Kirchhoff's Current Law states that the total current entering any node equals the total current leaving. The algebraic sum of all currents at a node is zero.

What if the sum is not zero?

A current is missing, incorrectly measured, or there is a measurement error. The residual shows the missing current needed to balance the node.

Does KCL apply to AC circuits?

Yes. KCL applies to instantaneous currents and to AC phasor currents. The sum of all phasor currents at a node is zero.

What about capacitors storing charge?

KCL still holds. Current flowing into one plate of a capacitor equals current flowing out of the other plate. No net charge accumulates at any node.

KCL Circuit Calculator

ΣI_node = 0

I_in = I_out1 + I_out2 + …

KCL — Enter Currents at a Node

Enter positive values for currents entering the node and negative for currents leaving.

Enter currents at the node

KCL Verification

Sum of Currents
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A

Residual Error

—

KCL Status

—

Total In

—

Total Out

—

Missing I (if any)

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Figure 1: At any junction, the total current flowing in must equal the total current flowing out. If the sum is not zero, a current is missing or incorrectly measured.

Table of Contents

Fundamentals

What Is Kirchhoff’s Current Law?
KCL Rules

Worked Examples

Simple Three-Branch Node
Finding a Missing Current
Multi-Node Circuit

Deep Dive

KCL and Nodal Analysis
Applications

Reference

Frequently Asked Questions
Related Circuit Analysis Calculators

What Is Kirchhoff’s Current Law?

Kirchhoff’s Current Law (KCL) states that the total current entering any node (junction) in a circuit equals the total current leaving that node. Equivalently, the algebraic sum of all currents at a node is zero. This is a consequence of charge conservation — charge cannot accumulate at a point in a circuit.

KCL is the companion to KVL and together they form the foundation of all circuit analysis. The Parallel Circuit Calculator is a direct application of KCL: the total supply current equals the sum of all branch currents.

KCL Rules

ΣI = 0 at any node.
Convention: currents entering are positive, currents leaving are negative (or vice versa).
I_in1 + I_in2 = I_out1 + I_out2 + ... + I_outn

Worked Example — Simple Three-Branch Node

Given: I₁ = 100 mA (entering), I₂ = 60 mA (leaving), I₃ = ? (leaving)

KCL: I₁ = I₂ + I₃

I₃ = 100 − 60 = 40 mA (leaving)

Worked Example — Finding a Missing Current

Given: Four wires at a junction. I₁ = 2 A in, I₂ = 0.5 A out, I₃ = 1 A out, I₄ = ?

I₄ = 2 − 0.5 − 1 = 0.5 A out

The Current Divider Calculator applies KCL at the splitting node of parallel branches.

Worked Example — Multi-Node Circuit

Given: V_s = 12 V, three parallel branches: R₁ = 100 Ω, R₂ = 220 Ω, R₃ = 470 Ω

I₁ = 12/100 = 120 mA, I₂ = 12/220 = 54.5 mA, I₃ = 12/470 = 25.5 mA

KCL: I_total = 120 + 54.5 + 25.5 = 200 mA

Verifying: I_total = V/R_total = 12/60 = 200 mA ✓. The Circuit Current Calculator can verify each branch independently.

KCL and Nodal Analysis

Nodal analysis applies KCL systematically at every node in a circuit, expressing all branch currents in terms of node voltages (using Ohm’s law). This creates a set of simultaneous equations that can be solved for all node voltages. It is particularly efficient for circuits with many loops but few nodes. The Thevenin Equivalent Calculator simplifies complex networks so you don’t need full nodal analysis for single-load problems.

Applications

KCL is used in every branch of electronics: power distribution (ensuring current balance at busbars), IC design (current mirrors, differential pairs), PCB analysis, fault detection (unexpected currents indicate faults), and digital logic (current summing at nodes). The Power Dissipation Calculator uses the currents found by KCL to check component ratings.

Frequently Asked Questions

Does KCL work for AC?

Yes. KCL applies to instantaneous currents in any circuit. For AC phasor analysis, KCL is applied to complex current phasors. The sum of all phasor currents at a node is zero.

What about capacitors — can charge accumulate?

KCL still holds. The current “through” a capacitor is the displacement current (C × dV/dt). No net charge accumulates at any node — current flowing into one plate of a capacitor causes equal current to flow out of the other plate.

How many KCL equations do I need?

For a circuit with N nodes, you need N − 1 independent KCL equations (one node is chosen as the reference/ground). Combined with component equations (Ohm’s law), this gives enough equations to solve the circuit.

Can I use KCL at a supernode?

Yes. When a voltage source connects two nodes, they form a supernode. Apply KCL to the boundary of the supernode — the sum of all currents entering and leaving the supernode boundary is zero.

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Last updated: March 2026