Calculators
Hexagonal Number Calculator
Calculate the nth hexagonal number exactly with a formula breakdown, privately in your browser.
Count dots in a hexagonal arrangement.
The nth ordinary hexagonal number is H(n) = n × (2n − 1). The first five positive values are 1, 6, 15, 28, and 45. Successive layers add 1, 5, 9, 13, and so on, increasing by 4 each time. For n = 10, H(10) = 10 × 19 = 190. We include H(0) = 0 for an empty arrangement. Enter a non-negative index of up to 100 digits without separators, signs, decimals or scientific notation. Leading zeros are accepted. Browser BigInt arithmetic keeps the entire result exact. This tool calculates ordinary hexagonal numbers from their indices; it does not calculate centered or generalized hexagonal numbers or test sequence membership. All processing stays in your browser.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What is a hexagonal number?
An ordinary hexagonal number counts dots arranged in a hexagonal pattern. The sequence starts 1, 6, 15, 28, 45. Successive differences are 5, 9, 13, 17, increasing by 4.
How is the nth hexagonal number calculated?
Use H(n) = n × (2n − 1). For n = 10, this gives 10 × 19 = 190.
Are these centered hexagonal numbers?
No. Ordinary hexagonal numbers use n × (3n − 1) ÷ 2. Centered hexagonal numbers follow a different formula, and generalized hexagonal numbers also allow negative indices. This calculator uses ordinary non-negative indices only.
Can I enter zero or decimal indices?
Zero returns zero for an empty arrangement. Negative and fractional indices are rejected. Enter digits only without signs, commas or exponent notation; leading zeros are accepted.
Are large results rounded or uploaded?
No. BigInt arithmetic produces exact integers for indices up to 100 digits. Calculations stay in your browser, and you can copy the full result.