Nº Hexagonal n
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
H_n = n(2n−1)
About this calculator
The hexagonal number calculator computes the nth hexagonal number using the formula H_n = n(2n − 1). Hexagonal numbers are figurate numbers that represent a regular hexagon formed by dots or circles. For example, H_1 = 1, H_2 = 6, H_3 = 15, H_4 = 28, and so on. This sequence appears in various mathematical and natural contexts.
The operation is simple: enter a positive integer n and the tool applies the formula H_n = n(2n − 1) to return the result. The calculation is instantaneous and requires no advanced knowledge. It is useful for students exploring number sequences, teachers preparing examples, or enthusiasts interested in mathematical patterns.
Use this calculator when you need to quickly find a specific hexagonal number, verify properties of figurate numbers, or solve problems involving hexagonal arrangements in geometry, combinatorics, or diagrams. It can also be handy in games or puzzles that use hexagonal numbers.
Caution: the formula is only valid for positive integer n. For n = 0, the result would be 0 (not hexagonal). Also, hexagonal numbers should not be confused with centered hexagonal numbers (which follow a different formula). Always double-check the index n.
Frequently asked questions
What is a hexagonal number?
A hexagonal number is a figurate number that can be represented as a regular hexagon of dots. The formula for the nth hexagonal number is H_n = n(2n − 1).
What is the first hexagonal number?
The first hexagonal number is H_1 = 1 × (2×1 − 1) = 1.
Are hexagonal numbers the same as triangular numbers?
No, hexagonal numbers are different. Each hexagonal number is twice a triangular number minus the index, but they are distinct sequences.
Can I use negative or decimal n?
No, the formula is defined only for positive integer n. Negative or decimal values do not produce valid hexagonal numbers.
What is the difference between a hexagonal number and a centered hexagonal number?
Regular hexagonal numbers follow H_n = n(2n−1), while centered hexagonal numbers use a different formula (3n(n−1)+1) and represent hexagons with a central dot.