Ramp Slope Calculator

Background.

A ramp slope calculator turns two measurements into an answer you can take to a building department. Give it the rise you have to climb and either the slope you are aiming for or the horizontal room you actually have, and it returns the ramp run, the slope as a 1:N ratio, as a percentage and as an angle, the surface length along the slope, the number of separate ramp runs and landings the design needs, and a verdict against the standard you pick.

The verdict is the part that matters, and it is why this page exists rather than a generic rise-over-run tool. Slope alone does not tell you whether a ramp is legal. Under the 2010 ADA Standards a running slope of 1:12 is the maximum for new construction (405.2), but Table 405.2 permits steeper runs in existing sites, buildings and facilities where space limitations make them necessary — and it caps how much rise you may climb at those steeper slopes. Steeper than 1:12 but not steeper than 1:10 buys you 6 inches of rise. Steeper than 1:10 but not steeper than 1:8 buys you 3 inches. Footnote 1 to that table says plainly that a slope steeper than 1:8 is prohibited, with no exception for a short rise. So 1:9 is not simply worse than 1:12; it is either permissible for three inches of rise in an existing building or not permissible at all, and this calculator tells you which.

The other end of the scale matters too. ADA 403.3 defines a walking surface as one no steeper than 1:20, and a ramp as anything steeper. If your slope comes out at 1:20 or gentler you are not building a ramp, Section 405 does not apply to it, and the handrails, landings and edge protection that Section 405 would have required are not triggered by the slope. The calculator says so rather than reporting a compliant ramp that is not a ramp.

Residential work is governed differently, so the standard is a dropdown rather than an assumption. IRC Section R311.8 splits residential ramps in two: the ramp serving the egress door required by R311.2 has a maximum slope of 1 unit vertical in 12 units horizontal, and every other ramp is allowed 1 in 8. A 1:8 ramp is code-legal in a house and is far too steep for anyone to self-propel a wheelchair up, which is exactly the sort of thing a single-number slope calculator will never tell you. Pick the right option and the verdict is written against the right clause. One warning belongs right here rather than further down: two incompatible reproductions of R311.8 are in circulation in municipal building-department handouts, and only one of them contains that 1:8 allowance — the other holds every residential ramp to 1:12. Both were read verbatim while this page was built, and the result note names both. Confirm the text your jurisdiction has actually adopted before you rely on a residential verdict here.

Height forces geometry as well. ADA 405.6 caps the rise of any single ramp run at 30 inches, and 405.7 requires a landing at the top and bottom of each run, so a 36 inch rise is not one 36 foot ramp: it is two runs with three landings, and at the ADA minimum landing length of 60 inches that is 51 feet of total length rather than 36. Sites get lost on that difference. The calculator reports runs, landings and total length separately so the number you check against your survey is the real one.

Two limits are stated here and repeated beside the result rather than hidden in an FAQ. First, this page checks running slope, rise per run and landing count only — not clear width, not the 1:48 cross slope, not surface finish, not handrail geometry, not edge protection, not landings at a change in direction. A ramp can pass every check on this page and still fail an inspection. Second, the clauses quoted are from the 2010 ADA Standards and from IRC Section R311.8, but adopted editions and local amendments vary by jurisdiction, and a ramp on a commercial site may be subject to the ADA, a state accessibility code and the adopted building code at once, with the strictest governing. Have a licensed architect, engineer or accessibility specialist confirm the design and sign it off before work proceeds.

What is ramp slope calculator?

Ramp slope is the ratio of a ramp's vertical rise to its horizontal run. It is written three interchangeable ways: as a ratio (1:12), as a percentage (8.33%), and as an angle (4.76 degrees). Building and accessibility codes are written in the ratio form, so that is the form a compliance check has to reason about.

The vocabulary is worth getting straight. Rise is the vertical distance climbed. Run is the horizontal distance travelled, measured along the ground, not along the sloping surface. Surface length is the sloping distance itself, the hypotenuse of rise and run, and it is what you buy decking or handrail by. A ramp run is one continuous sloped segment between landings; a ramp may be several runs. Running slope is the slope in the direction of travel, and cross slope is the slope across it, which the ADA limits separately to 1:48.

The page covers straight ramp runs with a constant slope, checked against the 2010 ADA Standards for Accessible Design or IRC Section R311.8. It does not cover curved ramps, vehicle or parking-garage ramps, loading docks, kerb ramps and their flared sides, or platform lifts, and it does not design a ramp's structure, footings or drainage. It reports geometry and a slope verdict; it is not a permit and it is not a substitute for a designer of record.

How to use this calculator.

1. 01Choose what you are working out: the run needed to hit a target slope, or the slope you get from the run you already have.
2. 02Choose the standard. The 2010 ADA Standards for public accommodations and commercial facilities; IRC R311.8 egress-door option for the ramp serving a dwelling's required egress door; IRC R311.8 other option for any other residential ramp.
3. 03Measure the total rise in inches, from the lower finished surface to the upper finished surface. Include the threshold, not just the grade.
4. 04In the first mode, enter the target slope as the N in 1:N — 12 for the ADA maximum, 16 or 20 for a gentler ramp that is easier to self-propel.
5. 05In the second mode, enter the horizontal run you have, in feet, counting only the sloped part and not the landings.
6. 06Leave the maximum rise per run at 30 inches unless you have a reason to lower it; that is the ADA 405.6 limit and it is what splits a tall ramp into runs. It is ignored for the IRC options, which set no rise cap.
7. 07Set the landing length in the direction of travel. 60 inches is the ADA 405.7.3 minimum; under the IRC it is your own figure because the required dimension is worded differently in different editions.
8. 08Read the total length first to see whether the ramp fits, then read the verdict and the code note beside it before you commit to anything.

The formula.

The geometry is one right triangle and four lines of arithmetic. Converting the rise to feet, the run for a target 1:N slope is rise × N; going the other way, the slope denominator for a known run is N = run ÷ rise. The percentage is 100 ÷ N, the angle is arctan(1 ÷ N) in degrees, and the surface length is √(rise² + run²). For the worked example on this page a 36 inch rise is 3 feet, so a 1:12 ramp needs 3 × 12 = 36 feet of run, the slope is 100 ÷ 12 = 8.3333333333%, the angle is 4.7636416907 degrees, and the surface length is √(3² + 36²) = √1305 = 36.1247837364 feet.

The two directions are exact inverses, and the test suite asserts it: solving for the run at 1:15 and feeding that run straight back recovers 1:15 to ten decimal places. The direction of the relationship is worth stating in words because it is easy to get backwards. A larger N means a gentler ramp and a longer run, so "steeper than 1:12" means N is less than 12, not more.

The run segmentation is where the code enters the arithmetic. ADA 405.6 caps the rise of any one ramp run at 30 inches, so the number of runs is the ceiling of rise ÷ 30 and, because 405.7 puts a landing at the top and the bottom of each run with intermediate landings shared between consecutive runs, the number of landings is runs + 1. Total length is the sloped run plus every landing. In the worked example a 36 inch rise gives ⌈ 36 ÷ 30 ⌉ = 2 runs, 3 landings, and 36 + 3 × 5 = 51 feet of total length. IRC Section R311.8 sets no rise cap at all, so under either IRC option the run count is 1 and the landing count is 2 regardless of how tall the ramp is.

The verdict is driven by exactly one scalar — the slope denominator N — and it classifies the unrounded value, never the rounded display. The ADA bands are: N below 8 prohibited outright by footnote 1 to Table 405.2; 8 up to but not including 10 permitted in existing facilities only, with a 3 inch rise cap; 10 up to but not including 12 permitted in existing facilities only, with a 6 inch rise cap; 12 up to but not including 20 compliant in new construction under 405.2; and 20 or gentler not a ramp at all under 403.3. Because the code phrase is "not steeper than 1:12", exactly 1:12 complies, and every one of those four edges is tested just below, exactly at, and just above in the test suite. For an IRC egress-door ramp, N of 12 or more complies, 8 up to 12 is available only under the technical-infeasibility exception, and below 8 does not comply. For any other IRC residential ramp the single limit is 1:8, so N of 8 or more complies.

All arithmetic runs in arbitrary-precision decimal and is rounded once, at the return boundary, to ten decimal places. The one exception is the arctangent, which has no arbitrary-precision implementation here: it is evaluated in double precision and lifted straight back into decimal, so its error floor is around 1e-16 — five orders of magnitude below the last digit reported. Nothing is rounded before it is classified.

A worked example.

Frequently asked questions.

References& sources.

1. [1]United States Department of Justice — 2010 ADA Standards for Accessible Design (28 CFR Part 36, revised as of 2010). Sections 403.3 (walking-surface slope 1:20 and cross slope 1:48), 405.2 and Table 405.2 with footnote 1 (ramp running slope 1:12; existing-facility allowances of 6 in of rise between 1:12 and 1:10 and 3 in between 1:10 and 1:8; steeper than 1:8 prohibited), 405.3, 405.5, 405.6, 405.7, 405.7.3, 405.7.4, 405.8 and 405.9.
2. [2]United States Access Board — ADA Accessibility Standards, Chapter 4: Accessible Routes, Section 405 Ramps. The Access Board is the agency that writes the underlying guidelines the DOJ adopts, and is used here as an independent copy of the same clause text.
3. [3]International Code Council — International Residential Code, Section R311.8 Ramps (R311.8.1 Maximum slope, R311.8.2 Landings required, R311.8.3 Handrails required, R311.8.3.1 Height). Named as the governing residential section. ICC's reader is access-gated and returns HTTP 403 to automated retrieval, so the clause text used on this page was taken from the two municipal reproductions cited below rather than from here.
4. [4]Town of Essex, Connecticut, Building Department — Residential Stairways and Ramps handout reproducing the 2015 International Residential Code portion of the 2018 Connecticut State Building Code. Verbatim source for the two-tier R311.8.1 slope limit (1:12 for the egress-door ramp, 1:8 for all others, exception for technical infeasibility), for the R311.8.2 wording that gives a 36 in landing width perpendicular to the ramp and no landing length, and for R311.8.3 through R311.8.3.3 including the 34 to 38 in handrail height.
5. [5]City of Richmond, Kentucky, Codes Enforcement — Section R311.8 Ramps handout. Verbatim source for the second, incompatible reproduction of R311.8 that is also in circulation: a single-tier R311.8.1 holding every ramp to one unit vertical in 12 units horizontal with no 1:8 allowance, and an R311.8.2 requiring a minimum 3 ft by 3 ft landing at the top and bottom of ramps, where doors open onto ramps, and where ramps change direction.