About the Fibonacci Calculator
The Fibonacci sequence starts 0, 1, 1, 2, 3, 5, 8, and every new term is the sum of the two before it. This calculator has three modes. Choose the n-th number to get F(n) exactly, even for positions in the thousands. Choose a list to see the first n terms ready to copy. Choose the checker to test whether a number appears in the sequence and learn its position. All results are exact whole numbers, calculated with big-number arithmetic in your browser.
Updated October 2026
How to use the Fibonacci Calculator
- 1Pick what you want: the n-th number, a list of the first n numbers, or a Fibonacci check.
- 2Type the position, the length of the list or the number you want to test.
- 3Read the answer; very long values show a short form plus all digits below.
- 4Use the ratio row to see how neighbouring terms approach the golden ratio.
- 5Press Copy result to copy the number or the whole list.
Where Fibonacci numbers appear
Fibonacci numbers show up in counting problems, such as the number of ways to climb stairs taking one or two steps at a time. They appear in the branching of some plants, the arrangement of seeds and petals, and in computer science, where they are used for search techniques and as a standard example of recursion. Popular claims about them in art and nature are often exaggerated, but the maths is real.
The first terms
- F(0) to F(10): 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55
- F(20) = 6,765
- F(30) = 832,040
- F(50) = 12,586,269,025
- F(100) = 354,224,848,179,261,931,521
Using the three modes
Use the n-th number mode when you need one value, for example for homework or to test a program. Use the list mode when you need the sequence up to a point; copy it straight into a spreadsheet. Use the checker when you meet a number and want to know whether it belongs, which is a common puzzle question. All three use exact whole numbers, so nothing is rounded.
Related tools
For other sequences and counting problems, the Factorial Calculator, the Permutation and Combination Calculator and the Prime Number Calculator are useful. The Ratio Calculator helps if you want to explore ratios like the golden ratio yourself, and the Scientific Notation Converter makes huge Fibonacci numbers easier to read.
Features
- Exact n-th Fibonacci number up to position 20,000
- List of the first 1 to 500 terms
- Fibonacci number checker with the position
- Golden-ratio approximation from consecutive terms
- Copy the list as comma-separated text
- No rounding, however large
- Runs in your browser
Frequently asked questions
What is the Fibonacci sequence?
It is the list 0, 1, 1, 2, 3, 5, 8, 13, 21 and so on, where each number is the sum of the two before it. It is named after the Italian mathematician Leonardo of Pisa, known as Fibonacci, who described it in a book published in 1202.
Does the sequence start at 0 or 1?
Both conventions are used. This calculator starts at F(0) = 0 and F(1) = 1, which is the standard in mathematics. If your textbook starts at F(1) = 1 and F(2) = 1, the values are the same; only the numbering of position 0 differs.
How do I find the 100th Fibonacci number?
Choose the n-th number mode and type 100. The calculator returns F(100) = 354224848179261931521 exactly. Adding the two previous terms by hand is slow and error-prone, and decimal calculators lose digits beyond about F(78).
How can I tell if a number is a Fibonacci number?
A positive whole number x is a Fibonacci number exactly when 5x² + 4 or 5x² − 4 is a perfect square. The checker applies this test with big numbers and, if the answer is yes, also shows which position the number holds.
What does the Fibonacci sequence have to do with the golden ratio?
Divide any term by the one before it and the result gets closer to 1.6180339887, the golden ratio. The ratio row shows this for the position you choose; by F(30) it matches the golden ratio to about eight decimal places.
Is there a limit to the position I can enter?
You can calculate up to position 20,000 for a single number, which has over 4,000 digits, and list up to 500 terms. Beyond that the page would be slow without being useful. For the checker, numbers up to 4,000 digits are accepted.