Fibonacci Sequence Generator
The Fibonacci sequence starts with 0 and 1, and each following number is the sum of the two before it: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on. Enter how many terms you want and this tool lists them all, reports the last term, the sum of every term in the list, and the ratio of the final two terms, which converges toward the golden ratio φ ≈ 1.618034. Every value is computed with arbitrary-precision big integers, so even the hundredth or thousandth term is exact rather than rounded. Everything runs locally in your browser — nothing is uploaded.
How to use
- Enter the number of terms you want to generate (1 to 1000).
- Read the last (Nth) term, the sum of all listed terms and the golden-ratio approximation.
- Scroll the full sequence and copy it with one click.
- Try 10 terms (0, 1, 1, 2, 3, 5, 8, 13, 21, 34 — sum 88) to check the output.
Frequently asked questions
- Where does the sequence start?
- This generator uses the standard convention F(0) = 0, F(1) = 1, so the first ten terms are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34. The 'last term' stat is the final number in the list you generated.
- Are large terms exact?
- Yes. Calculations use JavaScript big integers, so terms with hundreds of digits are computed exactly with no floating-point rounding. For example F(100) — which appears as the 101st value because the list starts at F(0) — is exactly 354224848179261915075.
- What is the golden-ratio number?
- It is the ratio of the last term to the one before it. As the sequence grows this ratio converges to the golden ratio φ ≈ 1.6180339887, which is why Fibonacci numbers and φ are so closely linked.
Related tools
Random Number Generator
Generate cryptographically random numbers in any range — with or without duplicates, optionally sorted.
Lottery Number Generator
Generate random tickets for 8 popular lotteries (Powerball, EuroMillions, Lotto 6/45, Loto 6, 双色球…) — uses crypto-secure RNG.
Add Page Numbers to a PDF
Number the pages of a PDF — position, style, starting number and whether to skip the cover — and download it. Nothing is uploaded.
Collatz Conjecture (3n+1) Sequence
Generate the Collatz sequence for any positive integer — halve when even, triple-plus-one when odd — and see the number of steps, the peak value reached and the full path to 1.
Coffee Brew Ratio Calculator
Pour-over, French press, AeroPress, espresso, cold brew — calculate coffee and water amounts from any ratio with method-specific defaults.
Baker's Percentage Calculator
Scale bread recipes by baker's percentage — enter your flour weight and each ingredient as a percentage of flour to get exact gram weights, total dough weight and hydration.