Calculators
Centered Hexagonal Number Calculator
Calculate exact centered hexagonal numbers from a ring count, with the next term and digit count, privately in your browser.
Count dots in a centered hexagon with n complete rings around one central dot. Enter 0 or a positive whole number of up to 100 digits. Calculations stay in your browser.
Count dots in concentric hexagonal rings.
Start with one central dot and surround it with n complete hexagonal rings. Ring k adds 6k dots, so H(n) = 1 + 6(1 + 2 + … + n) = 3n(n + 1) + 1. Using ring counts n = 0, 1, 2, 3, 4 gives 1, 7, 19, 37, 61. For example, three rings contain 1 + 6 + 12 + 18 = 37 dots. This calculator uses zero-based ring counts: n = 0 is the center alone. Some sequence references instead number the center as term 1. These are centered hexagonal numbers, distinct from ordinary hexagonal numbers n(2n − 1). Enter a non-negative integer of up to 100 digits. Leading zeros and surrounding whitespace are accepted; signs, decimals, separators and scientific notation are rejected. Exact BigInt arithmetic preserves every digit. Results include the next term and decimal digit count. No input is uploaded or stored.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What is the formula?
With n rings around a central dot, H(n) = 3n(n + 1) + 1. Each ring k adds 6k dots.
What does zero mean?
Zero rings means the central dot alone, so H(0) = 1. The next counts are 7, 19, 37 and 61.
Are these ordinary hexagonal numbers?
No. Ordinary hexagonal numbers use n(2n − 1). Centered hexagonal numbers describe complete rings surrounding a central dot.
How large can the input be?
Enter a non-negative integer of up to 100 digits. BigInt arithmetic keeps results exact, and calculations stay in your browser.