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Parallel Resistor Calculator

Compute equivalent resistance of two or more resistors in parallel. Runs locally in your browser.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance
Input interpretation
Enter values to calculate.
Result
—
Assurance
Engineering
Declared partition coverage
PASS · 3/3 declared partitions (named-R, array-R, invalid-domain) · Matrix
Known limitations
  • Ideal resistors; no temperature/tolerance stack
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Equivalent resistance of N≥2 parallel resistors.
Scope
Ideal lumped resistors; DC/resistive AC
Verification
Engine tested · Source checked · v1.0.0 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance· View Manifest · CVP overview · Specification
Versions
Calculation 1.0.0 · CVP protocol 1.0.0-proposed
CVP identity
3/3 property · digest 7f0dcbf6653f
Legacy regression
10/10 tests · Production surface contract 3/3
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.
Supplemental domain review
Internal · Pass · electrical-engineer
Named expert review
Not performed
CVP suite
2/2 golden · 5/5 CVP boundary · 4/4 invalid · 3/3 property · 1/1 cross-interface · 1/1 CVP contract · Manifest
Sources
  • IEC 60050 — IEV — Parallel connection of resistors
  • Horowitz & Hill — The Art of Electronics — Resistor networks
Sources
Evidence
2 legacy golden · 5 legacy boundary · legacy regression suite · 2/2 oracle-backed golden · 4/4 invalid · Artifact integrity PASS · CalculatorX electrical review
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.

Parallel1/Req = 1/R1 + 1/R2 + …
iIdeal lumped resistors only. Series networks are out of scope for v1.

How to use

1

Enter at least two resistances

Use R1…R8 (or the list field). Each used value must be > 0.

2

Add more parallel branches if needed

Empty fields are ignored.

3

Read equivalent resistance Req

1/Req = Σ 1/Ri. Req is always less than the smallest branch.

Example calculations

Common configurations with formula and result.

ϟ

Two 100 Ω

R1=R2=100

Req = R/2
50 Ω
ϟ

100 · 200 · 300 Ω

Three unequal

1/Req = Σ 1/Ri
≈ 54.545 Ω

Parallel Resistor calculator specification

Version 1.0.0 · Engine tested · Supplemental domain review · Internal · 2026-08-08

Calculation status

Review policy · Evidence · Reviewed by CalculatorX electrical review (electrical-engineer)

Definition
For resistors in parallel, conductances add: 1/Req = Σ 1/Ri. Two equal resistors give Req = R/2.
What it calculates
Equivalent resistance of N≥2 parallel resistors.
Inputs
  • At least two of R1…R8 or R_ohm[] — each > 0 (Ω)
Outputs
  • R_eq (Ω)
  • G_S (S)
  • n
  • R_ohm echo
Formula
1/Req = Σ 1/Ri
Assumptions
  • Ideal lumped resistors; DC/resistive AC
Units
  • Ω → Ω, S
Boundary conditions
  • Fewer than two → NEEDS_TWO_INPUTS
  • ≤ 0 → VALUE_MUST_BE_POSITIVE
  • Non-finite → INVALID_NUMBER
Example
100∥100 → 50 Ω
Validation cases

3 published on this page · 10/10 tests · Production surface contract 3/3 · View evidence

  • R1=100, R2=100 → R_eq=50
  • 100,200,300 → R_eq≈54.545
  • only R1 → error NEEDS_TWO_INPUTS
Sources
  • IEC 60050 — IEV — Parallel connection of resistors
    Supports: Conductance addition for parallel networks
  • Horowitz & Hill — The Art of Electronics — Resistor networks
    Supports: 1/Req = Σ 1/Ri
Last reviewed
2026-08-08
Reviewed by
CalculatorX electrical review (electrical-engineer)
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Compute parallel equivalent resistance (1/R_{eq} = \sum 1/R_i).

Default: 100 Ω ∥ 100 Ω → 50 Ω.

Supported and not supported

Supported — N≥2 parallel resistors via R1…R8 or R_ohm[] · API electrical.parallel_resistor

Not supported — Series networks, ladder/bridge topology, temperature coefficients

Agent / API notes

Capability id: electrical.parallel_resistor · tool id: parallel-resistor · pin calculation_version: 1.0.0.

Stable errors: NEEDS_TWO_INPUTS, INVALID_NUMBER, VALUE_MUST_BE_POSITIVE.

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Frequently asked questions

Key distinctions behind the calculation.

How do parallel resistors combine?

Conductances add: 1/Req = Σ 1/Ri. The equivalent is always smaller than the smallest resistor.

What if I enter only one resistor?

The API returns NEEDS_TWO_INPUTS — provide at least two.