Hexagonal Number Calculator

This hexagonal number calculator gives the nth hexagonal number, a figurate number that counts dots arranged in a pattern of nested hexagons sharing a corner. Enter the index n and the calculator returns the nth hexagonal number along with the ones either side of it. Hexagonal numbers follow the simple formula n times (2n minus 1), giving the sequence 1, 6, 15, 28, 45 and so on. Interestingly, every hexagonal number is also a triangular number, and the even-indexed triangular numbers are exactly the hexagonal numbers. The formula, a worked example and the assumptions are set out below.

Index n (1 to 100,000,000)

Next hexagonal number

Previous hexagonal number

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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