How to calculate slope

1. Rise, run, and the one formula

Every slope is described by two measurements. The rise is how far the surface goes up (or down) vertically. The run is how far it travels horizontally over that same stretch. Steepness is simply the rise compared with the run, and there is one formula behind all the ways people write it: percent grade = (rise ÷ run) × 100. If a path climbs 2 ft over a horizontal distance of 40 ft, that is 2 ÷ 40 × 100 = 5%. The units do not matter as long as both measurements use the same one, because the division cancels them out — 2 m over 40 m is also 5%.

The single trap to avoid is measuring the run along the ground surface instead of horizontally. The run is the flat, level distance — the shadow the slope would cast straight down — not the sloping distance you would walk. On a gentle grade the difference is tiny, but on a steep one it matters, which is why surveyors measure the horizontal run separately from the slope length.

2. Three ways to write the same slope

The confusing part of slope is that the same steepness has three common notations, and different trades prefer different ones:

• Percent grade — (rise ÷ run) × 100. Used on road signs, in civil earthworks and for driveways. A 6% grade rises 6 units for every 100 of run.
• Angle in degrees — atan(rise ÷ run). Used by carpenters, surveyors and anyone setting a tool to an angle. It runs from 0° (level) toward 90° (vertical).
• Ratio “1 in n”— n = run ÷ rise. Used for wheelchair ramps and drainage falls. “1 in 12” means one unit up for every twelve along.

These are not interchangeable numbers you can swap freely — 8.33%, 4.76° and 1 in 12 are three descriptions of one and the same slope. To convert a percent to degrees, take the inverse tangent of the percent divided by 100: degrees = atan(percent ÷ 100). To go back, percent = tan(degrees) × 100. The slope calculator shows all three at once so you never have to convert by hand.

3. A worked example, step by step

Say a driveway drops 3 ft over a horizontal run of 40 ft and you want to know if it is too steep. First the percent grade: 3 ÷ 40 = 0.075, times 100 = 7.5%. Now the angle: atan(3 ÷ 40) = atan(0.075) = 4.29°. And the ratio: 40 ÷ 3 = 13.3, so it is about 1 in 13. Finally the slope length — the actual surface you will pave — is √(3² + 40²) = √(9 + 1600) = √1609 = 40.1 ft, only slightly more than the run because the grade is gentle.

The metric version is identical in method. A ramp that rises 0.5 m over a 6 m run is 0.5 ÷ 6 × 100 = 8.33%, atan(0.5 ÷ 6) = 4.76°, and a ratio of 6 ÷ 0.5 = 1 in 12. Notice you never change the formula between countries — only the units you read the length in. That is why this is one calculator for the US, Canada, the UK, Australia and New Zealand, with a button to switch between imperial and metric.

4. Slope conversion chart

Common slopes written as a percent, an angle and a ratio, worked out from atan(rise ÷ run). Your own numbers go into the calculator for an exact figure.

The number that surprises people is 100%: it is a 45° angle, not a cliff. A slope only becomes vertical as the percent heads toward infinity, because the run shrinks toward zero. That is one reason drainage and ramps use ratios and degrees rather than percent for steep work — the percent scale stretches out at the top.

5. Slope length versus run

The run is the horizontal distance, but the surface you actually build — the ramp deck, the paved driveway, the length of pipe — runs along the slope, and that is always a little longer. It is the hypotenuse of the rise-and-run triangle, so slope length = √(rise² + run²). For the 1-in-12 ramp above, a 12-unit run with a 1-unit rise gives √(1 + 144) = √145 = 12.04 units of decking. The gentler the slope, the closer the slope length is to the run; the steeper it gets, the more the two diverge.

This matters when you are ordering materials or setting out a ramp to a fixed landing height. If a ramp must rise 30 in at a 1-in-12 grade, the run has to be 30 × 12 = 360 in (30 ft) and the ramp surface itself is √(30² + 360²) ≈ 361 in long. Get the run wrong and the grade comes out too steep, so it pays to work back from the rise you must achieve.

6. Where slope is used on site

Slope turns up in almost every trade. Ground and landscaping crews grade sites to shed water, typically giving finished ground a fall away from buildings so surface water drains off. Paths and driveways are set to a comfortable, safe grade. Ramps for accessibility are held to a maximum slope — 1 in 12 (8.33%) is the figure most commonly specified, though the exact limit and the required landings depend on the rules for your project and location, so confirm them before you build.

Plumbers and drainlayers set a fall on waste and drain pipes so they self-clean without running dry — the drain slope calculator gives the code-referenced minimum where one is available. Roofers describe steepness as pitch (rise per 12) rather than percent; the roof pitch calculator handles that and the rafter lengths. In every case you measure two numbers — the rise and the run — and the same maths turns them into whatever notation your trade uses. More estimating tools sit on the tools page.

Common questions

How do you calculate slope?

Divide the vertical rise by the horizontal run and multiply by 100 for the percent grade: slope = (rise ÷ run) × 100. A rise of 1 over a run of 12 is 1 ÷ 12 × 100 = 8.33%. For the angle in degrees take the inverse tangent, atan(rise ÷ run) = atan(1 ÷ 12) = 4.76°.

What is a 1:12 slope in percent and degrees?

A 1:12 slope — one unit of rise for every twelve of run — is 8.33% and 4.76°. It is the maximum slope commonly specified for a wheelchair ramp (for example under the ADA in the US), but the exact limit depends on the rules for your project, so always check the requirement that applies to you.

How do I convert percent grade to degrees?

Take the inverse tangent of the percent divided by 100: degrees = atan(percent ÷ 100). So 5% is atan(0.05) = 2.86°, 10% is 5.71°, and 100% is atan(1) = 45°. A 100% grade is not vertical — it is 45°, because the rise equals the run.

What is the difference between slope, grade, gradient and pitch?

They all describe steepness, just in different trades. Grade and gradient usually mean the percent or ratio (roads, drainage, land). Slope is the general word and is often given as a percent or an angle. Pitch is the roofing term, given as rise per 12 (for example 4:12). The underlying maths — rise over run — is identical.