Fibonacci Calculator

Where does the sequence start?

With F(1) = 1 and F(2) = 1, so the first ten terms are 1, 1, 2, 3, 5, 8, 13, 21, 34, 55. Many textbooks begin at F(0) = 0, F(1) = 1. From F(1) onward the terms are identical (F(10) is 55 either way); this page simply has no 0 term.

What is the maximum number of terms?

Thirty. If you enter a larger N, the calculator silently uses 30 and prints the first 30 numbers, ending at F(30) = 832040. The check field is a separate input and can be much larger.

What happens with N below 1 or a decimal?

N is rounded down to a whole number. 7.9 becomes 7. Anything that rounds down to less than 1, including 0, negatives and a cleared field, returns the error "N must be at least 1".

Is 0 a Fibonacci number according to the checker?

The checker answers No for 0 and for negative numbers, because this tool’s sequence starts at 1. Many references do count 0 as F(0), so you may see a different answer elsewhere. Only whole numbers of 1 or more can return Yes; 1.5, for example, returns No.

How does the Fibonacci membership check work, and is it reliable for big values?

It steps through the sequence until it reaches or passes your number and compares for equality, which is exact for every integer up to JavaScript’s safe integer limit of 9,007,199,254,740,991. Above that limit the result line says the value is too large to check exactly instead of guessing.

Why is the ratio line not exactly the golden ratio?

The line shows F(N) ÷ F(N−1) for the number of terms you asked for, which only approaches φ = 1.618034 as N grows. At N = 10 it is 1.617647, and at N = 30 it equals 1.618034 to six decimals. At N = 2 it is 1.000000, and at N = 1 it shows N/A because there is no previous term.

Does it show the nth term without listing all earlier ones?

It always lists the terms up to N and also prints F(N) on its own line. Use N = 30 to get F(30). It cannot jump to F(100) or beyond because of the 30-term cap.