Square Frustum Calculator

Name: Square Frustum - Geometry Calculator
Author: Jürgen Kummer

Calculations at a square frustum, a special case of a regular frustum with four base corners. This is a square pyramid with the apex truncated parallel to the base.
Enter both side lengths a and b and height h. Choose the number of decimal places, then click Calculate.

Formulas:

s = \sqrt{\frac{1}{4} \cdot {(a - b)}^{2} + h^{2}}

e = \sqrt{\frac{[4 \cdot s^{2} + {(a - b)}^{2}]}{4}}

L = (a + b) \cdot \sqrt{{(a - b)}^{2} + 4 h^{2}}

A = L + (a^{2} + b^{2})

V = \frac{h}{3} \cdot [(a^{2} + b^{2}) + \sqrt{a^{2} \cdot b^{2}}]

Lengths and heights 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 square frustum forms the base of the bent pyramid and the obelisk. Two identical square truncated pyramids, put together at their base, form a square bifrustum, i.e. one with four base corners. A similar body made up of a truncated pyramid and a pyramid is a frustum pyramid. A square frustum has four planes of symmetry. Two pass through the centers of the four opposite parallel sides, the other two through the four opposite corners and through the two opposite steep edges. Like its square base and its opposite smaller square side, it is rotationally symmetrical at an angle of 90 degrees and multiples thereof to the axis through the centers of the two parallel square surfaces.

The term frustum generally refers to a shape between two parallel planes. In a square frustum, the two opposite sides are squares of different sizes, whose centers are connected by a straight line perpendicular to these sides or planes.

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