Fibonacci Calculator: Your Simple Number Companion

Formula: F(n) = F(n-1) + F(n-2), where F(0) = 0 and F(1) = 1

Note: Maximum position is 78 to prevent number overflow. The ratio between consecutive numbers approaches the Golden Ratio (φ ≈ 1.618034)

This fibonacci calculator computes numbers in the Fibonacci sequence. Use it to find specific Fibonacci numbers and view related details.

What It Does

The tool computes the Fibonacci number at a position you specify. It also shows the full sequence up to that number. For positions 2 and above, it calculates the ratio between the last two numbers.

How to Use This Tool

  1. Type a number between 0 and 78 into the input box. The number represents the position in the Fibonacci sequence.
  2. Click the calculate button to run the calculation.
  3. The result displays on the screen.

Interpreting the Output

You see three main outputs. The first output shows the Fibonacci number for your entry. The second shows the complete Fibonacci sequence up to your entry. The third output, when applicable, displays the ratio between the last two sequence values. This ratio is compared to the Golden Ratio.

Limitations and Special Notes

The calculator only accepts numbers from 0 to 78. This range prevents calculation errors due to number limits in JavaScript. For numbers outside this range, the tool shows a warning message.

Examples and Use Cases

For example, if you enter 5, the tool outputs that the 5th Fibonacci number is 5. The full sequence will list F(0) = 0, F(1) = 1 up to F(5) = 5. This tool is useful for students and anyone interested in mathematics.

The calculator helps when you need clear results. It provides instant results and shows the connection between consecutive Fibonacci numbers through the ratio displayed.

Try the calculator next time you work on math problems or explore number sequences. It offers a straightforward way to learn more about Fibonacci numbers.