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Geometry

Pyramid Volume Calculator

V = (1/3) base × h. Free online Pyramid Volume Calculator. Calculate pyramid volume online — fast, accurate, mobile-friendly, no signup needed.

Volume = ⅓ · base-area · height.
Volume
83.333333

Derivation

  1. ├── 01Givenb = 25, h = 10
  2. ├── 02Formulae.b × e.h / 3
  3. ├── 03Substitutee.25 × e.10 / 3
  4. └── 04Compute Volume83.333333
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 Volume Calculator

The Pyramid Volume Calculator computes Volume from 2 inputs: base area, height. V = (1/3) base × h.

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 Volume Calculator sits in that toolkit — it V = (1/3) base × h. 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.b × e.h / 3

Where

b
Base area
h
Height
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Base area = 25, Height = 10.

  1. 01Start by noting the input — Base area: 25.
  2. 02Start by noting the input — Height: 10.
  3. 03Substitute these values into the formula: e.b × e.h / 3
  4. 04Compute Volume: the calculator returns 83.3333.
  5. 05Cross-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 Volume 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

Base area halved

b = 12.5 (from 25)

Keep every other input at its default and halve the base area. See how volume responds.

  1. 01New Base area: 12.5
  2. 02Baseline Volume: 83.3333
  3. 03New Volume: 41.6667
  4. 04Volume decreases by 50% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Base area doubled

b = 50 (from 25)

Keep every other input at its default and double the base area. See how volume responds.

  1. 01New Base area: 50
  2. 02Baseline Volume: 83.3333
  3. 03New Volume: 166.667
  4. 04Volume increases by 100% → use this sensitivity to plan for real-world variation.
03 · PATTERN

Height halved

h = 5 (from 10)

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

  1. 01New Height: 5
  2. 02Baseline Volume: 83.3333
  3. 03New Volume: 41.6667
  4. 04Volume decreases by 50% → use this sensitivity to plan for real-world variation.
04 · PATTERN

Height doubled

h = 20 (from 10)

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

  1. 01New Height: 20
  2. 02Baseline Volume: 83.3333
  3. 03New Volume: 166.667
  4. 04Volume increases by 100% → 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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