Pyramid frustum calculator
Use this pyramid frustum calculator with square base and top (sides a1 and a2) or with any similar areas G1 and G2. For a1 = 6, a2 = 4 and h = 3 the volume is 76 and the surface area 115.25, with the calculation steps.
Example: Known values: Square base and top (side lengths) · Bottom side a1 6 · Top side a2 4 · Height h 3 → Result: Volume V = 76 · Surface area S = 115.2456. Source: Wikipedia – Pyramidenstumpf. Updated: .
How it is calculated
A pyramid frustum is what remains when you cut the tip off a pyramid parallel to its base. It has a base area B1, a smaller similar top area B2 and the height h between them. The volume depends only on these three quantities.
The formulas
- Volume: V = h ÷ 3 · (B1 + √(B1 · B2) + B2)
- Square frustum: B1 = a1², B2 = a2²
- Slant height of a face: hs = √(h² + ((a1 − a2) ÷ 2)²)
- Lateral surface area: L = 2 · (a1 + a2) · hs
- Surface area: S = B1 + B2 + L
How to use it
Choose side lengths or areas and enter the values together with the height. Example: a1 = 6, a2 = 4 and h = 3 give V = 3 ÷ 3 · (36 + 24 + 16) = 76, hs = 3.16, L = 63.25 and S = 115.25. The completed apex lies h · a2 ÷ (a1 − a2) = 6 above the top face. The unit is up to you; areas are in its square, the volume in its cube.
Frequently asked questions
How do you calculate the volume of a pyramid frustum?
V = h ÷ 3 · (B1 + √(B1 · B2) + B2). For a1 = 6, a2 = 4 and h = 3 that is 3 ÷ 3 · (36 + 24 + 16) = 76.
How do you calculate the lateral area?
For a square frustum: L = 2 · (a1 + a2) · hs with hs = √(h² + ((a1 − a2) ÷ 2)²). It consists of four equal trapezoids.
Does the formula work for triangles or hexagons?
Yes, the volume formula holds for any base shape as long as the top is similar to the base. Choose “Any base and top”.
What is the difference between a pyramid and a frustum?
A frustum lacks the cut-off tip; there is a second face on top. With a2 = 0 it becomes a pyramid.
How tall is the imaginary apex?
It sits h · a2 ÷ (a1 − a2) above the top face. For 6, 4 and 3 that is 6 units.
Sources and legal basis
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