Slope Calculator

Calculate slope from rise and run or from two points, and get percent, degrees and a 1:n ratio all at once. Includes a quick percent ↔ degrees converter and the ADA 1:12 maximum ramp slope for reference.

8.33% slope

Angle: 4.76° · Ratio: 1:12.00

ADA max ramp slope is 1:12 (~8.33%). This slope is at or under the ADA maximum.

Percent slope = rise ÷ run × 100. Angle = arctan(rise ÷ run). ADA maximum ramp slope (2010 ADA Standards, Section 405.2) is 1:12. How we calculate →

Rise over run: the basic slope formula

Slope compares vertical change (rise) to horizontal change (run). As a percentage, slope = (rise ÷ run) × 100 — so a ramp that climbs 3 inches over a 36-inch run has a slope of 3 ÷ 36 × 100 = 8.33%. As an angle, slope = arctan(rise ÷ run) in degrees, which for that same ramp comes out to about 4.76°. Percent and degrees measure the same slope differently — a common mix-up is treating a "10% slope" as 10 degrees, but it's actually closer to 5.71°, since percent and angle only match at very small slopes.

Slope from two points

Given two coordinates (x1, y1) and (x2, y2), slope m = (y2 − y1) ÷ (x2 − x1), and the line's full equation is y = mx + b, where b = y1 − m·x1. If x1 equals x2, the line is vertical and slope is undefined (there's no rise-over-run ratio for an infinite run of zero) — the calculator flags this instead of dividing by zero.

Percent, degrees and ratio — converting between them

To go from percent to degrees: angle = arctan(percent ÷ 100). To go from degrees to percent: percent = tan(angle in radians) × 100. The "1 in N" ratio notation (common for ramps and grading) means a rise of 1 for a run of N, so N = 100 ÷ percent — a 1:12 ratio is exactly 100 ÷ 12 = 8.33%.

ADA ramp slope requirements

Under Section 405.2 of the 2010 ADA Standards for Accessible Design, the maximum running slope for a ramp on an accessible route is 1:12 (about 8.33%, roughly 4.76°). Providing a gentler slope than that maximum is recommended wherever space allows, since it's easier to use for a wider range of people. Limited exceptions exist for alterations to existing sites with tight space constraints — up to 1:10 for rises of 6 inches or less, and up to 1:8 for rises of 3 inches or less — but 1:12 is the general-purpose standard for new construction.

Common slope applications

Beyond ramps, slope percentage and degrees show up in roofing (roof pitch), road grades, drainage design, and hiking trail difficulty. A 3:12 roof pitch (common residential slope) works out to 25%, about 14 degrees — steep enough to shed water and snow without needing steep-slope safety gear required above roughly 6:12 (50%, ~27°) on many job sites.

Frequently asked questions

How do you calculate slope as a percentage?

Divide the rise by the run and multiply by 100. A ramp rising 3 inches over a 36-inch run has a slope of 3 ÷ 36 × 100 = 8.33%.

How do you convert slope percentage to degrees?

Take the arctangent of (percent ÷ 100). A 10% slope is arctan(0.10) ≈ 5.71° — not 10 degrees, since percent grade and angle in degrees aren't the same measurement.

What is the ADA maximum ramp slope?

1:12, or about 8.33% (roughly 4.76°), per Section 405.2 of the 2010 ADA Standards for Accessible Design. Limited exceptions for short-rise alterations allow up to 1:10 or 1:8.

How do you find the slope between two points?

Slope m = (y2 − y1) ÷ (x2 − x1). For points (0,0) and (10,5), m = 5 ÷ 10 = 0.5, which is a 50% slope and about 26.57°.

What does a 1:12 ratio mean?

It means 1 unit of rise for every 12 units of run — equivalent to 8.33% slope. The general form is 1:N, where N = 100 ÷ percent slope.

Is a steeper slope a bigger or smaller ratio number?

Smaller — a 1:8 ratio (12.5%) is steeper than a 1:12 ratio (8.33%), because the run gets shorter relative to the rise as slope increases.

Researched & verified by the Calcuris Data & Research Team. How we build and check our tools →