Fibonacci Calculator
Fibonacci terms and the golden ratio.
Enter your values
Enter the term number n you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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)
At a glance
| What it does | Fibonacci terms and the golden ratio. |
|---|---|
| Category | Math |
| Inputs needed | Term number n |
| Main output | F(20) |
| Formula | F(n) = F(n−1) + F(n−2) |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Term number n
- Enter the term number n you are working with.
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.
What do I need to enter into the Fibonacci Calculator?
Just 1 value: term number n. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Fibonacci Calculator work out the answer?
Each Fibonacci number is the sum of the previous two, and consecutive ratios converge to the golden ratio 1.618. It applies the formula F(n) = F(n−1) + F(n−2) and shows the working so you can check each step by hand.
Is the Fibonacci Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.