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Square Pyramid Block Count Calculator — result sheet
Count the unit blocks in a stepped square pyramid whose layers have side lengths from one block through the entered base side.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Total blocks = 1² + 2² + … + n² = n(n + 1)(2n + 1) ÷ 6, where n is the base side length; base-layer blocks = n².
A stepped square pyramid is counted layer by layer: the bottom layer has n² blocks, the next has (n−1)², and so on until one block remains. Reversing that order gives the same sum of squares. The result is a discrete geometry model, not a claim about a particular game’s item rules or a construction specification.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Base side length — blocks; minimum 1; maximum 100000
Worked example
| Input | Value |
|---|---|
| Base side length | 5 |
A 5-by-5 base pyramid has 55 blocks: 25 + 16 + 9 + 4 + 1.
Assumptions and limits
- Each block is a unit cube and every layer is a complete square grid.
- The base side length is a positive whole number of blocks.
- The pyramid has one layer for every integer side length from n down to 1.
- No hollowing, stair gaps, decorative blocks, or support structure is removed from the count.
- The calculator counts blocks and does not calculate material cost, mass, stability, or a real-world building design.
- Large values are bounded so the result remains a safe finite integer in the browser.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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