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Kirchhoff's Law Calculator

Apply Kirchhoff’s voltage law to a series loop or current law to a parallel node with N resistors.

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 (series, parallel, invalid-domain) · Matrix
Known limitations
  • DC series/parallel demo only — not a netlist solver
  • Core CVP does not include live graph, viewport, or pointer interaction.
Model
Series KVL loop or parallel KCL node currents/voltages.
Scope
Ideal DC; single loop/node
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
2/2 property · digest 3dd7bc4d45dd
Legacy regression
7/7 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 · 3/3 CVP boundary · 2/2 invalid · 2/2 property · 1/1 cross-interface · 1/1 CVP contract · Manifest
Sources
  • IEC 60050 — Kirchhoff's laws — KVL / KCL
  • Nilsson/Riedel — Electric Circuits — KVL and KCL
Sources
Evidence
2 legacy golden · 3 legacy boundary · legacy regression suite · 2/2 oracle-backed golden · 2/2 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.

Series (KVL)I = Vs / ΣR; Vi = I·Ri
Parallel (KCL)V = Is / Σ(1/Ri); Ii = V/Ri
iIdeal lumped DC demo. Not a general SPICE netlist solver.

How to use

1

Choose series or parallel

Series sums resistances; parallel combines as 1/Req = Σ 1/Ri.

2

Enter the resistance values

Each used resistance must be greater than zero.

3

Read the equivalent resistance

Clear unused fields. Req updates from the filled resistors only.

Example calculations

Common configurations with formula and result.

ϟ

Series 12 V

100 Ω + 200 Ω

I = 12/300
0.04 A · drops 4 V / 8 V

Kirchhoff's Law 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
Series mode: I = Vs/ΣR and ΣV_drop = Vs (KVL). Parallel mode: V = Is/Σ(1/R) and ΣI_branch = Is (KCL).
What it calculates
Series KVL loop or parallel KCL node currents/voltages.
Inputs
  • mode series|parallel
  • Vs (series) or Is (parallel)
  • ≥1 resistor
Outputs
  • R_eq
  • I_A or V
  • V_drop or I_branch
  • …
Formula
KVL / KCL with Ohm's law
Assumptions
  • Ideal DC; single loop/node
Units
  • V, A, Ω
Boundary conditions
  • Bad mode → INVALID_MODE
  • Missing Vs/Is or R → MISSING_REQUIRED_INPUT
Example
12 V · 100∥200 series → I=0.04 A
Validation cases

1 published on this page · 7/7 tests · Production surface contract 3/3 · View evidence

  • series 12V 100+200 → I=0.04
Sources
  • IEC 60050 — Kirchhoff's laws — KVL / KCL
    Supports: Loop voltage and node current summation
  • Nilsson/Riedel — Electric Circuits — KVL and KCL
    Supports: Series current and parallel voltage identities
Last reviewed
2026-08-08
Reviewed by
CalculatorX electrical review (electrical-engineer)
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Apply Kirchhoff’s laws on a simple series loop or parallel node.

Default: series 12 V · 100 Ω + 200 Ω → I = 0.04 A.

Agent / API notes

Capability id: electrical.kirchhoff · tool id: kirchhoff · pin 1.0.0.

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Frequently asked questions

Key distinctions behind the calculation.

Is this a full circuit solver?

No. v1 covers one series loop or one parallel node only.

Bad mode?

API returns INVALID_MODE.