Slope and Grade Calculator

What this calculator does

Either measure a slope you have — rise and run — or specify a grade you want to build over a known run. It returns the percent grade, the 1-in-N ratio, the angle in degrees, the fall per foot in inches, the total rise, and the true slope length along the incline. It also flags whether the result is gentle enough for an accessible ramp and steep enough to drain.

Four ways of saying the same thing, because four different trades each insist on their own.

Four units, one slope

Slope is a ratio of vertical change to horizontal distance. Everyone agrees on that and nobody agrees on how to express it:

Percent grade — rise ÷ run × 100. Used in civil engineering, road design, and site grading. Two feet over thirty is 6.7 percent.

Ratio (1 in N) — how many units of run per unit of rise. Used in accessibility standards, plumbing and rail. Two feet over thirty is 1 in 15.

Degrees — the actual angle. Used in roofing, machining and anything involving a protractor or a digital level.

Inches per foot — fall over a foot of run. Used by plumbers and by anyone setting a drain with a level and a tape.

The calculator gives all four because a job routinely involves people using different ones. The site plan says 2 percent, the plumber says quarter-inch per foot, and the accessibility consultant says 1:12 — and two of those are the same number.

Percent and degrees are not the same thing

Worth stating plainly, because the confusion is widespread and occasionally consequential.

A 100 percent grade is 45 degrees. Not 90.

Percent grade is rise over run. When rise equals run, that ratio is 1, or 100 percent — and the angle is 45 degrees. A vertical wall has an infinite grade percentage, not a 100 percent one.

The two scales track loosely at shallow angles — 5 percent is 2.86 degrees, 10 percent is 5.71 — which is precisely why they get conflated. By 50 percent (26.6 degrees) they have separated badly, and beyond that the relationship is not remotely linear.

If somebody says “a 45 percent slope,” it is worth establishing which they mean, because the difference between 45 percent (24 degrees) and 45 degrees (100 percent) is the difference between a steep driveway and a cliff.

Run is horizontal

The run is the horizontal distance, measured level. Not the distance along the ground.

On gentle slopes the difference is negligible. On steep ones it is not: a 30-foot slope length at a 50 percent grade has a horizontal run of about 26.8 feet. Measuring along the ground and calling it the run understates the grade.

This is why surveyors use a level line and a rod, and why a tape dragged up a hill gives the wrong answer. The calculator returns the slope length separately so you can see the difference — it is the same hypotenuse arithmetic the stair calculator uses for stringer stock and the roof geometry calculator uses for rafters.

The numbers that matter in practice

Drainage away from a building: about 5 percent over the first ten feet — roughly six inches of fall. This is one of the highest-value details in residential construction and one of the most commonly wrong, because settled backfill and later landscaping quietly reverse it. Water pooling against a foundation is the cause of an enormous share of basement problems.

General site drainage: 2 percent minimum. Below that, water stops moving reliably and any construction tolerance becomes a puddle.

Drain pipe: a quarter-inch per foot (about 2 percent) is the traditional minimum for small waste lines. Larger drainage runs often use 1 percent. Note the counter-intuitive upper bound in waste plumbing — too steep can let water outrun solids and leave them stranded, which is why plumbers care about even slope rather than maximum slope. The french drain calculator covers the drainage-trench case in detail.

Accessible ramps: 1:12 maximum, or 8.33 percent. Gentler is better. And a ramp is far more than its slope — landings at intervals, handrails on both sides, edge protection, a level landing at top and bottom, and surface requirements. The slope is necessary and nowhere near sufficient.

Driveways: 15 percent is steep and about the practical limit for ordinary vehicles in ordinary weather; over that, ice becomes a serious problem and vehicles ground out on transitions.

Roofs: expressed as rise per 12 inches of run rather than percent — a 6/12 pitch is 50 percent grade and 26.6 degrees.

Measuring a slope with what you have

Level and tape. Hold one end of a level at the high point, level it, and measure straight down from the free end to the ground. That drop over the level’s length is your rise and run. A four-foot level makes the arithmetic easy.

String line. For longer runs, a string with a line level, pulled taut. Same method, more distance, more sag error — pull it tight and check the level in the middle.

Phone. Most smartphones have a usable inclinometer. Adequate for a rough check, not for setting a drain.

Laser level or transit. What you want for anything over about twenty feet, and what any grading contractor will use.

What this leaves out

• Cross slope, which matters on paths and driveways independently of the running slope.
• Compound and varying slopes. Real ground is not a plane; break it into segments.
• Code requirements, which vary and are more specific than any of the rules of thumb above.
• Ramp design beyond slope — landings, handrails, width, edge protection, surface.
• Soil stability. A slope that drains is not automatically a slope that stays put, which is where the retaining wall calculator picks up.
• Cut and fill volumes. The excavation calculator converts a grading change into cubic yards and truckloads.