Math

Fibonacci Calculator

Fibonacci terms and the golden ratio.

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Results update instantly as you type — no submit needed.

Results
F(20)
6,765
Sum of first n terms
17,710
Ratio to previous term
1.61803396
Golden ratio
1.61803399
Sequence
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377

Quick answer

Each Fibonacci number is the sum of the previous two, and consecutive ratios converge to the golden ratio 1.618.

F(n) = F(n−1) + F(n−2)

How to use the Fibonacci Calculator

  1. 1Enter which Fibonacci term you want.
  2. 2Read the value and running sum.
  3. 3Compare the ratio to the golden ratio.

Frequently asked questions

Where does Fibonacci appear in nature?

Sunflower spirals, pine cones and branching patterns approximate it.

Does it start at 0 or 1?

This tool uses F(0)=0, F(1)=1, the standard mathematical convention.