰} \]

Step 4: Calculate Slope Ratio

\[ \frac{50}{5.5} \approx 9.09 \] \[ \text{Slope Ratio} = 1 : 9.1 \] This means for every **1 foot of rise**, the driveway runs **9.1 feet horizontally**.

Step 5: Calculate Slope Angle

\[ \theta = \arctan\left(\frac{5.5}{50}\right) \] \[ \theta \approx 6.3^\circ \]

Results Summary

• Grade: 11.0%
• Grade (per mill): 110.0‰
• Slope Ratio: 1 : 9.1
• Slope Angle: 6.3°

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What Each Result Means

• Grade (%) - The slope as a percentage of the horizontal length. Typical driveway grades are between 2% and 15%.
• Grade per mill (‰) - Slope expressed in parts per thousand, useful for civil design in metric countries.
• Slope Ratio - Horizontal run compared to vertical rise, showing how many units of horizontal travel occur for each unit of rise.
• Slope Angle (°) - The angle between the driveway surface and flat ground, useful for clearance checks and drainage design.

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