Mathematics

Fibonacci Calculator

Calculate the exact Fibonacci number at index n, with F(0)=0 and F(1)=1.

01Input and settings

The calculation runs in your browser. You can use the tool without installing software.

02Result

Waiting for input
Waiting for input

Enter your values or load the example to see the result here.

About this tool: Fibonacci Calculator

Calculate the exact Fibonacci number at index n, with F(0)=0 and F(1)=1.

The sequence begins 0, 1, 1, 2, 3, 5, 8. Enter an index rather than a count of terms. Fast doubling and integer arithmetic calculate the exact value without recursively expanding every previous term, up to the displayed input limit.

How the calculation works

F₀ = 0; F₁ = 1; Fₙ = Fₙ₋₁ + Fₙ₋₂

Worked example

Index n (starts at 0)
10
F(10) = 55

Questions and answers

What does this tool do?

Calculate the exact Fibonacci number at index n, with F(0)=0 and F(1)=1. The sequence begins 0, 1, 1, 2, 3, 5, 8. Enter an index rather than a count of terms. Fast doubling and integer arithmetic calculate the exact value without recursively expanding every previous term, up to the displayed input limit.

What affects precision and input format?

These operations preserve integer or decimal precision with string and integer arithmetic. Input size is limited to keep the page responsive.

Where are the calculations performed?

The calculation runs in your browser. You can use the tool without installing software.

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