Slope Calculator (Degrees, Percent Grade, Ratio)
Enter an angle in degrees, a percent grade, or a slope ratio (1:N) and instantly convert it to the other two formats. Free tool for roads, roofs, ramps, and railways.
What Is a Slope Calculation?
A slope describes how much a surface rises vertically over a given horizontal distance, and it shows up everywhere from road signs and roof pitches to accessibility ramps and railway lines. Different fields use different notations: road signs typically show a percent grade like "8%", building and civil codes often use a ratio like "1:12", and surveying or math contexts use an angle in degrees like "4.76°".
This tool takes any one of angle, percent grade, or ratio (1:N) and instantly calculates the other two using trigonometry (the tangent function). It is useful whenever you need to compare specifications written in different notations, or check a code-mandated slope limit against the format you are working with.
How to Use the Slope Calculator
- Choose the input format Select whether you have an angle in degrees, a percent grade, or a 1:N ratio.
- Enter the value Type in the number that matches the format you selected.
- Read the converted results The other two formats are calculated automatically and shown together.
Tips for getting more out of it
- As the angle approaches 90°, the ratio N approaches 0; as the slope becomes gentler and closer to 0°, N grows very large.
- Percent grade can exceed 100%. A 100% grade corresponds to 45° (a 1:1 ratio), and anything steeper than that goes above 100%.
- Railway gradients are often expressed in permille (‰, parts per thousand) rather than percent — divide a permille value by 10 before entering it as a percent grade.
- Road grade signs are almost always in percent, while some building codes express ramp and stair slopes as a ratio, so double-check which notation a specification uses before comparing.
When to Use This Slope Calculator
Reading road grade signs
Convert a road sign showing "10% grade" into degrees to understand how steep the hill actually is.
Checking ramp compliance
Convert an accessibility ramp ratio such as 1:12 into a percentage or degrees to check it against building code limits.
Comparing roof pitch notations
Convert a roof pitch given as a ratio or angle into percent grade to compare it with other specifications.
Comparing railway and trail gradients
Convert railway or hiking trail gradients (given in permille, percent, or ratio) into a single consistent format for comparison.
Glossary
- Angle
- The angle between the slope and the horizontal plane, measured in degrees. 0° is flat and the steepness increases as it approaches 90°.
- Percent grade
- The ratio of vertical rise to horizontal run expressed as a percentage (rise ÷ run × 100). Commonly used on road signs.
- Ratio (1:N)
- A notation expressing how far the slope travels horizontally (N) for every 1 unit it rises vertically. A larger N means a gentler slope, e.g. 1:12 means 12 units of horizontal run per 1 unit of rise.
Frequently Asked Questions
Side Note — The World's Steepest Streets and Railways
For years, Baldwin Street in Dunedin, New Zealand was recognized as the steepest residential street in the world, with a maximum grade of around 35% (roughly 19 degrees). It is steep enough to leave pedestrians short of breath, and the street has even become a local attraction thanks to an annual event where giant chocolate candies are rolled down it.
On railways, conventional adhesion trains (which rely purely on friction between wheel and rail) are limited in how steep a grade they can climb, with most mainlines topping out around 20 to 35 permille (2% to 3.5%). One of the steepest adhesion-worked railways in Japan is the Hakone Tozan Railway at 80 permille (8%), more than double a typical mainline grade. Slopes steeper than that typically require a rack railway, where a toothed rail and matching gear on the train provide extra grip.
In accessibility design, many building codes set the maximum slope for a wheelchair ramp at around 1:12 (about 8.3%, or roughly 4.8 degrees). That figure comes from decades of practical experience about the steepest grade a person can safely self-propel a wheelchair up and down.