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Geometry

Square Pyramid Calculator

Pyramid properties. Free online Square Pyramid Calculator. Calculate square pyramid online — fast, accurate, mobile-friendly, no signup needed.

Square pyramid — volume = ⅓ · base² · h.
Volume
120
Slant height
10.440307

Derivation

  1. ├── 01Givena = 6, h = 10
  2. ├── 02FormulaVolume: t² × e.h / 3
  3. ├── 03Substitutet² × e.10 / 3
  4. ├── 04Compute Volume120
  5. ├── 05FormulaSlant height: √((t / 2)²+a²)
  6. ├── 06Substitute√((t / 2)²+6²)
  7. └── 07Compute Slant height10.440307
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 Square Pyramid Calculator

The Square Pyramid Calculator computes Volume from 2 inputs: base edge, height. Pyramid 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 Square Pyramid Calculator sits in that toolkit — it pyramid 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

Volume = t² × e.h / 3 | Slant height = √((t / 2)²+a²)

Where

a
Base edge
h
Height
Volume
Output value
Slant height
Output value
§03Practical Example

Step-by-step walkthrough

Scenario

Apply the formula to a realistic set of inputs: Base edge = 6, Height = 10.

  1. 01Start by noting the input — Base edge: 6.
  2. 02Start by noting the input — Height: 10.
  3. 03Substitute these values into the formula: Volume = t² × e.h / 3 | Slant height = √((t / 2)²+a²)
  4. 04Compute Volume: the calculator returns 120.
  5. 05Compute Slant height: the calculator returns 10.4403.
  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 Square Pyramid 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 edge halved

a = 3 (from 6)

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

  1. 01New Base edge: 3
  2. 02Baseline Volume: 120
  3. 03New Volume: 30
  4. 04Volume decreases by 75% → use this sensitivity to plan for real-world variation.
02 · PATTERN

Base edge doubled

a = 12 (from 6)

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

  1. 01New Base edge: 12
  2. 02Baseline Volume: 120
  3. 03New Volume: 480
  4. 04Volume increases by 300% → 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: 120
  3. 03New Volume: 60
  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: 120
  3. 03New Volume: 240
  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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