# Rise Over Run Calculator

URL: https://speedycalculator.com/calculators/math/rise-over-run/
Last updated: 2026-10-30

> The rise over run calculator works out the slope between two points as rise ÷ run, plus the percentage grade, angle, y-intercept and distance.

## Inputs

- Point 1 – x
- Point 1 – y
- Point 2 – x
- Point 2 – y

## Results

- Slope (rise ÷ run)
- Rise Δy
- Run Δx
- Percentage grade
- Angle
- y-intercept
- Distance

## Formula

```
Slope m = rise ÷ run = (y₂ − y₁) ÷ (x₂ − x₁)
```

## Explanation

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

FieldWhat to enterPoint 1 – xA numberPoint 1 – yA numberPoint 2 – xA numberPoint 2 – yA 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)

## 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.

## FAQ

**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.


## Sources

- [OpenStax – College Algebra 2e](https://openstax.org/details/books/college-algebra-2e)
- [OpenStax – Precalculus 2e](https://openstax.org/details/books/precalculus-2e)