Wedge-Cuboid Calculator

Name: Wedge-Cuboid - Geometry Calculator
Author: Jürgen Kummer

Calculations at a wedge-cuboid. Here, a wedge-cuboid is a cuboid with a matching ramp attached. A ramp is a perpendicular wedge, hence the name for this shape.
Enter length, width and both heights. Choose the number of decimal places, then click Calculate. The slanted angle is the acute angle between s and h₂.

Formulas:

α = \arccos [\frac{{(h_{2} - h_{1})}^{2} + s^{2} - a^{2}}{2 (h_{2} - h_{1}) s}]

s = \sqrt{a^{2} + {(h_{2} - h_{1})}^{2}}

d_{1} = \sqrt{a^{2} + b^{2} + {h_{1}}^{2}}

d_{2} = \sqrt{a^{2} + b^{2} + {h_{2}}^{2}}

A = a b + s b + b h_{1} + b h_{2} + a (h_{1} + h_{2})

V = a b h_{1} + a b \cdot \frac{h_{2} - h_{1}}{2}

Lengths, width, heights and diagonals and 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.

The sides of a wedge-cuboid are four distinct rectangles and two identical, opposite right trapezoids. Both trapezoids and two of the opposite rectangles are parallel to each other. The other two opposite rectangles, the base and the slanted side, are not. A wedge-cuboid is mirror-symmetrical to the bisecting plane between the two right trapezoids, to which it is parallel.
Door wedges often have this shape; here, the cuboid behind the wedge serves as reinforcement and to facilitate handling. The visible part of roof beams on a pitched roof is often a cuboid with a wedge at each of two opposite ends. Both wedges are the same size and mirrored, so the beam can be thought of as being composed of two identical wedge-cuboids. A wedge-cuboid can also be viewed as a very simplified form of a car, with the slanted side at the front and the long side at the bottom. The reason for this is aerodynamics; the slanted side has less air resistance because the air can flow over the top. A wedge cuboid is therefore an aerodynamic variation or extension of a cuboid.

Calculation of volume and other dimensions: wedge-cuboid

Last updated on 07/10/2026. Author: Jürgen Kummer

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