Calculate ramp length from rise and run, angle, grade or a 1:N slope ratio, and get the ramp angle, slope percentage and ratio, or the ramp height.

Optional settings
Starts at 30in; blank uses 30in in any unit. Used only for the lower-bound run/landing count; changing it does not change governing rules.

Ramp Length Formula

The ramp length is the distance measured along the sloped surface. This is different from the horizontal run and different from the vertical rise. If you know the rise and the angle, the ramp length can be calculated directly with trigonometry.

RL = (H) / (sin(a))

Where:

  • RL = ramp length along the slope
  • H = vertical rise
  • a = ramp angle measured from the horizontal

This calculator is most useful when you need the actual sloped distance for ramp layout, material estimation, handrail length planning, or converting between rise, run, angle, and grade.

Useful Rearrangements

If you are solving for a different value, these equivalent forms are helpful:

H = RL sin(a)
a = sin⁻¹((H) / (RL))
R = (H) / (tan(a))
RL = √(H² + R²)
Grade (%) = (H) / (R) × 100 = tan(a) × 100

Rise, Run, and Length: Know the Difference

  • Rise is the vertical change in elevation.
  • Run is the horizontal distance covered.
  • Length is the actual ramp surface distance from bottom to top.

A common input mistake is entering the horizontal run where the calculator expects the vertical rise. If the rise is wrong, the length will also be wrong.

How to Calculate Ramp Length

  1. Measure the total vertical rise from the lower surface to the upper surface.
  2. Select the mode for your known horizontal run, sloped length, rise:run ratio, angle or grade. Measure angles from the horizontal.
  3. Select each dimension’s unit independently; the calculator converts the actual lengths. In angle mode, choose degrees or radians.
  4. The calculator returns the sloped ramp length.

If you already know the horizontal run instead of the angle, use the Pythagorean relationship to get the ramp length directly.

If You Know the Slope Ratio Instead of the Angle

Many ramps are described using a slope ratio such as 1:12, which means 1 unit of rise for every 12 units of horizontal run. For a general ratio of 1:n:

R = nH
RL = H√(1 + n²)
a = tan⁻¹((1) / (n))
Grade (%) = (100) / (n)

This makes it easy to convert between ratio-based designs and angle-based inputs.

Quick Reference by Angle

The multiplier below shows approximately how many feet of ramp length are needed for each 1 foot of rise.

Angle Approx. Grade Length Multiplier
5° 8.75% 11.47 × rise
10° 17.63% 5.76 × rise
15° 26.79% 3.86 × rise
20° 36.40% 2.92 × rise
30° 57.74% 2.00 × rise
45° 100.00% 1.41 × rise

Quick Reference by Slope Ratio

Slope Ratio Angle Grade Length per 1 ft of Rise
1:12 4.76° 8.33% 12.04 ft
1:10 5.71° 10.00% 10.05 ft
1:8 7.13° 12.50% 8.06 ft
1:6 9.46° 16.67% 6.08 ft

Example 1

A ramp rises 4 ft and the ramp angle is 30°.

RL = (4) / (sin(30^°)) = 8

The ramp length is 8 ft.

Example 2

A ramp rises 24 in and uses a 1:12 slope ratio.

R = 12 × 24 = 288
RL = √(24² + 288²) ≈ 288.99

The ramp length is approximately 288.99 in, or about 24.08 ft.

Tips for Accurate Inputs

  • Use the angle from the horizontal, not from the vertical.
  • Use consistent units when calculating by hand. In this calculator, each dimension has its own unit selector and is converted before the geometry is evaluated.
  • Make sure your calculator mode matches the angle unit: degrees or radians.
  • As the angle gets smaller, the required ramp length increases very quickly.
  • For a positive horizontal run, sloped length must be greater than rise. Equality describes a vertical segment, outside this ramp calculation.

Common Questions

Can I calculate ramp length from rise and run?
Yes. Use the right-triangle relationship between rise, run, and sloped length.

RL = √(H² + R²)

How do I convert grade percentage to angle?
If you know the grade percentage, divide by 100 to get the slope as a decimal, then use the inverse tangent.

a = tan⁻¹((G) / (100))

Why is the ramp length always longer than the rise?
Because the ramp length follows the slope, and the sloped side of a right triangle is always at least as long as the vertical side.

Planning Notes

Ramp length is only one part of a complete ramp layout. Sloped surface length excludes level landings. The calculator’s minimum run count is the total rise divided by the selected maximum rise per run, rounded up; minimum intermediate landings are one fewer. This is a lower bound, not a designed layout. Top and bottom landings and any switchback footprint must be planned separately.

The U.S. Access Board ramp guide generally limits running slope to 1:12 and rise per run to 30 in within its scope and exceptions. At 1:12, 30 in of rise needs 30 ft of horizontal run; 30 ft is not a universal maximum run length. A slope comparison alone cannot establish compliance: width, cross slope, landings, surfaces, handrails, edge protection and other applicable requirements also matter. A custom rise limit or a steeper ratio does not grant accessibility approval.