Fibonacci Calculator

Solve Fₙ = Fₙ₋₁ + Fₙ₋₂ step by step — free fibonacci calculator with worked examples, real-world defaults and instant answers.

Fₙ = Fₙ₋₁ + Fₙ₋₂

Index n (1–78)

F(20)6,765

Ratio Fₙ/Fₙ₋₁1.618034

Golden ratio φ1.6180339887…

1
Start 0, 1 and keep adding the last two:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …
2
The 20-th Fibonacci number:
F(20) = 6,765
3
Consecutive ratios close in on the golden ratio:
F(20)/F(19) = 1.618034 → φ = (1+√5)/2 ≈ 1.618034

Fibonacci numbers count rabbit generations, sunflower spirals and staircase climbs — and their ratios converge to the golden ratio φ, which gives Binet's closed formula Fₙ = (φⁿ − ψⁿ)/√5. Indexing here: F(1) = 1, F(2) = 1 (F(0) = 0).

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Fibonacci — nth term plus the golden-ratio convergence.

About Fibonacci Calculator

The Fibonacci Calculator solves Fₙ = Fₙ₋₁ + Fₙ₋₂ for you with the full working shown — every substitution, every unit, every step, exactly the way a good teacher writes it on the board. Fibonacci numbers count rabbit generations, sunflower spirals and staircase climbs — and their ratios converge to the golden ratio φ, which gives Binet's closed formula Fₙ = (φⁿ − ψⁿ)/√5.

How to use Fibonacci Calculator

1Enter your known values in the input fields (sensible real-world defaults are pre-filled).
2The tool substitutes them into Fₙ = Fₙ₋₁ + Fₙ₋₂ and recomputes live.
3Read the answer in the result box, then expand the step-by-step solution to see the full working.
4Copy the method into your notebook, or change inputs to explore how the result behaves.

Why use Fibonacci Calculator?

✓Solves Fₙ = Fₙ₋₁ + Fₙ₋₂ instantly as you type — no submit button, no waiting
✓Step-by-step solution shown for every calculation, not just the final answer
✓Realistic example values pre-loaded so you can see a worked example immediately
✓100% free, no sign-up, runs entirely in your browser — your numbers never leave your device
✓Mobile-friendly and fast enough to use mid-homework or mid-lesson

Frequently asked questions

What formula does the Fibonacci Calculator use?+

It uses Fₙ = Fₙ₋₁ + Fₙ₋₂. The steps section shows the formula with your actual numbers substituted, so you can follow (and verify) every stage of the calculation rather than trusting a black box.

What should I keep in mind when using this calculator?+

Is the Fibonacci Calculator free to use?+

Completely free, with no sign-up or limits. All computation happens client-side in your browser, so it is fast, private, and works even on slow connections once the page has loaded.

Can I use this for homework, teaching or exam prep?+

That is exactly what it is built for. The step-by-step working mirrors how solutions are presented in class, so you can check homework, build worked examples for teaching, or practise method recall before exams.

Embed Fibonacci Calculator on your website

Want Fibonacci Calculatoron your own site? Paste this snippet into any HTML page — it's free, with no API key or sign-up. The tool loads in an iframe and keeps working exactly as it does here.

Embed code

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