Frustum-Pyramid Calculator

Calculations at a frustum-pyramid, an object made of a regular frustum and a matching regular pyramid attached on the larger base.
Enter the number of vertices at the base, the side lengths at the base and at the transition between frustum and pyramid, as well as two of the three heights. Choose the number of decimal places, then click Calculate.

	Vertices at the base n:			Example with n=4 2n+1 faces, 4n edges, 2n+1 vertices Base: regular polygon Joining faces: n isosceles trapezoids, n isosceles triangles
	Side length at base (a):
	Side length at transition (b):
	Frustum height (i):
	Pyramid height (j):
	Total height (h):
	Surface area (A):
	Volume (V):
	Surface-to-volume ratio (A/V):
	Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   decimal places.

Lengths and heights have the same 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). A/V has this unit ^-1.

A frustum-pyramid can also be seen as a regular bipyramid in which one of the two apexes has been straight cut off. If both apexes are truncated in the same way, a bifrustum is formed.
Frustum-pyramids have the same symmetry properties as the corresponding regular pyramids. They are mirror-symmetric about every plane passing through a vertex or edge of the base, through the directly opposite vertex or edge of the base, and through the apex. There are as many planes of symmetry as there are vertices or edges at the base; this number is denoted here as n. These frustum-pyramids are rotationally symmetric about an axis through the apex and the center of the base at an angle of 360 degrees divided by the number of vertices at the base.

Last updated on 03/29/2026. Author: Jürgen Kummer

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