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% · ratio · angleGeometry onlyFree

Slope &
Gradient

Convert a slope between percent grade, ratio (1:n), and angle, and calculate the inclined length. The result is geometric only and does not select or verify a regulatory limit.

Who it's for: architects, civil engineers, and landscape designers converting consistent rise/run measurements at design development or construction documents.

Slope from rise & run
% grade = (rise / run) × 100 · ratio 1:n where n = run / rise · angle = arctan(rise / run) · slope length = √(rise² + run²).
Slope
Grade · ratio · angle

How to use this calculator

1
Enter the Rise
The vertical height gained — use any consistent unit (inches, feet, or meters). A wheelchair ramp that climbs 1 ft has a rise of 1.
2
Enter the Run
The horizontal distance traveled. If the ramp covers 12 ft of floor space, the run is 12. Rise and run must be in the same unit.
3
Click Calculate slope
Results appear immediately as percent grade, ratio, angle, and inclined length.
4
Read the grade, ratio, and angle
Grade (%) is the most common spec format. Ratio 1:n is used in accessibility codes. Angle in degrees is used in structural and geotechnical contexts.

The formula

Rise divided by run gives the slope — expressed four equivalent ways at once.

% grade = (rise ÷ run) × 100
Ratio 1:n, where n = run ÷ rise
Angle = arctan(rise ÷ run), in degrees
Slope length = √(rise² + run²).

Worked example

Example
A slope rises 1 unit over a horizontal run of 12 units. Grade = 8.33%, ratio = 1:12, angle = 4.76°, and inclined length = 12.042 units.

When this estimate will be off

  • Assumes a constant slope along the full run. A ramp or grade that changes along its length needs a separate calculation for each segment.
  • Rise and run must be in the same unit. Mixing feet for the rise and inches for the run without converting first produces a meaningless grade.
  • The calculator does not identify whether a surface is a ramp, walking surface, curb ramp, driveway, roof, or site grade.
  • Applicable accessibility, drainage, safety, and building-code limits must be selected and checked separately.

Frequently asked questions

A common mistake: Assumes a constant slope along the full run. A ramp or grade that changes along its length needs a separate calculation for each segment.

Percent grade is rise divided by run, multiplied by 100. A 5% grade means you gain 5 units of height for every 100 units of horizontal travel. It is the standard format in civil engineering grading specs and ADA compliance documents.

No. It converts geometry only. The applicable standard, element type, exceptions, landings, widths, cross slope, and other requirements must be evaluated separately.

Take the inverse tangent (arctan) of the grade as a decimal. For a 10% slope: arctan(0.10) ≈ 5.71°. For a 1:12 ramp: arctan(1/12) ≈ 4.76°. This calculator performs the conversion automatically from the rise and run you enter.

A ratio of 1:n means you travel n horizontal units for every 1 unit of vertical rise. A 1:20 slope is gentler than a 1:4 slope — the larger n, the shallower the incline. This format is used in accessibility codes because it makes the relationship to the 1:12 ramp limit immediately readable.

Sources

  • Right-triangle geometry — tangent, arctangent, and Pythagorean theorem applied to user-entered rise and run

This free Slope / Gradient Calculator is built and maintained by DataDrivenAEC, using the relevant codes and standards. It does not substitute for professional judgment.