Calculations at a ramp. A ramp, slope or perpendicular wedge is a right prism with a right triangle as base and an opposite triangle of the same shape. The edge w, which describes the width of the ramp, is perpendicular to each of the three sides a, b and c of the base triangle.
Enter two of the three lengths a, b and c and the width w. Choose the number of decimal places, then click Calculate.
Formulas:
c = √ a² + b²
α = arccos( (b² + c² - a²) / (2bc) )
β = 90° - α
A = a * b + w * ( a + b + c )
V = abw / 2
Lengths and width have the same unit (e.g. meter), the area has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit -1.
Ramp is a term from geometry as well as from everyday language, with the geometric ramp describing the idealized and simplified form. Ramps in everyday life can be more complicated. In architecture, ramps are used to overcome differences by rolling, in contrast to stairs, which impede rolling. Such ramps can also be curved, for example. This type of ramp is much flatter than the one shown as an example in the image above. Their angle of incline β is generally only a few degrees, and their gradient is usually given in percent, which can be converted using the slope calculator.
The geometric ramp is axially symmetrical to the plane that runs perpendicularly through the middle of the wide edges w. If the two sides a and b of the base triangle are the same length, you get a somewhat more regular ramp. Then there is another plane of symmetry through the right angles between a and b and the middle of the opposite sides c of the two triangles. Then the angles α and β are also equal and are 45 degrees.