HomeCalculatorsMathNumber Theory & Discrete MathFibonacci Calculator
Math calculator

Fibonacci Calculator

Fibonacci numbers F_n for n ≤ 1000. F_0=0, F_1=1. Same engine as Sequence. Exact BigInt. Runs locally.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Specification checked · 12/12 tests · Production surface contract 4/4 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
Model
F_n and the partial sum F_0+⋯+F_n.
Scope
F_0=0, F_1=1
Verification
Engine tested · 12/12 tests · Production surface contract 4/4 · Specification checked · v1.0.0
Named expert review
Optional · Not performed
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Specification basis
Evidence
4 golden · 2 boundary · 6 property · Production surface contract 4/4 · Artifact integrity PASS
Production
Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (1 capability; 163 remain CURRENT) @ 2026-09-19T00:00:17.039Z
Semantic contract
PASS

Formulas

Core equations used by this calculator.

RecurrenceF_n = F_{n−1} + F_{n−2}
Partial sumF_0+⋯+F_n = F_{n+2} − 1
iIntegers. Exact BigInt. n ≤ 1000. Not Pascal’s triangle. Not a closed Binet float.

How to use

1

Enter n

n=0 is allowed. F_0=0.

2

Read F_n

Linear recurrence lives on /calc/math/sequence.

Example calculations

Common configurations with formula and result.

ϟ

F_10

0,1,1,2,3,5,8,13,21,34,55

F_10
55
ϟ

F_0

Indexing

F_0
0

Fibonacci calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
F_0=0, F_1=1, F_n = F_{n-1}+F_{n-2}. This page is mode=fibonacci on the sequence engine. Linear recurrence with p=q=1, a0=0, a1=1 is the same sequence.
What it calculates
F_n and the partial sum F_0+⋯+F_n.
Inputs
  • n
Outputs
  • term
  • sum
  • prev
Formula
F_n = F_{n−1} + F_{n−2}
Assumptions
  • F_0=0, F_1=1
  • Integers
  • Not Pascal / Binet float
Units
  • dimensionless
Boundary conditions
  • n>1000 → VALUE_ABOVE_MAX
  • unknown mode → INVALID_MODE
Example
n=10 → 55
Validation cases

2 published on this page · 12/12 tests · Production surface contract 4/4 · View evidence

  • n=10 → 55
  • n=0 → 0
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Calculation version
1.0.0

Other calculators in this family: Arithmetic Sequence Calculator, Factorial Calculator, GCF Calculator, Geometric Sequence Calculator, LCM Calculator, Modular Inverse Calculator, Modulo Calculator, Permutation Combination Calculator . Explore all Number Theory & Discrete Math.

→ Arithmetic Sequence Calculator Nth term and partial sum of an integer arithmetic sequence. Same engine as Sequence. Not geometric. Runs locally. › → Factorial Calculator Calculate n! for integers 0 ≤ n ≤ 5000. Fast local exact integers with shareable, machine-readable results. › → GCF Calculator Find the GCF, GCD, or HCF of two or more integers. Exact BigInt Euclidean fold with factor and prime cross-checks. Free, no sign-up. › → Geometric Sequence Calculator Nth term and partial sum of an integer geometric sequence. Same engine as Sequence. Not arithmetic. Runs locally. › → LCM Calculator Find the LCM of two or more integers with exact arithmetic and independent verification. Free, no sign-up. › → Modular Inverse Calculator Modular inverse of a modulo m when gcd(a,m)=1. Same engine as Euclidean remainder. Not a second GCF page. Runs locally. › → Modulo Calculator Integer remainder with a = q·m + r and 0 ≤ r < |m|. Euclidean convention, not JavaScript truncated %. › → Permutation Combination Calculator Exact P(n,k) and C(n,k) for integers 0 ≤ k ≤ n ≤ 1000. Multiplicative BigInt, local-first. Not the factorial calculator. ›
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Frequently asked questions

Key distinctions behind the calculation.

Is this a second sequence solver?

No. It is mode=fibonacci on math.sequences.

Do you use Binet’s formula?

No. Exact iterative BigInt. Float64 Binet is out of scope.