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Fibonacci Calculator

Calculate Fibonacci numbers and list the sequence.

How it is calculated

The sequence starts with F1 = 1 and F2 = 1, and every later term is the sum of the two before it: F(n) = F(n-1) + F(n-2). The tool builds the sequence term by term up to the n you enter, shows the n-th term as the value and lists all terms from F1 to Fn. Counting here begins at 1, so there is no F0 = 0 term. n must be a whole number from 1 to 90. The limit is there because larger terms no longer fit in a 64-bit integer, so exact results stop at 90. Decimals, zero and negative numbers return no result.

Worked example

Enter n = 10. Starting from 1, 1, each new term adds the previous two: 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8, 5 + 8 = 13, 8 + 13 = 21, 13 + 21 = 34, 21 + 34 = 55. The sequence is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and the 10th term, the value shown, is 55.

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Common mistakes

  • Expecting the sequence to start at 0. Here F1 = 1, so the 10th term is 55; sources that count F0 = 0 as the first term differ by one position.
  • Entering a decimal such as 7.5 or a value above 90, which returns no result.
  • Confusing the position n with the value. F(10) is 55, not 10.
  • Expecting the golden ratio from a single term. It appears only as the ratio of two consecutive large terms.

About this calculator

This tool calculates the nth term of the Fibonacci sequence and lists the full sequence up to that term, where each number is the sum of the two numbers before it (0, 1, 1, 2, 3, 5, 8, 13, 21...), starting from the first two seed values. Because each term depends on the ones before it, computing a specific term far out in the sequence by hand quickly becomes tedious, which is exactly the kind of repetitive calculation this tool skips straight to.

It is used by students learning recursion, sequences and series in math or computer science courses, and by programmers testing recursive versus iterative algorithm implementations, since the Fibonacci sequence is one of the most common examples used to teach and benchmark recursion. It also shows up in biology and art discussions, where Fibonacci numbers and the related golden ratio are used to describe patterns like branching in plants, shell spirals and certain aesthetic proportions.

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