Rise over run is the everyday way to describe steepness – stair stringers, roof pitches, ramps and graphs. A 4-in-12 roof rises 4 units for every 12 across.
How to use the Rise Over Run Calculator
- Point 1 – x
- Point 1 – y
- Point 2 – x
- Point 2 – y
Results update as you type, and everything is calculated in your browser.
How it works
The rise is the vertical change and the run the horizontal change. Slope × 100 gives the percentage grade; the arctangent gives the angle.
Inputs explained
| Field | What to enter |
|---|---|
| Point 1 – x | A number |
| Point 1 – y | A number |
| Point 2 – x | A number |
| Point 2 – y | A number |
What each result means
- Slope (rise ÷ run) = ([Point 2 – y] – [Point 1 – y])÷([Point 2 – x] – [Point 1 – x])
- Rise Δy = [Point 2 – y] – [Point 1 – y]
- Run Δx = [Point 2 – x] – [Point 1 – x]
- Percentage grade = ([Point 2 – y] – [Point 1 – y])÷([Point 2 – x] – [Point 1 – x])×100
- Angle = deg(atan(([Point 2 – y] – [Point 1 – y])÷([Point 2 – x] – [Point 1 – x])))
- y-intercept = [Point 1 – y] – ([Point 2 – y] – [Point 1 – y])÷([Point 2 – x] – [Point 1 – x])×[Point 1 – x]
- Distance = sqrt(([Point 2 – x] – [Point 1 – x])^2 + ([Point 2 – y] – [Point 1 – y])^2)
Formula
Slope m = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁)
Worked example
Inputs — Point 1 – x: 0; Point 1 – y: 1; Point 2 – x: 12; Point 2 – y: 5.
Results — Slope (rise ÷ run) = 0.33333333; Rise Δy = 4; Run Δx = 12; Percentage grade = 33.3333 %; Angle = 18.4349 °; y-intercept = 1; Distance = 12.64911064.
Key terms
- Rise
- Vertical change.
- Run
- Horizontal change.
Frequently asked questions
What is rise over run?
Vertical change divided by horizontal change – the slope.
How do I convert a slope to an angle?
Angle = arctan(slope).
What is a 4/12 roof pitch in degrees?
About 18.43°.
Can rise be negative?
Yes – the line goes downhill.