Ramp Slope Formula: Ratio, Percent, Run and Length

Use horizontal run in the denominator

Ramp slope is vertical rise divided by horizontal run. If a ramp rises 0.6 metres over a horizontal run of 7.2 metres, the slope is 0.6/7.2 = 1/12, approximately 0.083333. The denominator is the level projection on the ground, not the length measured along the inclined surface. Draw the right triangle before choosing values: rise is the vertical leg, run is the horizontal leg, and the ramp surface follows the hypotenuse. Mixing these lengths produces a different ratio even though each measurement is real.

Convert a ratio into percent grade

Multiply rise/run by 100 to obtain percent grade. A 1:12 rise-to-run ratio is approximately 8.3333%, while 1:20 is 5%. The second number means that every one unit of rise has the stated number of horizontal units of run. Check the order whenever a drawing labels a ratio, since swapping rise and run changes its meaning drastically. A percent is not an angle: an 8.3333% grade is not an inclination of 8.3333 degrees.

Calculate angle and sloping surface length

The angle above horizontal is θ = arctan(rise/run). For the 0.6 m and 7.2 m example, θ is approximately 4.7636°. The inclined length is √(0.6² + 7.2²) = √52.2, approximately 7.2250 m. It is slightly longer than the horizontal run, as the right-triangle geometry requires. If an angle calculator operates in radians, convert the result before reporting degrees. Keep the ratio unrounded until this step to avoid a needless discrepancy between the reported grade and angle.

Solve for the needed run

Rearrange slope = rise/run to get run = rise/slope. For a mathematical target of 1:15 and a rise of 0.45 m, the run is 0.45 × 15 = 6.75 m. Equivalently, using percent grade p gives run = 100 × rise/p. This determines the inclined run’s horizontal projection only. Level landings, turns and approach areas occupy additional space and must not be included in that run while keeping the same rise, because doing so would understate the slope of the inclined part.

Distinguish running slope from cross slope

Running slope follows the direction of travel. Cross slope is the sideways slope across the route. A single side-view triangle measures only the first of these; it says nothing about the other. Similarly, an average rise over an entire route can conceal a short, steeper section. For a route made from separate inclined runs and level landings, assess each run using its own rise and horizontal run. A single overall fraction does not show the steepest local portion.

Keep arithmetic separate from accessibility requirements

The U.S. Access Board’s ADA guide describes a maximum running slope of 1:12 for covered ramps, alongside other provisions and defined exceptions. That one number is not a complete design specification and should not be applied as a universal rule for every jurisdiction or purpose. Width, landings, handrails, cross slope and the applicable context also matter. The linked official guide explains that scope. This page’s examples demonstrate geometry; they do not establish that a proposed ramp complies with the rules that apply to a particular site.

Check measurements and report the convention

Use the same unit for rise and run before dividing. For example, 6 inches over 6 feet becomes 6/72 = 1/12, not 6/6. Record whether the reported value is a ratio, a percentage or an angle, and label the horizontal run separately from the inclined length. If measured values are approximate, rounding the final result appropriately is more informative than printing many decimals. Repeating the calculation with independently checked measurements can reveal a unit or endpoint error before the result is used in further planning.

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