Skip to content
Calcapedia
Menu
Home & Garden

Ramp Slope Calculator

Find how long a ramp needs to be for its height and slope. Or check the slope of a ramp that fits your space, with its length, angle and landings.

Level: Grades 8–10

  • Common Core standard 8.G.B.7Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.
  • Common Core standard HSG.SRT.C.8Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Printable worksheet

Ramp Slope Calculator

Know the answer you need? Pick an input to work backward.

Inputs
What do you want to find?

Measure from the lower ground or floor to the top surface, such as the door threshold.

1:12 is the steepest running slope the 2010 ADA Standards allow for new ramps. Gentler slopes, such as 1:16 or 1:20, are easier to climb.

The 2010 ADA Standards limit each ramp run to a 30 in rise.

The 2010 ADA Standards call for landings at least 60 in long.

Result

Minimum horizontal run

24 ft

A 24 in rise at 1:12 needs at least 24 ft of run, in 1 run.

Slope ratio (rise : run)
1:12
Ramp surface length
24.08 ft
Angle
4.76 °
Grade
8.33%
Ramp runs
1
Intermediate landings
0
Overall length with intermediate landings
24 ft
Handrails
Needed under the ADA Standards (rise over 6 in)

See the step-by-step solution ↓

Step-by-step solution

  1. A 1:12 slope runs 12 inches along the ground for every inch it climbs, so multiply the rise by 12

    24×12=288 in

  2. Divide by 12 to turn inches into feet

    28812=24 ft

  3. The run, rise and ramp surface form a right triangle, so the Pythagorean theorem gives the length of the sloped surface

    2882+242=288.9983 in

  4. Find the angle: arctan turns rise ÷ run into degrees

    arctan24288=4.7636 °

  5. Find the grade: the slope as a percent, or the rise for every 100 of run

    24288×100=8.3333%

  6. Each run may climb at most 30 in, so divide the rise by that and round up. A level landing goes between runs

    2430=0.8=rounded up:1 runs, 0 landings

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find out how long a ramp needs to be, or how steep a ramp that fits your space would be. A ramp's slope is its rise (how high it climbs) divided by its run (how far it stretches along the ground). It's usually written as a ratio such as 1:12. That means one unit up for every twelve along the ground.

A gentler slope is easier for someone in a wheelchair, pushing a stroller or using a walker. But a gentler ramp also takes up more ground. Planning a ramp means balancing those two things.

This calculator works in two directions. Give it the rise and the steepest slope you'll accept. It finds the shortest run that works, the length of the sloped surface, the angle and the grade (the slope as a percent).

Or give it the rise and the run you have room for. It tells you the slope, and whether it's within your limit. It also counts how many separate runs the ramp needs when each run's rise has a limit, and the level landings (flat resting spots) between them.

Where it's used

Why this math matters outside the classroom:

  • Home access. Families adding a ramp to a 24 in porch at 1:12 plan for at least 24 ft of run before choosing a straight or L-shaped layout.
  • Ramp surfaces. Builders find the deck length for a 288 in run and a 24 in rise as √(288² + 24²) ≈ 289 in.
  • Slope angles. Students convert a 1:12 slope to an angle with arctan(1 ÷ 12) ≈ 4.76° and compare it with a 1:20 path at 2.86°.
  • Checking a site. Contractors with 20 ft of space for a 24 in rise find a 1:10 slope, too steep for a 1:12 limit by 4 ft.
  • Loading ramps. Movers choosing a ramp for a 36 in truck bed see that a 10 ft ramp gives a 1:3.33 slope, about 16.7°.

Grade level and standards: Grades 8–10; Common Core State Standards for Mathematics 8.G.B.7, HSG.SRT.C.8. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose what you want: the ramp length for a maximum slope, or the slope of a ramp that fits your space.
  2. Enter the total rise in inches and the maximum slope as 1 : N (12 for 1:12).
  3. If you're checking a ramp, enter the run you have room for, in feet, measured flat along the ground.
  4. If your rules differ, change the maximum rise per run and the landing length. Then read the results.

What the inputs mean

Total rise (height to climb)
Measure straight up, from the ground where the ramp will start to the surface it will reach. On sloping ground, measure at the spot where the ramp will meet the ground.
Maximum slope: 1 unit of rise per
The 2010 ADA Standards for Accessible Design (the US accessibility rules) allow a slope no steeper than 1:12 for new ramps. They treat any walking surface steeper than 1:20 as a ramp. Ramps at homes aren't always covered by the ADA, but local codes often use similar numbers.
Maximum rise for one run before a landing
Under the 2010 ADA Standards, a single ramp run may rise at most 30 in. Taller climbs are split into runs, with level landings between them.
Length of each intermediate landing
The 2010 ADA Standards require level landings at least 60 in long at the top and bottom of each run. Landings where the ramp turns need at least 60 × 60 in.

Formula and method

minimum run = rise × N  (for a 1:N slope)
slope ratio = 1 : (run ÷ rise)
ramp length = √(run² + rise²)
angle = arctan(rise ÷ run);  grade = rise ÷ run × 100%
runs = rise ÷ maximum rise per run, rounded up;  intermediate landings = runs − 1

N is the second number in a 1:N slope: how far the ramp runs along the ground for each unit it climbs. The rise, the run and the ramp surface form a right triangle. So the Pythagorean theorem (the rule for a right triangle's sides) gives the surface length. Arctan turns rise ÷ run into an angle. A 1:12 slope is a grade of 8.33% and an angle of about 4.76°.

Intermediate landings are the flat spots between runs, and they add to the ramp's overall length on the ground. You also need landings at the top and bottom. Those aren't added in, because they often use existing porch or path space.

Worked example

A ramp to a door 24 in above the path, at the 1:12 maximum, with a 30 in limit per run.

  1. Minimum run: 24 × 12 = 288 in = 24 ft.
  2. Ramp surface: √(288² + 24²) = 288.9983 in, about 24.08 ft.
  3. Angle: arctan(24 ÷ 288) = 4.7636°; grade 8.3333%.
  4. Runs: 24 ÷ 30 = 0.8, rounded up to 1, so no intermediate landing.

Result: The ramp needs at least 24 ft of run along the ground, in a single run, with landings at the top and bottom. It also needs handrails, because the rise is over 6 in.

Understanding the result

When you're finding the length, the run is a minimum. A longer ramp is gentler and easier to use. When you're checking a ramp, a bigger second number means a gentler slope (1:16 is gentler than 1:10).

If the ramp needs more than one run, its overall length includes a level landing between each pair of runs. Turning the ramp at a landing, in an L or U shape, can fit the same run into a smaller yard.

Assumptions and limitations

  • Each run keeps the same slope all the way along, and the landings are level.
  • The rise is measured straight up and the run is measured flat along the ground.
  • It doesn't design the ramp's structure, edge protection, surface or drainage.
  • Accessibility rules differ between the ADA Standards, building codes and other guidelines. Work at a home may fall under local codes only. Check what applies to your project.
  • It doesn't work out cross slope (the tilt from side to side), clear width or handrail details.

Frequently asked questions

How long does a ramp need to be?

At 1:12, multiply the rise in inches by 12 to get the run in inches. That works out to the same number as the rise, but in feet. So a 20 in rise needs at least 20 ft. A gentler 1:16 slope would need about 26.7 ft.

What angle is a 1:12 ramp?

About 4.76°, which is a grade of 8.33%. A 1:20 slope is about 2.86°, or 5%.

When does a ramp need a landing?

Under the 2010 ADA Standards, ramps need a level landing at the top and bottom of each run. A single run may rise at most 30 in. Longer ramps are split into runs with landings between them, which also give people a place to rest.

Does a short ramp need handrails?

The 2010 ADA Standards require handrails on ramp runs that rise more than 6 in. Local codes for homes may differ. Handrails can help many people even on shorter ramps.

Sources

How this calculator is checked

Method: Right-triangle geometry (run = rise × N, length by the Pythagorean theorem, angle by arctangent); default limits from the 2010 ADA Standards sections 405.2, 405.6, 405.7.3 and 405.8. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

Embed this calculator

Put this Ramp Slope Calculator on your own website or blog for free. Paste this code where you want it to appear: