Enter any 2 values into the Length of Slope Calculator to calculate the missing value. Here, the slope ratio S is defined as rise/run (grade), and the Length of Slope is the distance along the slope (the hypotenuse of the right triangle).

Length of Slope Calculator

Enter any 2 values to calculate the missing variable

Note: Slope ratio S is rise/run (e.g., 25% grade = 0.25). If you have a run:rise slope such as 4:1, then S = 1/4 = 0.25.

Length of Slope Formula and Calculator Guide

The length of slope is the actual distance measured along the sloped surface. In a right-triangle model, it is the hypotenuse. This calculator uses the slope ratio S = rise/run, where H is vertical rise and LOS is the slope length.

Variables

Variable Meaning Unit Notes
H Total vertical rise Use any length unit, but stay consistent
S Slope ratio defined as rise/run Unitless decimal
R Horizontal run Same unit as H
LOS Distance along the slope Same unit as H

Core Formulas

S = \frac{H}{R}
R = \frac{H}{S}
LOS = \sqrt{H^2 + R^2}
LOS = \sqrt{H^2 + \left(\frac{H}{S}\right)^2}
LOS = H\sqrt{1+\frac{1}{S^2}}

Common Slope Conversions

Many input errors come from entering the slope in the wrong format. Convert the slope to rise/run before using the calculator.

Given Format What to Enter for S Notes
25% grade 0.25 Percent grade divided by 100
4:1 run:rise 0.25 Because rise/run = 1/4
2:1 run:rise 0.50 Because rise/run = 1/2
1:1 slope 1.00 Rise equals run
45° angle 1.00 Equivalent to a 100% grade 
S = \frac{\text{grade \%}}{100}
S = \tan(\theta)

How to Use the Calculator

  1. Enter the total rise H.
  2. Convert the slope to S = rise/run.
  3. Use one unit system for all length values.
  4. Read the result as the distance measured directly along the slope face.

Examples

Example 1: A slope rises 3 m with a 25% grade.

S = \frac{25}{100} = 0.25
R = \frac{3}{0.25} = 12\text{ m}
LOS = \sqrt{3^2 + 12^2} = \sqrt{153} \approx 12.37\text{ m}

Example 2: A slope rises 8 ft and is described as 2:1 run:rise.

S = \frac{1}{2} = 0.5
R = \frac{8}{0.5} = 16\text{ ft}
LOS = \sqrt{8^2 + 16^2} = \sqrt{320} \approx 17.89\text{ ft}

Quick Checks

  • LOS is always at least as large as H. It can only equal H for a perfectly vertical line.
  • Smaller S means a flatter slope, which creates a longer run and longer slope length.
  • Larger S means a steeper slope, so the slope length gets closer to the rise.
  • S cannot be 0, because that would imply no rise/run relationship for this formula.

Common Input Mistakes

Mistake Why It Causes Problems Fix
Entering 25 instead of 0.25 25 is not 25% grade in rise/run form Divide percent by 100 first
Using run:rise directly as S The calculator expects rise/run Invert the ratio when needed
Mixing units Feet, inches, meters, and yards cannot be mixed without conversion Convert values before calculating
Confusing rise with slope length Rise is vertical; slope length is diagonal Model the slope as a right triangle

Where This Calculation Is Useful

  • Roof layouts and rafter planning
  • Road, driveway, and ramp design
  • Landscaping and retaining wall grading
  • Drainage swales and ditch geometry
  • Earthwork and embankment takeoffs

FAQ

Is slope ratio the same as percent grade?
Not exactly. Percent grade is the slope ratio multiplied by 100.

\text{grade \%} = 100S

What if my slope is given as an angle?
Convert the angle above horizontal into slope ratio first.

S = \tan(\theta)

Can I calculate horizontal run too?
Yes. Once you know the rise and slope ratio, the run follows directly.

R = \frac{H}{S}