Fibonacci Calculator
The Fibonacci sequence starts with 0 and 1, and then each number is the sum of the two before it: 0, 1, 1, 2, 3, 5, 8, and so on. This finds the number at any position you choose.
- Free
- Works offline after your first visit
- Saves on this device
- No sign-up
- Updated
How it works
Each Fibonacci number is the previous one plus the one before that. Counting from 0, the first two numbers are 0 and 1.
This calculator uses a closed formula built on the golden ratio, about 1.618, so it does not add up every step. The result is rounded to the nearest whole number, which is exact for positions up to 70.
Worked example
The Fibonacci number at position 10 is 55, and the number after it is 89.
Questions
Why does the sequence start at 0?
That is the usual convention. Some books start at 1 instead, which shifts every position by one.
Why stop at position 70?
Past that the numbers get very large, and the rounding in this calculator is no longer exact.
Where does the sequence show up?
It comes up in counting problems, some plant patterns and many computer exercises.
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