Find an exact Fibonacci term using F(0) = 0, F(1) = 1, and the sum-of-two rule.
F(10) = 55. Each new term is the sum of the two before it: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55.
F(9) + F(8) = 34 + 21 = 55.
Embed Fibonacci Calculator
Copy this iframe code into a page that permits embeds.
How to Use the Fibonacci Calculator
Enter the term index n. The calculator returns the exact value of F(n), the previous term when available, and the next term. It also shows a short preview of the sequence through the selected index.
This page uses the F(0) = 0 convention. Some textbooks list 1, 1 as their first two terms, so check the indexing before comparing answers.
The Fibonacci Recurrence
The sequence starts at 0 and 1. Add the two preceding values to get each later value. This is a recurrence: the current term depends on earlier terms rather than an independent multiplication.
Worked Example: The 10th Index
Starting with F(0) = 0 and F(1) = 1, continue adding adjacent terms. F(8) = 21 and F(9) = 34, so F(10) = 21 + 34 = 55. If a question says “tenth term” instead of F(10), first check whether its list begins at index 0 or 1.
Useful Fibonacci Patterns
Every third Fibonacci term is even: F(3) = 2, F(6) = 8, and F(9) = 34. Adjacent terms have no common factor greater than 1. These patterns can help check a result, but the recurrence gives the exact value.
Common Fibonacci Mistakes
Does the sequence start 0, 1 or 1, 1?
Both lists occur because some authors start at F(0) and others list from F(1). This calculator defines F(0) = 0 and F(1) = 1.
Does the index equal the term value?
No. For example, F(10) = 55.
Are large terms rounded?
No. The tool uses exact whole-number arithmetic through F(1000).
Fibonacci Calculator FAQs
What is F(0)?
F(0) = 0 in this calculator.
What is F(10)?
F(10) = 55.
How do you find the next Fibonacci term?
Add the two immediately preceding terms.
Editorial review
SolverCalc names Prof. Dr. Khalil Mudassar as its educational reviewer. The recurrence and indexing convention can be checked against the references below.
Sources
Disclaimer
For educational use. Check your class or textbook convention when the problem defines a different range, sequence index, or notation.