Frustum Calculator

Name: Frustum - Geometry Calculator
Author: Jürgen Kummer

Calculations at a general frustum or truncated general pyramid. This has arbitrary polygons as base and top surface, both are similar and parallel to each other. The general frustum can be straight or oblique, this does not matter for the volume.
Enter base and top surface area, height or volume, choose the number of decimal places. Then click Calculate. This formula also applies to general truncated cones. The surface of the general frustum is calculated as the sum of the individual surfaces of the sides and the bases.

Formula:

V = \frac{h}{3} \cdot (B + \sqrt{B T} + T)

Height has a one-dimensional unit (e.g. meter), the areas have this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter).

The general frustum is a special prismoid. It has some special cases where measurements other than just volume can be calculated. On the one hand, there is the regular frustum, with an equilateral polyhedron as the base and which is straight, i.e. with the upper surface exactly in the middle of the lower one. The square frustum is even more special. A regular bifrustum can be assembled from two identical regular frustums. A flatter pyramid placed on top of a frustum is called a bent pyramid. However, if you place the frustum at the base of the matching pyramid, then a frustum pyramid is created.
A regular frustum gets closer and closer to the truncated cone with an increasing number of corners. The calculation of the volume for the general frustum is the same as for the general truncated cone, which is not surprising since both only take into account the area of the base and top surfaces, not their shapes.
The general frustum has no symmetries, in contrast to the axisymmetric and rotationally symmetrical regular frustum.

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