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Fibonacci Calculator: Nth Number, Sequence and Check

This free Fibonacci calculator finds the nth Fibonacci number exactly, lists the first n terms of the sequence, or checks whether a number is a Fibonacci number.

By Debmedia Technologies LLP · Kolkata, India · Updated

What Is It and When Do You Need It?

The Fibonacci sequence adds the last two numbers to make the next one. It shows up in plant growth, spirals, art, trading charts and computer science exercises. Doing it by hand is easy for ten terms and impossible for the thousandth, which has over 200 digits.

This tool gives exact answers for any term up to the 10,000th and tests whether a number is in the sequence.

How to Use This Tool

  1. Choose nth number, list, or check.
  2. Enter n, or the number to test.
  3. Press Calculate.
  4. Copy the exact value or list from the result box.

How the Calculation Works

The terms are built by repeated addition with exact integers: F(0) = 0, F(1) = 1, F(n) = F(n−1) + F(n−2). For the check, a number x is Fibonacci when 5x² + 4 or 5x² − 4 is a perfect square.

The tool also prints the ratio F(n) ÷ F(n−1) so you can watch it settle near the golden ratio.

Worked Example

F(10) = 55 and F(20) = 6,765. The list of the first 10 terms is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. Is 144 Fibonacci? Yes: 5 × 144² − 4 = 103,676 = 322². Is 100? No.

Common Uses

  • Maths and coding exercises.
  • Studying the golden ratio.
  • Designing layouts and spirals.
  • Checking sequences in puzzles.

Tips and Common Mistakes

  • Some books start the sequence at 1, 1. This tool starts at F(0) = 0.
  • Every third Fibonacci number is even.
  • Consecutive Fibonacci numbers are always coprime.

Next, you may need the prime number checker, permutation and combination calculator, arithmetic and geometric series calculator, exponent and root calculator.

Everything runs in your browser. Nothing you type is uploaded, stored or sent to any outside service.

Frequently Asked Questions

It starts 0, 1 and each next number is the sum of the previous two: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 and so on.
The ratio of one Fibonacci number to the one before it approaches 1.6180339887, the golden ratio, as the numbers grow.
The tool calculates up to the 10,000th term exactly using big integers. Lists are limited to the first 1,000 terms.
A number x is Fibonacci if 5x² + 4 or 5x² − 4 is a perfect square. The tool uses exactly this test.

Disclaimer: results are calculated in your browser from the numbers you enter. Check important results before you rely on them for money, health, safety or legal decisions.