The Fibonacci sequence starts 1, 1, 2, 3, 5, 8, 13… Each new term equals the sum of the two before it.
About this calculator
The Fibonacci sequence starts 1, 1, 2, 3, 5, 8, 13… Each new term equals the sum of the two before it.
Enter how many terms you want. The calculator lists the sequence, highlights F_n, and totals the first n values. Fibonacci numbers appear in petal counts, pinecones, and the golden-ratio limit F_{n+1}/F_n → φ.
For other patterned lists try [[number-sequence]]. For φ directly use [[golden-ratio]]. For general powers see [[exponent]].
Common uses
- List the first 10 Fibonacci numbers for homework
- Find F_20 without manual addition
- Compare Fibonacci growth to powers of 2
- Check sums of initial Fibonacci terms
Frequently asked questions
What are the first 10 Fibonacci numbers?
1, 1, 2, 3, 5, 8, 13, 21, 34, 55. Each term after the second adds the two previous terms.
What is F_20?
6,765. The sequence grows fast — F_30 is already 832,040.
Does the sequence always start with 1, 1?
This calculator uses F_1 = F_2 = 1. Some texts start 0, 1, 1 — check your textbook convention.
How does Fibonacci relate to the golden ratio?
The ratio F_{n+1}/F_n approaches φ ≈ 1.618 as n grows. Use the golden-ratio calculator for φ directly.