Triangular Number Calculator

Summary

Enter n to compute the nth triangular number using T(n) = n(n+1)/2 and see the full sequence up to that term.

How it works

1. Enter a value of n (1 through 500) in the input field.
2. The calculator applies the closed-form formula T(n) = n × (n + 1) / 2.
3. The nth triangular number is displayed immediately.
4. A table below lists every triangular number from T(1) through T(n).
5. Use the Copy button to copy the result to your clipboard.

Use cases

• Verify triangular number values for math homework or number theory research.
• Find how many items fit in a triangular arrangement of n rows.
• Calculate handshake counts: n people each shaking hands once = T(n-1).
• Compute the sum of the first n positive integers quickly.
• Explore figurate numbers and their patterns in sequences.
• Cross-check results in combinatorics: T(n) = C(n+1, 2).

Frequently Asked Questions