# Slope Percentage Calculator

URL: https://speedycalculator.com/calculators/math/slope-percentage/
Last updated: 2026-10-30

> The slope percentage calculator converts rise and run into a slope percentage (grade), an angle in degrees and a 1 : n ratio – and works backwards from any of them.

## Inputs

- Rise (vertical change) (cm, m, mm, in, ft, yd, km, mi)
- Run (horizontal distance) (cm, m, mm, in, ft, yd, km, mi)

## Results

- Slope percentage
- Angle
- Ratio 1 : n
- Slope length

## Formula

```
Slope % = rise ÷ run × 100
Angle = arctan(rise ÷ run)
Ratio = 1 : (run ÷ rise)
```

## Explanation

Road gradients, wheelchair ramps, roofs, drainage pipes and hiking trails all use slope percentages. A 100% slope is a 45° angle – rise equals run – not a vertical wall. Building codes usually limit ramps to 1 : 12 (8.33%).

### How to use the Slope Percentage Calculator

- **Rise (vertical change)**
- **Run (horizontal distance)**
- Every result field is editable: type into **Slope percentage** or any other result and **Rise (vertical change)** plus every other field update to match.

Results update as you type, and everything is calculated in your browser.

### How it works

Divide the vertical rise by the horizontal run and multiply by 100. The angle is the arctangent of rise/run. Type a percentage or an angle into the results to find the matching rise for the run you entered.

### Inputs explained

FieldWhat to enterRise (vertical change)Units: cm, m, mm, in, ft, yd …Run (horizontal distance)Units: cm, m, mm, in, ft, yd …

### What each result means

- **Slope percentage** = [Rise (vertical change)]÷[Run (horizontal distance)]×100
- **Angle** = deg(atan([Rise (vertical change)]÷[Run (horizontal distance)]))
- **Ratio 1 : n** = [Run (horizontal distance)]÷[Rise (vertical change)]
- **Slope length** = sqrt([Rise (vertical change)]^2 + [Run (horizontal distance)]^2)

### Example values

How the main result changes when **Rise** changes and everything else stays at the example values above:

Rise (vertical change) (cm)Slope percentage (%)12.54.166718.756.25258.333331.2510.416737.512.55016.6667

## Worked example

Inputs — Rise (vertical change): 25 cm; Run (horizontal distance): 300 cm.

Results — **Slope percentage = 8.3333 %**; Angle = 4.7636 °; Ratio 1 : n = 1 : 12.000; Slope length = 301.04 cm.

## Key terms

- **Grade**: Another name for slope percentage.
- **Run**: The horizontal distance covered.

## FAQ

**Is a 100% slope vertical?**
No – 100% means the rise equals the run, an angle of 45°. A vertical wall has an infinite slope percentage.

**How do I convert a slope percentage to degrees?**
Angle = arctan(percentage ÷ 100). 10% ≈ 5.71°.

**What is a 1 : 12 slope?**
A rise of 1 for every 12 of run, about 8.33% or 4.76° – the usual maximum for wheelchair ramps.

**Can a slope be negative?**
Yes, a negative rise means downhill.


## Sources

- [OpenStax – College Algebra 2e](https://openstax.org/details/books/college-algebra-2e)
- [Wolfram MathWorld – Slope](https://mathworld.wolfram.com/Slope.html)