Mathematics · Algebra

Fibonacci Number Calculator

Calculate the nth Fibonacci number by recurrence.

Runs locally
Your numbers

Inputs and results stay in this browser. Change one value at a time to explore the relationship.

Your inputCalculatedPassed forward in chains
Fibonacci number Fₙ55
Next number89

Calculation steps

  1. Begin F₀=0 and F₁=1.
  2. Repeat the recurrence 10 times to obtain F_10=55.

Understand Fibonacci number

One idea, three depths

Choose how deeply to explain Fibonacci number

Calculate the nth Fibonacci number by recurrence.

Age 5Explain it to a 5-year-oldStart with a picture

Imagine using Fibonacci number to answer this question: calculate the nth fibonacci number by recurrence? Enter Index n; the calculator shows Fibonacci number Fₙ. For example: F₁₀=55. The answer tells you Fibonacci number Fₙ.

Age 15Explain it to a 15-year-oldConnect it to the formula

Each term adds the preceding two, beginning with F₀=0 and F₁=1. The rule is Fₙ=Fₙ₋₁+Fₙ₋₂. Its input values are Index n, and the main result is Fibonacci number Fₙ. For example: F₁₀=55.

CollegeExplain it at college levelState the model precisely

This calculator evaluates the stated fibonacci number relation over the valid integer domain stated below. The implemented relation is Fₙ=Fₙ₋₁+Fₙ₋₂, evaluated from Index n to produce Fibonacci number Fₙ. Each term adds the preceding two, beginning with F₀=0 and F₁=1. This calculator indexes the sequence from F₀=0.

Inputs and valid domain

  • Index n must be an integer, at least 0, at most 78.

Important boundary: This calculator indexes the sequence from F₀=0.

The formula

Fₙ=Fₙ₋₁+Fₙ₋₂

How the calculator works through it

It substitutes Index n into the formula and exposes every numerical step above. The main output is Fibonacci number Fₙ, accompanied by Next number.

Read the result correctly

The Fibonacci number Fₙ is the direct answer to “calculate the nth fibonacci number by recurrence.” Read it with the units shown beside the inputs; a sign, angle, percentage or rate changes what the number means.

A worked check

F₁₀=55.

Where this model stops being reliable

This calculator indexes the sequence from F₀=0.

Learn it by changing one value

Begin with the worked example, then change one value while keeping the others fixed. Compare the new result and calculation steps to identify which part of the formula changed.

Dictionary terms behind this calculator

Before studying the codeWhat you should know firstUse the calculator immediately, or check the foundations before reading the implementation.

These foundations help you understand why Fibonacci number works. They never block the calculator, and “optional” means useful context rather than a hidden requirement.

Hard requirements

  • Reading formulas and substituting values

    Fibonacci number uses Fₙ=Fₙ₋₁+Fₙ₋₂. You need to recognise what each side represents before substituting the stated inputs or rearranging the relationship.

    Review this foundation about 4 min

Strong support

Optional enrichment

  • Powers and exponents

    Powers are not required for every Fibonacci number calculation, but they make related algebraic forms and code easier to read.

    Review this foundation about 4 min
Learn the missing foundationsI already know these — show the code

Mathematics → algorithm → program

Implement this calculation in code

These are direct reference implementations of the calculator's principal relationship and first output. They run locally and include a small known-answer check where the language supports it.

Algorithm

  1. Begin with F0=0 and F1=1.
  2. Advance the pair (previous,current) n times.
  3. Return the previous value.
Python
            def fibonacci(n: int) -> int:
    previous, current = 0, 1
    for _ in range(n): previous, current = current, previous + current
    return previous
assert fibonacci(10) == 55
          
Current calculator valuesUpdates when you change an input above.
              
            
C
            #include <assert.h>
#include <stdint.h>
uint64_t fibonacci(uint64_t n){uint64_t p=0,q=1;while(n--){uint64_t t=p+q;p=q;q=t;}return p;}
int main(void){assert(fibonacci(10)==55);}
          
Current calculator valuesUpdates when you change an input above.
              
            
C++
            #include <cassert>
#include <cstdint>
std::uint64_t fibonacci(std::uint64_t n){std::uint64_t p=0,q=1;while(n--){auto t=p+q;p=q;q=t;}return p;}
int main(){assert(fibonacci(10)==55);}
          
Current calculator valuesUpdates when you change an input above.
              
            
Linux x86-64 assembly

x86-64 NASM · System V ABI · Linux · integer arguments in rdi, rsi and rdx

            ; uint64_t fibonacci(uint64_t n)
global fibonacci
section .text
fibonacci:
    xor eax, eax
    mov rdx, 1
.loop:
    test rdi, rdi
    jz .done
    lea rcx, [rax+rdx]
    mov rax, rdx
    mov rdx, rcx
    dec rdi
    jmp .loop
.done:
    ret
          
Current calculator valuesUpdates when you change an input above.
              
            
MATLAB
            function result = fibonacci(n)
    n = round(n); a = 0; b = 1;
    for k = 1:n, next = a + b; a = b; b = next; end
    result = a;
end
          
Current calculator valuesUpdates when you change an input above.
              
            
Wolfram Language
            ClearAll[mwCalculate];
mwCalculate[n_Integer?NonNegative] := Fibonacci[n];
          
Current calculator valuesUpdates when you change an input above.
              
            

Continue in mathematical software

The downloaded file includes your current inputs and first calculated result. It is created locally.

Floating-point answers can differ slightly by language, compiler and processor. Compare within a suitable tolerance rather than assuming every decimal representation will be identical.

Supporting sourcesAcademic referencesPrimary standards, textbooks and complete citations

Standards, reading and academic references

Use the calculator as the worked interaction, then consult the primary standards and academic textbooks listed below. MW SysArc links to the original sources; the explanation on this page is original and does not reproduce them.

Algebra and Trigonometry 2e

Read the related free OpenStax mathematics chapters
Cite this book
APA 7
Abramson, J. (2021). Algebra and trigonometry 2e. OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites
MLA 9
Abramson, Jay. Algebra and Trigonometry 2e. OpenStax, 2021, https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.
Chicago author-date
Abramson, Jay. 2021. Algebra and Trigonometry 2e. Houston, TX: OpenStax. https://openstax.org/books/algebra-and-trigonometry-2e/pages/1-introduction-to-prerequisites.

OpenStax entries are free to read online. Follow the licence shown on each linked source before redistributing or adapting its content.

Reuse the page responsiblyCite this pageAPA, MLA, Chicago, Harvard, BibTeX and RIS

These formats cite this calculator page itself. They are separate from the academic references above, which support the mathematical method and terminology.

APA 7

MW SysArc. (2026, July 21). Fibonacci Number Calculator. MW SysArc Tools. https://math.mwsysarc.com/algebra/fibonacci-number

MLA 9

MW SysArc. “Fibonacci Number Calculator.” MW SysArc Tools, 21 July 2026, https://math.mwsysarc.com/algebra/fibonacci-number. Accessed 31 Aug. 2026.

Chicago 17

MW SysArc. “Fibonacci Number Calculator.” MW SysArc Tools. Published July 21, 2026. Accessed August 31, 2026. https://math.mwsysarc.com/algebra/fibonacci-number.

Harvard

MW SysArc (2026) ‘Fibonacci Number Calculator’, MW SysArc Tools. Published 21 July 2026. Available at: https://math.mwsysarc.com/algebra/fibonacci-number (Accessed: 31 August 2026).

BibTeX and RIS records

BibTeX

@misc{mwsysarc_fibonacci_number_2026,
  author = {{MW SysArc}},
  title = {Fibonacci Number Calculator},
  howpublished = {MW SysArc Tools},
  year = {2026},
  url = {https://math.mwsysarc.com/algebra/fibonacci-number},
  note = {Published July 21, 2026; accessed August 31, 2026}
}

RIS

TY  - ELEC
AU  - MW SysArc
TI  - Fibonacci Number Calculator
T2  - MW SysArc Tools
PY  - 2026
DA  - 2026-07-21
Y2  - 2026-08-31
UR  - https://math.mwsysarc.com/algebra/fibonacci-number
N1  - Published July 21, 2026
ER  -

Clear answers

Frequently asked questions

What does the Fibonacci number do?

Calculate the nth Fibonacci number by recurrence.

How does the Fibonacci number work?

The calculator applies Fₙ=Fₙ₋₁+Fₙ₋₂. Each term adds the preceding two, beginning with F₀=0 and F₁=1.

What can I learn from the Fibonacci number?

It connects the mathematical rule to your chosen numbers and shows each calculation step. Change one input at a time to see how the result responds.

Does MW SysArc receive or store what I enter?

No. The calculation runs locally in your browser. MW SysArc does not receive or store your calculation inputs.

How should I use the result?

Use the steps to understand the method, then verify important school or professional work using the notation and rounding rules required in your setting.

Last reviewed . Calculations tested .

MW SysArc Certified