Nth Fibonacci Number Calculator

How it is calculated

The Fibonacci sequence starts 1, 1, 2, 3, 5, 8, … and each term is the sum of the two before it: F(n) = F(n−1) + F(n−2), with F(1) = F(2) = 1. This tool counts from 1, so n = 1 gives 1 and n = 10 gives 55; there is no F(0) input. The engine does not use a closed-form formula: it starts with 0 and 1 and adds step by step n − 1 times, so each answer is exact for the position you ask. Accepted n is a whole number from 1 to 90; decimals are cut to a whole number and anything outside the range returns nothing. Numbers beyond about n = 78 go through floating-point arithmetic and may lose their last digits, so treat very large results as approximate.

Common mistakes

• Counting from F(0) = 0. Here the first term is 1 and n = 10 gives 55. A source that starts with a leading 0 treats the same number as one position later.
• Assuming the answer comes from Binet's formula with a rounded golden ratio. The tool adds the terms, which stays exact for the allowed range.
• Entering n above 90 or a negative number and expecting a result; the tool returns nothing for values outside 1 to 90.
• Confusing the position with the value: n = 20 asks for the 20th number in the sequence, not for a number below 20.