Rise Over Run To Degrees Calculator

Convert a rise-over-run slope into degrees, percent grade, radians, and a normalized 1:N ratio for ramps, roofs, and sitework.

Share this calculator

Rise-over-run to degrees Convert a vertical rise and horizontal run into slope angle, percent grade, radians, and a normalized 1:N ratio.

Common presets

Reading the ratio

A 1:12 slope means one unit of rise for every 12 units of horizontal run. Lower N values mean a steeper angle.

Angle relationship

The angle comes from arctan(rise ÷ run). Percent grade uses the same ratio, multiplied by 100.

Enter rise and run Provide a rise and horizontal run to convert that slope into degrees and grade terms.

Also in Angle & Rotation

Angle Converter Coordinates Converter DMS Converter Rise Over Run To Percent Slope Calculator Rotation Speed Converter Slope Gradient Converter

Slope Helper

Rise-over-run to degrees calculator: slope angle, percent grade, and 1:N ratios explained

A rise-over-run to degrees calculator turns a simple geometry ratio into the angle and grade terms people actually use in ramps, roofs, grading, and accessibility work. Enter the vertical rise and horizontal run to see the matching slope angle, percent grade, radian value, and normalized 1:N format.

How rise and run become an angle

Rise-over-run is the tangent relationship of a slope triangle. Once you divide rise by run, the angle from horizontal comes from the inverse tangent function and the percent grade comes from the same ratio multiplied by 100.

That means one input pair gives several valid descriptions of the same incline. A 1:12 slope is about 4.76 degrees and 8.33 percent grade.

Angle = arctan(rise / run)

Converts the geometric ratio into degrees or radians.

Percent grade = (rise / run) × 100

Reports the same slope as a percentage of horizontal run.

1:12 = 8.33% ≈ 4.76°

Common accessibility and sitework reference point.

Why the horizontal run matters

Rise-over-run always uses horizontal distance, not the sloped path length along the surface. If you use the sloped length instead of the horizontal run, the resulting angle and percent grade will be understated.

That is one reason field slope checks can disagree if the measuring method changes. The ratio only means what you think it means when rise and horizontal run were measured consistently.

Common use cases and caution points

A focused rise-over-run calculator is handy when you already know the vertical and horizontal distances from a drawing, site measurement, framing detail, or ramp layout and want the angle without doing trigonometry manually.

It should not be treated as a standalone compliance decision. Accessibility rules and field measurements may distinguish running slope, cross slope, tolerances, and location-specific standards.

Further reading

Frequently asked questions

What is the difference between rise-over-run and percent grade?

Rise-over-run is the raw geometric ratio. Percent grade is that same ratio multiplied by 100, so a slope of 1 over 12 becomes about 8.33 percent.

 Can a negative rise produce a negative angle?

Yes. A negative rise with a positive run represents a descending slope, so the angle and percent grade become negative.

 Why is a zero run treated as vertical?

Because the surface rises without any horizontal distance. That pushes the angle to ±90 degrees and makes percent grade effectively infinite.

 Is 1:12 the same as 12 percent?

No. A 1:12 ratio means one unit of rise for every 12 units of run, which is about 8.33 percent grade, not 12 percent.

Related

More from nearby categories

These related calculators come from the same leaf category, nearby sibling categories, or the same top-level topic.

Rise Over Run To Percent Slope Calculator

Convert a rise-over-run slope into percent grade, then see the matching degrees, radians, and normalized 1:N ratio for drainage, ramps, roofs, and grading work.

Open calculator

Slope Gradient Converter

Convert between slope percent, angle in degrees, radians, and rise-over-run style gradient ratios for construction, road, and accessibility work.

Open calculator

DMS Converter

Convert decimal degrees into degrees-minutes-seconds and back again, with radians and gradians for mapping, surveying, and coordinate entry.

Open calculator

Angle Converter

Convert angles between degrees, radians, gradians, turns, arcminutes, arcseconds, and milliradians, with all equivalents shown at once.

Open calculator

Privacy choices

If you allow analytics, we may use Google Analytics and Microsoft Clarity to better understand how the site is used. Analytics remain off unless you accept.