Hexagonal Number Calculator

This hexagonal number calculator works out the nth hexagonal number, a figurate number that counts dots arranged in a pattern of nested hexagons sharing a common corner. Hexagonal numbers form a well known sequence in number theory, running 1, 6, 15, 28, 45 and upward, and they turn up in puzzles, programming challenges and maths courses that explore patterns within whole numbers. You simply enter an index n, any whole number from 1 up to 100,000,000, and the calculator applies the formula H(n) = n(2n minus 1) to return the exact result instantly. Alongside the main answer, it also shows the next hexagonal number and the previous one in the sequence, so you can see how the value you have chosen fits into the wider pattern without working out several terms by hand. For n = 4, for example, the calculator returns H(4) = 28, with 15 as the previous term and 45 as the next, and larger results are grouped with commas so big numbers stay easy to read. Because every hexagonal number is also a triangular number, specifically T(2n minus 1), the tool doubles as a quick way to explore that relationship. It is aimed at students, programmers and anyone curious about figurate numbers, and it uses exact integer arithmetic throughout, so results stay precise even at the top of the allowed range.

Index n (1 to 100,000,000)

H(4) = 28

Next hexagonal number45

Previous hexagonal number15

The formula

The nth hexagonal number is H(n) = n(2n minus 1). The sequence begins 1, 6, 15, 28, 45. Every hexagonal number is also the triangular number T(2n minus 1).

Worked example

For n = 4, H(4) = 4 times (2 times 4 minus 1) = 4 times 7 = 28. Enter 4 to confirm, and see 15 before and 45 after.

Frequently asked questions

What is a hexagonal number?

A figurate number counting dots in nested hexagons, given by n(2n minus 1): 1, 6, 15, 28 and so on.

Are hexagonal numbers also triangular?

Yes. Every hexagonal number is a triangular number, specifically T(2n minus 1).

What is the 4th hexagonal number?

28, which is also a perfect number.

Who this calculator is for

This calculator is for students, programmers and anyone exploring number theory.

What this calculator assumes

You enter a whole number within the stated range.
The exact integer algorithm is used.
Very large results are shown grouped for readability.

Formula and sources

Related calculators

Prime Factorization Calculator: break a number into prime factors.
LCM Calculator: lowest common multiple.
GCF Calculator: greatest common factor.

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