🌀 Fibonacci Sequence Calculator
By ToolNimba Editorial Team · Updated 2026-06-19
Enter a whole number n from 1 to 1000 to list the first n Fibonacci numbers. The sequence starts 0, 1, 1, 2, 3, 5, ... and each term is the sum of the previous two.
This Fibonacci calculator lists the first n numbers in the Fibonacci sequence and tells you the nth term along with the running sum. Type how many terms you want and the result updates instantly. The sequence starts 0, 1, 1, 2, 3, 5, 8, ... where every new term is just the sum of the two before it. Because the tool uses BigInt arithmetic, even very large terms come out exact with no rounding.
What is the Fibonacci Calculator?
The Fibonacci sequence is one of the most famous patterns in mathematics. It begins with two seed values, 0 and 1, and from there each term is defined as the sum of the previous two: F(n) = F(n-1) + F(n-2). So after 0 and 1 you get 1 (0+1), then 2 (1+1), then 3 (1+2), then 5 (2+3), and the numbers grow steadily from there. The rule is simple, but the sequence shows up everywhere, from the branching of plants to the spiral of a shell to the way rabbits were modelled in the original 13th-century problem by Leonardo of Pisa, known as Fibonacci.
A small but important detail is where you start counting. This calculator uses the common convention F(1) = 0, F(2) = 1, F(3) = 1, F(4) = 2, and so on, so the "first n numbers" are the n terms beginning from 0. Some textbooks instead index from F(0) = 0, and a few drop the leading 0 entirely and start at 1, 1, 2. None of these are wrong, they are just different labelling choices, so always check which convention a source uses before comparing the nth term.
Fibonacci numbers grow exponentially, roughly multiplying by the golden ratio (about 1.618) at each step. That means they get large fast: the 100th term already has 21 digits, and ordinary floating-point numbers lose precision long before that. This calculator avoids the problem by using BigInt, an integer type with unlimited size, so the digits you see are exact rather than rounded. To keep the page responsive, n is capped at 1000, which still produces a 209-digit final term.
When to use it
- Generating the first n Fibonacci numbers for a homework problem, coding exercise or interview prep.
- Looking up a specific term, such as the 20th or 100th Fibonacci number, without computing it by hand.
- Checking the output of your own Fibonacci function against an exact reference, including for large n.
- Exploring how quickly the sequence grows and how it relates to the golden ratio.
How to use the Fibonacci Calculator
- Enter n, the number of terms you want to list (a whole number from 1 to 1000).
- Read off the nth Fibonacci number and the sum of the first n terms in the result boxes.
- Scroll the full list of the first n terms below, or use Copy list to grab them all.
- Try the quick presets (5, 10, 20, 50, 100 terms) to see the pattern at different scales.
Formula & method
Worked examples
List the first 10 Fibonacci numbers and find the 10th term.
- Start with the two seeds: F(1) = 0 and F(2) = 1.
- F(3) = 0 + 1 = 1
- F(4) = 1 + 1 = 2
- F(5) = 1 + 2 = 3, then 3 + 2 = 5, 5 + 3 = 8, 8 + 5 = 13, 13 + 8 = 21, 21 + 13 = 34
- The full list is 0, 1, 1, 2, 3, 5, 8, 13, 21, 34
- The 10th term is the last one in the list
Result: 10th term = 34 · sum of the first 10 terms = 88
Find the 100th Fibonacci number.
- Apply F(n) = F(n-1) + F(n-2) repeatedly from the seeds 0 and 1.
- The terms grow exponentially, roughly multiplying by 1.618 each step.
- By the 100th term the value has 21 digits.
- Floating-point numbers cannot hold this exactly, so BigInt is used.
Result: 100th term = 218,922,995,834,555,169,026 (21 digits)
The first 15 Fibonacci numbers (F(1) = 0 convention)
| Term (n) | Fibonacci number F(n) |
|---|---|
| 1 | 0 |
| 2 | 1 |
| 3 | 1 |
| 4 | 2 |
| 5 | 3 |
| 6 | 5 |
| 7 | 8 |
| 8 | 13 |
| 9 | 21 |
| 10 | 34 |
| 11 | 55 |
| 12 | 89 |
| 13 | 144 |
| 14 | 233 |
| 15 | 377 |
Common mistakes to avoid
- Assuming everyone starts the sequence the same way. Some sources start 0, 1, 1, 2, others start 1, 1, 2, 3 and drop the leading 0. That shifts every index by one, so the "8th Fibonacci number" can be 13 or 21 depending on the convention. Check the starting point before comparing.
- Confusing the term index with its value. The 5th term and the value 5 happen to coincide early on, but they are different things. The 7th term is 8, not 7. Read the position from the list, not from the number itself.
- Expecting floating-point code to stay exact. Computing Fibonacci with ordinary numbers in a spreadsheet or with floating-point variables drifts into rounding error well before the 80th term. Use integer or BigInt arithmetic for exact large terms, which is what this tool does.
- Forgetting the sequence grows very fast. Fibonacci numbers grow exponentially, not linearly. The 100th term already has 21 digits and the 1000th term has 209, so asking for a huge n returns enormous numbers, not a long but small list.
Glossary
- Fibonacci sequence
- The sequence 0, 1, 1, 2, 3, 5, 8, ... in which each term is the sum of the two terms before it.
- Term
- A single number in the sequence, identified by its position n (the 6th term is 5).
- nth Fibonacci number
- The value at position n in the sequence, written F(n).
- Golden ratio
- The constant phi ≈ 1.618 that the ratio of consecutive Fibonacci numbers approaches as the sequence grows.
- BigInt
- A whole-number type with unlimited size, used so large Fibonacci terms stay exact instead of being rounded.
Frequently asked questions
What is the Fibonacci sequence?
The Fibonacci sequence is a list of numbers that starts 0, 1, 1, 2, 3, 5, 8, 13, ... where each term after the first two is the sum of the previous two. It is named after Leonardo of Pisa (Fibonacci) and appears in many natural patterns.
How do I find the nth Fibonacci number?
Start with 0 and 1, then repeatedly add the last two terms until you reach position n. This calculator does it for you: enter n and it lists every term and highlights the nth one, computed exactly even for large n.
Does the Fibonacci sequence start at 0 or 1?
Both conventions exist. This tool starts at 0 (so F(1) = 0, F(2) = 1, F(3) = 1), which is common in computing. Some textbooks drop the leading 0 and start 1, 1, 2. The pattern is the same, only the indexing shifts.
Why use BigInt for Fibonacci numbers?
Fibonacci numbers grow exponentially, so they quickly exceed what ordinary floating-point numbers can hold exactly. The 100th term already has 21 digits. BigInt stores arbitrarily large whole numbers, so every digit shown here is exact rather than rounded.
What is the largest n this calculator allows?
n is capped at 1000 terms to keep the page responsive. The 1000th Fibonacci number has 209 digits, and the full list of 1000 exact terms is shown, all computed with BigInt arithmetic.
What is the connection between Fibonacci and the golden ratio?
As the sequence grows, the ratio of each term to the one before it gets closer and closer to the golden ratio, phi ≈ 1.618. This is why Fibonacci numbers multiply by roughly 1.618 at each step and grow exponentially.