Triangular Number Calculator

The Triangular Number Calculator is a free online tool for checking if a number is a triangle number.

Triangular Number Calculator

Eg, Is 36 a triangular number? Enter 36 into the input box and click Calculate button.

What is a triangular number?

A triangle number refers to a certain number of points or circles that can form an equilateral triangle when arranged at equal distances. For example, 1, 3, 6, 10, 15, and 21 are all triangle numbers, which are represented graphically as follows

triangle numbers 1 to 21 Looking at the last graph, we can find that the points on each row of the equilateral triangle are increasing, as follows

triangle number 21 The first row is 1, the second row is 2, the third row is 3, the fourth row is 4, and so on. Row N should have N. Obviously, this is an arithmetic sequence. The starting number and tolerance are both 1. According to the formula of the sum of an arithmetic sequence, it can be deduced that the Nth triangle number is

T_n = n × (n + 1)2

With the formula, we can easily calculate the first 100 triangle numbers.

First 100 triangular numbers

1	3	6	10	15	21	28	36	45	55
66	78	91	105	120	136	153	171	190	210
231	253	276	300	325	351	378	406	435	465
496	528	561	595	630	666	703	741	780	820
861	903	946	990	1035	1081	1128	1176	1225	1275
1326	1378	1431	1485	1540	1596	1653	1711	1770	1830
1891	1953	2016	2080	2145	2211	2278	2346	2415	2485
2556	2628	2701	2775	2850	2926	3003	3081	3160	3240
3321	3403	3486	3570	3655	3741	3828	3916	4005	4095
4186	4278	4371	4465	4560	4656	4753	4851	4950	5050

How to use the triangular number calculator

The procedure to use the triangle number calculator is as follows:

1Enter the positive number.
2Click calculate button to check whether the input integer is a triangle number.
3Click the Reset button to start a new verification.

Solved examples using the triangular number calculator

Example 1: Is 36 a triangular number?

Enter 36 into the input box and click Calculate button, as shown in the figure, 36 is a triangular number.

Example 2: Is 150 a triangular number?

Enter 150 into the input box and click Calculate button, as shown in the figure, 150 is not a triangular number.

Triangular Number Calculator