Mathematics · Algebra
Fibonacci Number Calculator
Calculate the nth Fibonacci number by recurrence.
Inputs and results stay in this browser. Change one value at a time to explore the relationship.
Calculation steps
- Begin F₀=0 and F₁=1.
- 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
- Functions and input-output rules
A function viewpoint helps you see how changing an input changes the Fibonacci number result.
Review this foundation about 5 min
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
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
- Begin with F0=0 and F1=1.
- Advance the pair (previous,current) n times.
- 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
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);}
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);}
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
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
Wolfram Language
ClearAll[mwCalculate];
mwCalculate[n_Integer?NonNegative] := Fibonacci[n];
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 chaptersCite 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 .