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Geometry

Pyramid Frustum

Pyramid frustum properties. Free online Pyramid Frustum. Calculate pyramid frustum online — fast, accurate, mobile-friendly, no signup needed.

Frustum — a pyramid with its top cut off parallel to its base.
Volume
430

Derivation

  1. ├── 01Givena = 8, b = 5, h = 10
  2. ├── 02Formulae.h / 3 × (t²+t × a+a²)
  3. ├── 03Substitutee.10 / 3 × (t²+t × 8+8²)
  4. └── 04Compute Volume430
Did you know?

The cone and pyramid share a single volume formula: V = (1/3) × base × height. Democritus (~450 BCE) asserted it; Eudoxus proved it a century later.

§01What is

Understanding the Pyramid Frustum

The Pyramid Frustum computes Volume from 3 inputs: bottom edge, top edge, height. Pyramid frustum properties.

Geometry is what turns raw measurements into useful answers about space — how much paint, how big a yard, how much material a project will need. Every craftsperson, architect, and DIYer reaches for these formulas regularly. The Pyramid Frustum sits in that toolkit — it pyramid frustum properties. Enter your numbers above and the result updates instantly; every step of the math is shown in the Derivation panel so you can see exactly how the answer was reached.

§02The Formula

How it’s calculated

e.h / 3 × (t²+t × a+a²)

Where

a
Bottom edge
b
Top edge
h
Height
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Bottom edge = 8, Top edge = 5, Height = 10.

  1. 01Start by noting the input — Bottom edge: 8.
  2. 02Start by noting the input — Top edge: 5.
  3. 03Start by noting the input — Height: 10.
  4. 04Substitute these values into the formula: e.h / 3 × (t²+t × a+a²)
  5. 05Compute Volume: the calculator returns 430.
  6. 06Cross-check the answer by opening the Derivation panel above — every line of math is shown so you can follow the computation end-to-end.
§04Variants

Common Pyramid Frustum Problems

The formula gets rearranged depending on which variable you need. Here are the patterns you’ll run into in the real world — find the one that matches your problem and follow the worked steps.

01 · PATTERN

Bottom edge halved

a = 4 (from 8)

Keep every other input at its default and halve the bottom edge. See how volume responds.

  1. 01New Bottom edge: 4
  2. 02Baseline Volume: 430
  3. 03New Volume: 203.333
  4. 04Volume decreases by 52.7% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Bottom edge doubled

a = 16 (from 8)

Keep every other input at its default and double the bottom edge. See how volume responds.

  1. 01New Bottom edge: 16
  2. 02Baseline Volume: 430
  3. 03New Volume: 1203.33
  4. 04Volume increases by 179.8% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Top edge halved

b = 2.5 (from 5)

Keep every other input at its default and halve the top edge. See how volume responds.

  1. 01New Top edge: 2.5
  2. 02Baseline Volume: 430
  3. 03New Volume: 300.833
  4. 04Volume decreases by 30% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Top edge doubled

b = 10 (from 5)

Keep every other input at its default and double the top edge. See how volume responds.

  1. 01New Top edge: 10
  2. 02Baseline Volume: 430
  3. 03New Volume: 813.333
  4. 04Volume increases by 89.1% → use this sensitivity to plan for real-world variation.
§05FAQ

Frequently asked questions

Yes. The calculator implements the standard formula as documented and returns exact floating-point results. No approximations are used unless noted in the formula.
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