Square Pyramidal Number

Calculate the sum of squares from 1 to n using n(n + 1)(2n + 1) / 6.

Author

Prof. Mei-Ling Wu

Math editorial contributor

Taiwanese genomics researcher at National Taiwan University, leading studies on pharmacogenomics in East Asian populations

Reviewed by

Prof. Kenji Tanaka

Math content reviewer

Japanese materials scientist at Kyoto University, known for breakthroughs in sustainable polymer research

Last updatedFebruary 22, 2026

PublishedFebruary 22, 2026

Table of Contents

  1. Reference values
  2. Calculator
  3. Reference table
  4. FAQs
  5. Methodology and review
  6. Related conversions

12 Integer n =

650 Sum of Squares

Representative value from the Square Pyramidal Number reference table.

Reference Values

Browse 23 reference values with individual detail pages for quick lookup.

Browse all reference values

Square Pyramidal Number

Calculate the sum of squares from 1 to n using n(n + 1)(2n + 1) / 6.

Calculated Result

Reference Table

Use this complete table for quick lookup and internal linking to specific value pages.

Square Pyramidal Number Reference
n1² + ... + n²
0 Integer n0 Sum of Squares
1 Integer n1 Sum of Squares
2 Integer n5 Sum of Squares
3 Integer n14 Sum of Squares
4 Integer n30 Sum of Squares
5 Integer n55 Sum of Squares
6 Integer n91 Sum of Squares
7 Integer n140 Sum of Squares
8 Integer n204 Sum of Squares
9 Integer n285 Sum of Squares
10 Integer n385 Sum of Squares
12 Integer n650 Sum of Squares
15 Integer n1,240 Sum of Squares
20 Integer n2,870 Sum of Squares
25 Integer n5,525 Sum of Squares
50 Integer n42,925 Sum of Squares
75 Integer n143,450 Sum of Squares
100 Integer n338,350 Sum of Squares
250 Integer n5,239,625 Sum of Squares
500 Integer n41,791,750 Sum of Squares
1,000 Integer n333,833,500 Sum of Squares
5,000 Integer n41,679,167,500 Sum of Squares
10,000 Integer n333,383,335,000 Sum of Squares

Frequently Asked Questions

Common questions about Square Pyramidal Number, formulas, and typical use cases.

What does the Square Pyramidal Number calculator do?

It helps with evaluating discrete sums and sequence formulas in algebra and statistics.

What formula does the Square Pyramidal Number calculator use?

Sum of squares = n(n + 1)(2n + 1) / 6.

What inputs are valid?

n must be a non-negative integer up to 10,000 for exact safe integer output.

When would I use this?

evaluating discrete sums and sequence formulas in algebra and statistics

Methodology and Review

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