Fibonacci Calculator

The Fibonacci sequence starts at F(0) = 0 and F(1) = 1, and every later term is the sum of the two before it, so this calculator gets F(n) by walking that addition forward one step at a time from the start rather than by any closed-form shortcut. Position 10, the default, takes nine additions to reach 55; position 78, the field's upper limit, still runs the identical loop just 78 times, which is why the ceiling exists at all — 78 is roughly where the running total approaches the largest integer JavaScript can represent exactly, and one more step would start losing precision silently rather than throwing an error. Alongside F(n) the tool reports F(n) divided by F(n-1), the ratio of consecutive terms, which is a genuinely famous fact rather than an arbitrary extra output: as n grows, that ratio settles in on the golden ratio, roughly 1.618, and by n in the twenties the calculator's own rounding to five decimal places can no longer tell the ratio apart from that limiting value.

Entering a non-whole number like 7.8 is accepted and simply floored to 7 before the loop begins, so the position field behaves like an integer selector even though nothing in the input configuration enforces that directly. What this tool does not do is compute any Fibonacci number beyond the 78-position cutoff, and it does not offer the closed-form Binet formula as an alternative computation path even though that formula exists and would reach the same answer without iterating.