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 CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance · all published modes
Input interpretation
Enter values to calculate.
Result
—
Verified scope
all published modes
Assurance
Core
Declared partition coverage
PASS · 5/5 declared partitions (arithmetic, geometric, fibonacci, linear-recurrence, invalid-domain) · Matrix
Known limitations
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
F_n and the partial sum F_0+⋯+F_n, with an engine-linked stem figure of F_k through n.
Scope
The Result Card includes an engine-linked stem figure of F_k (marker is published term; at most 16 indices). Same iterative recurrence as REST/MCP. Terms array is not a REST field. Huge BigInt terms omit the figure.
Verification
Engine tested · Specification checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Core assurance · all published modes· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed · Evidence 2026-09-22.discrete-algebra-cvp
Verification revision
2026-09-22.discrete-algebra-cvp · 3/3 property · digest fe9aed69431a
Legacy regression
12/12 tests · Production surface contract 6/6
Trust layers
Verification VERIFIED · Production CURRENT · Overall CVP state: VERIFIED under CVP 1.0.0-proposed
Reference
O1 model · O2 expected_values · O2 numerical_behavior
Interfaces
PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
Supplemental domain review
Not performed
Named expert review
Not performed
CVP suite
5/5 golden · 3/3 CVP boundary · 6/6 invalid · 3/3 property · 4/4 cross-interface · 1/1 cross-calculator · 6/6 CVP contract · Manifest
Specification basis
  • ISO 80000-2:2019 Quantities and units — Mathematics
Specification basis
Evidence
4 legacy golden · 2 legacy boundary · legacy regression suite · 5/5 oracle-backed golden · 6/6 invalid · Artifact integrity PASS
This calculator CURRENT · Public schema 1.0.0 matches · Semantic contract ✓ · Production attested · Public/cache ✓ · Origin ✓
Semantic contract
PASS
Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

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 = 0 is allowed. Maximum 1000. Iterative BigInt, not a closed Binet float.

How to use

1

Enter n

n=0 is allowed. F_0=0.

2

Read F_n

The figure shows a stem plot of F_k through 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, with an engine-linked stem figure of F_k through n.
Inputs
  • n
Outputs
  • term
  • sum
  • prev
Formula
F_n = F_{n−1} + F_{n−2}
Assumptions
  • The Result Card includes an engine-linked stem figure of F_k (marker is published term; at most 16 indices). Same iterative recurrence as REST/MCP. Terms array is not a REST field. Huge BigInt terms omit the figure.
  • 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 6/6 · 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. ›

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.