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Calculating the slope or grade of a surface is a fundamental concept in mathematics, geography, construction, and other fields. It indicates the steepness or inclination of a surface relative to a horizontal plane. The slope can be measured in degrees or as a ratio, often expressed as a percentage.

The simplest way to calculate the slope or grade of a surface is by using the ratio of the vertical height difference (rise) to the horizontal distance (run).

This relationship can be expressed using the following formula:

Slope Grade (%) = (Height difference / Horizontal distance) * 100

Where:

**Height difference**refers to the difference in height between the start and end of the slope. This is often referred to as the 'rise' or 'drop'. It should be measured in the same unit as the horizontal distance.**Horizontal distance**refers to the horizontal component of the slope, not the actual distance along the slope. This is often referred to as the 'run'. It should be measured in the same unit as the height difference.

It's important to note that while this formula is simple and straightforward, it assumes a straight line (linear slope) between the start and end point of the slope. For more complex surfaces, like a hill, the actual slope can vary significantly.

A slope grade of 0% would indicate a completely flat surface, while a slope grade of 100% means that for every horizontal unit of distance, there's an equal rise or drop in height. A slope grade of over 100% means the rise or drop in height is greater than the horizontal distance.

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