Nº Triangular n
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
T_n = n(n+1)/2
About this calculator
The Triangular Number n Calculator computes the nth triangular number, defined as the sum of the first n natural numbers. The formula T_n = n(n+1)/2 is used to quickly obtain the value without summing individually. For example, the fifth triangular number is 1+2+3+4+5 = 15, which equals 5×6/2 = 15.
This tool is useful in contexts such as counting objects in triangular arrangements, combinatorial analysis, and sequence problems. For instance, arranging 10 balls in rows forming a triangle gives T_4 = 10. It also appears in probability and statistics, e.g., in binomial distributions.
When using the calculator, ensure you enter a non-negative integer. For n=0, T_0=0. Remember that triangular numbers grow quadratically, so large n may yield very high results. The calculator does not accept negative or non-numeric inputs.
Frequently asked questions
What is a triangular number?
A triangular number represents the sum of the first n natural numbers, forming an equilateral triangle of dots. For example, T_3 = 1+2+3 = 6.
How do I calculate the 100th triangular number?
Use the formula T_100 = 100×101/2 = 5050. Simply enter 100 in the calculator.
Can I use negative numbers?
No. The calculator only accepts non-negative integers. Negative numbers have no meaning for triangular numbers.
What is the relationship between triangular and square numbers?
Every square number is the sum of two consecutive triangular numbers. For example, 4 = T_1 + T_2 = 1 + 3.
What happens if I enter n=0?
For n=0, the result is 0, as the sum of zero terms is zero.