# Rise Over Run Calculator

Calculate slope as rise over run, convert to angle and grade percentage. Enter two points or rise/run values directly. Free online slope calculator.

## What this calculates

Calculate slope as rise over run from two points or by entering rise and run directly. Get the slope value, angle of inclination in degrees, and grade percentage used in construction and road design.

## Inputs

- **Input Mode** — options: Two Points (x1,y1) and (x2,y2), Rise and Run values directly — Choose how to provide the rise and run.
- **Point 1: X** — Used in two-points mode.
- **Point 1: Y** — Used in two-points mode.
- **Point 2: X** — Used in two-points mode.
- **Point 2: Y** — Used in two-points mode.
- **Rise (vertical change)** — Used in direct mode. The vertical change.
- **Run (horizontal change)** — Used in direct mode. The horizontal change.

## Outputs

- **Slope (rise/run)** — The slope as a decimal value.
- **Rise** — The vertical change between the two points.
- **Run** — The horizontal change between the two points.
- **Angle of Inclination** — formatted as text — The angle the slope makes with the horizontal, in degrees.
- **Grade (slope percentage)** — formatted as text — The slope expressed as a percentage (rise/run x 100). Common for roads and ramps.

## Details

"Rise over run" is the most intuitive way to understand slope. The rise is how much you go up (or down), and the run is how far you go horizontally.

**The Formula:**

slope = rise / run = (y2 - y1) / (x2 - x1)

**Converting to Angle:**

The angle of inclination is the angle the line makes with the horizontal:

angle = arctan(slope)

A slope of 1 means a 45-degree angle. A slope of 0 means flat (0 degrees).

**Grade Percentage:**

Grade percentage is the slope expressed as a percent: grade = (rise / run) x 100. A 6% grade means the road rises 6 feet for every 100 feet of horizontal distance. This format is standard on road signs and construction plans.

**Common Examples:**

- A wheelchair ramp should have a maximum slope of 1:12 (8.33% grade, about 4.8 degrees)
- A typical residential staircase has a slope around 7:11 (63.6% grade, about 32.5 degrees)
- Highway grades rarely exceed 6% (about 3.4 degrees)

## Frequently Asked Questions

**Q: What does rise over run mean?**

A: Rise over run is a way to express slope. The 'rise' is the vertical change (how much you go up or down) and the 'run' is the horizontal change (how far you go sideways). Dividing rise by run gives the slope as a single number. A rise of 3 and run of 4 gives a slope of 0.75.

**Q: How do I convert slope to an angle?**

A: Use the arctangent (inverse tangent) function: angle = arctan(slope). For a slope of 1 (rise equals run), the angle is 45 degrees. For a slope of 0.5, the angle is about 26.57 degrees. Most scientific calculators and programming languages have an atan or arctan function.

**Q: What is grade percentage?**

A: Grade percentage expresses slope as a percent: (rise/run) x 100. A 10% grade means 10 feet of rise for every 100 feet of horizontal distance. Road signs use this format because it is easy to visualize. A 100% grade equals a 45-degree angle (slope of 1).

**Q: What is a safe ramp slope?**

A: The ADA (Americans with Disabilities Act) requires wheelchair ramps to have a maximum slope of 1:12, which is an 8.33% grade or about 4.76 degrees. Steeper ramps are dangerous for wheelchair users. For outdoor ramps exposed to rain or ice, even gentler slopes like 1:16 or 1:20 are recommended.

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Source: https://vastcalc.com/calculators/math/rise-over-run
Category: Math
Last updated: 2026-04-08