Elevation Grade Calculator

Vertical Distance (Rise):

Horizontal Distance (Run):

1. What is Elevation Grade Calculator?

Elevation Grade

Definition: This calculator determines the grade or slope of an area, given its vertical distance (rise) and horizontal distance (run). It provides the grade as a decimal, percentage, angle of elevation in degrees, and as a ratio.

Purpose: It helps engineers, surveyors, and construction professionals assess the steepness of terrain for projects like road construction, retaining walls, and landscaping.

2. How Does the Calculator Work?

The calculator uses the following equations:

Grade (Decimal): \( \text{grade} = \frac{\text{rise}}{\text{run}} \)
Grade in Percentage: \( \text{grade percentage} = \text{grade} \times 100 \)
Angle of Elevation: \( \text{angle} = \arctan\left(\frac{\text{rise}}{\text{run}}\right) \)
Grade as Ratio: Expressed as 1 in \( \frac{\text{run}}{\text{rise}} \)

Where:

\( \text{rise} \): The vertical distance or change in elevation;
\( \text{run} \): The horizontal distance covered by the slope;
\( \text{grade} \): The slope as a decimal;
\( \text{grade percentage} \): The slope as a percentage;
\( \text{angle} \): The angle of elevation in degrees.

Steps:

Enter the vertical distance (rise) and select its unit.
Enter the horizontal distance (run) and select its unit.
Click "Calculate" to compute the grade, grade percentage, angle of elevation, and ratio.
Results are displayed with 4 decimal places or in scientific notation if less than 0.001.

3. Importance of Elevation Grade Calculation

Calculating elevation grade is crucial for:

Road Construction: Ensures safe slopes for roads, especially in hilly areas where zig-zag patterns may be needed for steep terrain.
Retaining Walls: Helps design walls to prevent landslides by assessing slope steepness.
Landscaping: Assists in planning drainage and terrain modifications for safety and functionality.

4. Using the Calculator

Example 1: Calculate the elevation grade (as per Omni Calculator example):

Vertical Distance (Rise): 12 m;
Horizontal Distance (Run): 200 m;
Grade: \( \text{grade} = \frac{12}{200} = 0.0600 \);
Grade in Percentage: \( 0.06 \times 100 = 6.0000\% \);
Angle of Elevation: \( \text{angle} = \arctan\left(\frac{12}{200}\right) \approx 3.4336^\circ \);
Grade as Ratio: \( \frac{200}{12} \approx 16.6667 \), so 1 in 16.6667;
Result: Grade = 0.0600, Grade in Percentage = 6.0000%, Angle of Elevation = 3.4336 degrees, Grade as Ratio = 1 in 16.6667.

Example 2: Calculate with different units:

Vertical Distance (Rise): 50 ft;
Horizontal Distance (Run): 1000 ft;
Convert to meters: Rise = 15.24 m, Run = 304.8 m;
Grade: \( \text{grade} = \frac{15.24}{304.8} = 0.0500 \);
Grade in Percentage: \( 0.05 \times 100 = 5.0000\% \);
Angle of Elevation: \( \text{angle} = \arctan\left(\frac{15.24}{304.8}\right) \approx 2.8624^\circ \);
Grade as Ratio: \( \frac{304.8}{15.24} = 20 \), so 1 in 20;
Result: Grade = 0.0500, Grade in Percentage = 5.0000%, Angle of Elevation = 2.8624 degrees, Grade as Ratio = 1 in 20.

Example 3: Calculate with flat terrain:

Vertical Distance (Rise): 0 m;
Horizontal Distance (Run): 100 m;
Grade: \( \text{grade} = \frac{0}{100} = 0 \);
Grade in Percentage: \( 0 \times 100 = 0\% \);
Angle of Elevation: \( \text{angle} = \arctan(0) = 0^\circ \);
Grade as Ratio: Flat (0 slope);
Result: Grade = 0.0000, Grade in Percentage = 0.0000%, Angle of Elevation = 0.0000 degrees, Grade as Ratio = Flat (0 slope).

5. Frequently Asked Questions (FAQ)

Q: What is elevation grade?
A: Elevation grade, also known as slope, is the steepness of a terrain, expressed as the ratio of vertical distance (rise) to horizontal distance (run), as a percentage, or as an angle.

Q: What does a grade of 1 mean?
A: A grade of 1 (or 100%) means that for every unit of horizontal distance, there is an equal unit of vertical change, corresponding to a 45-degree angle.

Q: How steep is a 5% grade?
A: A 5% grade means that for every 100 units of horizontal distance, there is a 5-unit vertical rise, corresponding to an angle of about 2.86 degrees, which is relatively gentle.