Slope and Elevation Difference Calculator

How is slope calculated?

Slope is the elevation difference between two points divided by the horizontal distance between them: slope = rise / run. Multiply by 100 to get the percent grade.

Example: a road that climbs 5 m over a horizontal distance of 100 m has a slope of 5 / 100 = 0.05, which is 5 percent.

Percent, ratio and degrees

The same slope can be written three ways:

• Percent: how many units it rises per 100 units of run. 5 percent.
• Ratio: how many units of run are needed for 1 unit of rise. 1:20.
• Degrees: the angle with the horizontal. From tan α = slope, 2.86 degrees.

Percent and degrees must not be confused: a 100 percent slope is 45 degrees, not 90.

Rise and end level from a slope

The rise is the horizontal distance times the slope. A 50 m pipe laid at 2 percent falls 50 × 0.02 = 1 m. Adding the rise to the start level gives the end level: from level 250 m, a 1.5 percent descent over 400 m ends at 250 − 6 = 244 m.

Road grade and intermediate levels

With the levels of two points and the horizontal distance between them, the grade is (level difference) / (distance). On a constant grade, the level of any point in between is the start level plus grade times distance.

Horizontal distance from a slope measurement

A length taped along the ground is a slope length. If the elevation difference is known, the horizontal distance follows from the Pythagorean theorem: L = √(S² − Δh²). A slope length of 13 m with a 5 m rise gives 12 m horizontally.

Where is it used?

Ramp length, the fall of drain and sewer pipes, screed and terrace falls, road and site grading, roof pitch, excavation batter and slopes from levelling readings are all the same calculation.

Limits

The calculator is for lines with one constant slope. It does not give permitted slope limits, which come from the relevant code.