Fibonacci Calculator
Find the nth Fibonacci number with every digit, list the first terms, or test whether a number is a Fibonacci number and where it comes.
The sequence starts 0, 1, 1, 2, 3, 5, 8, so the 0th term is 0 and the 1st is 1.
Worked examples
A large term
n = 100
354,224,848,179,261,915,075
21 digits.
Checking a number
144
Yes, number 12
5 × 144² + 4 = 103,684, which is 322².
About Fibonacci Calculator
The Fibonacci sequence begins with 0 and 1, and each number after that is the sum of the two before it: 0, 1, 1, 2, 3, 5, 8, 13, 21 and on. It turns up in the spirals of shells and pine cones, in how some plants arrange their leaves, and in computer algorithms. The ratio of one term to the one before gets closer and closer to the golden ratio, about 1.618.
The numbers grow fast. The 100th Fibonacci number is 354,224,848,179,261,915,075, and the 1,000th has 209 digits. The page uses a fast method that needs only a handful of steps, with whole-number arithmetic, so even the 100,000th term is found in full, and you can copy all its digits. You can also list the first terms, or test whether a number belongs to the sequence. The test uses the fact that a number is a Fibonacci number only when 5n² + 4 or 5n² - 4 is a perfect square, and the page then tells you its position.
How to use Fibonacci Calculator
- Choose to find the nth number, list the first n numbers, or check a number.
- Enter n, or the number to check.
- Read the result and its number of digits, or the list.
- Use the Copy button to take a long answer elsewhere.
Common uses
- Maths homework and sequence puzzles
- Checking a Fibonacci number from a program
- Exploring the golden ratio
- Seeing how fast exponential growth becomes large
Frequently asked questions
Where does the sequence start?
Here it starts with the 0th term as 0 and the 1st term as 1. Some sources start with 1, 1, so check how yours counts.
What is the 10th Fibonacci number?
It is 55, counting the 0th term as 0: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55.
What is the link to the golden ratio?
Dividing a term by the one before it gets closer to 1.6180339887 as you go along. The page shows this ratio for the term you find.
How does the checker work?
A number n is in the sequence only if 5n² + 4 or 5n² - 4 is a perfect square. The page tests that and then finds the position.
How large an n can I use?
Up to 100,000 for a single term, and up to 1,000 for a list.