Triangular Number Calculator
Find triangular numbers and test whether a number is triangular.
What is Triangular Numbers?
Triangular numbers count how many dots fill a triangle: 1, 3, 6, 10, 15, … — the sequence you get by adding the counting numbers in turn. T(n) = n(n + 1) ÷ 2, which is the same closed form that sums an arithmetic series, and it is the identity behind the answer to the classic "how many handshakes?" question.
How it works
The forward direction is one multiplication. The reverse — "is 55 triangular?" — is answered exactly by testing whether 8x + 1 is a perfect square, which is what solving n(n + 1)/2 = x for n reduces to, so a hit also reports which T(n) it is and a miss reports the two triangular numbers it sits between.
- Enter your input. Type or paste your input into the field above — the tool responds instantly.
- Review the result. Output updates live as you type. Everything runs entirely in your browser.
- Copy or download. Use the Copy button to grab the result, or Download to save it as a file.
Examples
Realistic sample
Type or paste any realistic input — the tool computes the result locally and instantly.
Common mistakes
Expecting a server round-trip
Nothing is uploaded — every tool in this category runs entirely in your browser.