Calculate signed inclination from rise and run, convert it to percent grade, pitch, ratio, and diagonal, or solve rise, run, and two-point slope in reverse.

Inclination Formula

The following formula is used to calculate an inclination from an angle.

m = tan (θ)
  • Where m is slope (rise divided by horizontal run); inclination angle is θ
  •  Î¸ is the angle formed between the line and the x-axis.

To calculate the amount of inclination, take the tangent of the angle formed between the line and the x-axis.

Inclination Definition

What is inclination?

A line’s slope is its vertical change divided by horizontal change; its inclination angle describes its direction relative to the horizontal. The line need not cross the x-axis.

An inclination is another word for the slope of a line. Typically, the term inclination is used when analyzing the slope through the angle instead of the coordinate points.

Example Problem

How to calculate an inclination?

First, measure the angle formed between the line and the x-axis. For this example, the angle is found to be 50 degrees.

For a tangent function that expects radians, convert degrees by multiplying by π/180. A degree-mode calculator can use 50° directly.

= 50/57.2958

= .87266 radians.

Finally, calculate the inclination using the formula above:

m = tan ( Î¸ )

m = tan ( .87266)

m = 1.191