The Ramp Slope Calculator determines the rise, horizontal run, sloping length and inclination angle of a ramp. The calculation uses right-triangle geometry to find the ramp dimensions from two known quantities. The results support preliminary design, slope selection and checks of the inclined section’s geometry.
Basic geometry. The inclined section is the hypotenuse of a right triangle. The rise H is the vertical difference in level, A is the horizontal run and L is the actual length along the slope. All three dimensions are measured in metres (m).
Slope coefficient. The ratio of rise H to horizontal run A gives the dimensionless longitudinal slope coefficient. This coefficient is used to express the slope as a percentage, an angle in degrees and a 1:x ratio.
ks = H / A
Slope percentage shows how many metres the surface rises over 100 m of horizontal distance. For example, a 5% slope rises 0.05 m for every 1 m of horizontal run.
Slope (%) = 100 × ks
Ratio 1:x. The number x represents the horizontal distance corresponding to one unit of rise. For example, 1:20 means a 1 m rise over 20 m horizontally, equivalent to a 5% slope.
x = 1 / ks = A / H
Inclination angle. The angle α between the sloping surface and the horizontal is calculated using the arctangent of the slope coefficient. To convert radians to degrees, the result is multiplied by 180 / π, where π ≈ 3.14159.
α (°) = arctan(ks) × 180 / π
When the given slope is a percentage, its coefficient is found by dividing by 100. For a 1:x ratio, the reciprocal of x is used. For an angle in degrees, the tangent is taken after converting the angle to radians.
Calculation principle. Two independent quantities are needed to determine the geometry uniquely. The last two parameters changed by the user become the inputs. The remaining dimensions and slope formats are calculated from that pair, without averaging them with earlier results.
When two dimensions are known, the missing side of the right triangle is calculated first, followed by the slope coefficient and angle. The following relationships apply:
L = √(H2 + A2).A = √(L2 - H2).H = √(L2 - A2).When a slope and one dimension are known, the slope coefficient is determined first, then the other sides are calculated:
A = H / ks, followed by L = √(H2 + A2).H = A × ks, followed by L = √(H2 + A2).A = L / √(1 + ks2), followed by H = A × ks.Geometric restrictions. For a ramp with a positive rise, input dimensions and slope must be greater than zero. The sloping length L must exceed both H and A. The inclination angle must be greater than 0° and less than 90°. If these conditions are not met, no valid result can be calculated for the chosen geometric model.
Numerical example. With a rise of 0.5 m and a horizontal run of 10 m, the slope coefficient is 0.05. This corresponds to a 5% grade, a 1:20 ratio and an angle of approximately 2.86°.
L = √(0.52 + 102) ≈ 10.012 m
Thus, the horizontal run is 10 m and the actual sloping length is approximately 10.012 m. The difference is due to the vertical rise.
Rounding. Dimensions in the main input fields are displayed to 0.01 m, while the results are shown to 0.001 m. Percentages, angles and 1:x ratios are displayed to two decimal places. Intermediate calculations retain higher precision, so rounding displayed values does not change the underlying calculation geometry.
Assumptions. The calculation assumes a constant longitudinal slope along one straight inclined section. No correction factors or safety factors are applied. The calculated sloping length covers only the inclined surface, without adding horizontal landings.
For accessible ramps, a longitudinal slope of about 5% (1:20) is often considered. At this grade, a rise of 0.30 m requires 6 m of horizontal run. Steeper grades reduce the required length, but their acceptability depends on the building’s purpose and national requirements.
European requirements. EN 17210:2021, “Accessibility and usability of the built environment - Functional requirements”, sets out general principles for accessible buildings and surroundings. Specific limits on slope, flight length and landing dimensions are defined by the applicable national documents.
These values are provided to compare the geometric calculation with practical requirements. The calculator does not automatically select a regulatory limit or cap the result at a fixed percentage. A design must be checked against the rules applicable in the relevant country, building type and use.
The horizontal run is calculated by dividing the rise by 0.05. For example, a rise of 0.30 m requires 6 m horizontally, while the sloping length is approximately 6.007 m. For another grade, the corresponding slope coefficient is used.
A percentage describes the rise relative to the horizontal run, while a 1:x ratio states how many units of horizontal distance correspond to one unit of rise. For example, 1:20 equals 5%, and 1:12 is approximately 8.33%. Both formats describe the same geometry and can be converted without additional factors.
The horizontal run is measured as a horizontal projection, while the sloping length is measured along the inclined surface. With a positive rise, the hypotenuse of a right triangle is always longer than its horizontal side. The difference increases as the rise increases for a fixed horizontal run.
Yes. Any two independent geometric dimensions - rise, horizontal run or sloping length - are sufficient to calculate the slope. If only the horizontal run and sloping length are known, the rise is found using the Pythagorean theorem. The result can then be expressed as a percentage, an angle in degrees and a 1:x ratio.
There is no single maximum percentage applicable to every case across Europe. EN 17210 sets general functional accessibility requirements, while national documents such as Germany’s DIN 18040-1 specify limits for particular building types. The calculated grade must be compared with the requirements for the specific project.