Fibonacci Calculator
Fibonacci terms and the golden ratio.
Enter your values
ⓘ Live results
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
- 1Enter which Fibonacci term you want.
- 2Read the value and running sum.
- 3Compare the ratio to the golden ratio.
Worked example
Using the values the calculator loads with:
Inputs
- Term number n20
Results
- F(20)6,765
- Sum of first n terms17,710
- Ratio to previous term1.61803396
- Golden ratio1.61803399
- Sequence0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377
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.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.