Calculate slope length from rise, horizontal run, angle, percent grade, or pitch, and reverse-solve rise, run, and angle with common length units.

Solve straight-slope geometry

Required: vertical rise or drop and horizontal run in the same unit.

Use a negative value for a downhill drop.

This is the diagonal distance along the surface.

Result

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 = (H) / (R)
R = (H) / (S)
LOS = √(H² + R²)
LOS = √(H² + ((H) / (S))²)
LOS = H√(1 + (1) / (S²))

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 = (grade \%) / (100)
S = tan(θ)

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 = (25) / (100) = 0.25
R = (3) / (0.25) = 12 m
LOS = √(3² + 12²) = √(153) ≈ 12.37 m

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

S = (1) / (2) = 0.5
R = (8) / (0.5) = 16 ft
LOS = √(8² + 16²) = √(320) ≈ 17.89 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.

grade \% = 100S

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

S = tan(θ)

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

R = (H) / (S)