Convertools

Triangular Number

Calculate the nth triangular number using T(n) = n(n + 1) / 2.

Author

Dr. Lars Eriksson

Math editorial contributor

Swedish environmental economist from Stockholm School of Economics, advisor to the EU on carbon pricing policy

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 =

78 Triangular Number

Representative value from the Triangular Number reference table.

Reference Values

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

Browse all reference values

Triangular Number

Calculate the nth triangular number using T(n) = n(n + 1) / 2.

Calculated Result

—

Reference Table

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

Triangular Number Reference
nT(n)
0 Integer n0 Triangular Number
1 Integer n1 Triangular Number
2 Integer n3 Triangular Number
3 Integer n6 Triangular Number
4 Integer n10 Triangular Number
5 Integer n15 Triangular Number
6 Integer n21 Triangular Number
7 Integer n28 Triangular Number
8 Integer n36 Triangular Number
9 Integer n45 Triangular Number
10 Integer n55 Triangular Number
12 Integer n78 Triangular Number
15 Integer n120 Triangular Number
20 Integer n210 Triangular Number
25 Integer n325 Triangular Number
50 Integer n1,275 Triangular Number
75 Integer n2,850 Triangular Number
100 Integer n5,050 Triangular Number
250 Integer n31,375 Triangular Number
500 Integer n125,250 Triangular Number
1,000 Integer n500,500 Triangular Number
5,000 Integer n12,502,500 Triangular Number
10,000 Integer n50,005,000 Triangular Number

Frequently Asked Questions

Common questions about Triangular Number, formulas, and typical use cases.

What does the Triangular Number calculator do?

It helps with counting pair combinations, stacked objects, and arithmetic series totals from 1 to n.

What formula does the Triangular Number calculator use?

Triangular number T(n) = n(n + 1) / 2.

What inputs are valid?

n must be a non-negative integer. The calculator caps n to preserve exact safe integer output formatting.

When would I use this?

counting pair combinations, stacked objects, and arithmetic series totals from 1 to n

Methodology and Review

This page combines a live calculator, precomputed reference values, and FAQ content from the same conversion definition to reduce mismatch between calculator output and lookup tables.

Editorial metadata (author, reviewer, and update date) is rendered on the page and in structured data. See our editorial policy, review process, and corrections policy.

For compliance-sensitive work, verify final values against project requirements, governing standards, and manufacturer documentation.