Kirchhoff's Current Law (KCL)

Kirchhoff's Current Law (KCL) says that the total current entering a node equals the total current leaving it, as long as charge is not building up at that node. In circuit form, that means the algebraic sum of currents at a junction is zero.

You will often see it written as

$$\sum I = 0$$

when you choose one sign convention and use it consistently.

What Kirchhoff's Current Law means

KCL is the circuit version of charge conservation. If a node is not storing net charge, then the charge per second arriving at that point must also leave.

That is why KCL is often called the junction rule. It applies at a point where branches meet, not around a closed loop.

In plain language, a node can split current, combine current, or redirect current, but it cannot create extra current from nowhere.

The KCL equation and sign convention

There are two equivalent ways to write KCL:

$$\sum I_{in} = \sum I_{out}$$

or

$$\sum I = 0$$

The second form is often easier when solving problems. For example, you can treat currents entering the node as positive and currents leaving as negative, then place every branch current into one equation.

The condition matters. This familiar node equation is the usual form for lumped-circuit analysis when the node is not accumulating charge appreciably.

Worked example: solving for an unknown branch current

Suppose $8\ \mathrm{mA}$ enters a node from the left and $1\ \mathrm{mA}$ enters from below. Two currents leave the same node: $3\ \mathrm{mA}$ through one branch and $I_x$ through the other. Find $I_x$.

Using entering currents as positive and leaving currents as negative, write KCL as

$$8 + 1 - 3 - I_x = 0$$

Now simplify:

$$6 - I_x = 0$$ $$I_x = 6\ \mathrm{mA}$$

So the unknown branch carries $6\ \mathrm{mA}$ away from the node. If you had assumed the opposite direction for $I_x$, the answer would have come out as $-6\ \mathrm{mA}$ instead. The negative sign would simply tell you the real current direction is opposite to your assumption.

This is the core KCL workflow: choose directions, write one node equation, solve, then interpret the sign of the result.

Common KCL mistakes

Mixing sign conventions

If you treat entering currents as positive in one term, do not switch halfway and treat leaving currents as positive too unless you rewrite the whole equation. Many KCL mistakes are just sign mistakes.

Misreading a negative answer

If you assume a current leaves the node and your result is negative, that does not mean the math failed. It means the actual current flows in the opposite direction.

Forgetting the condition behind KCL

KCL depends on the node not building up net charge in the lumped-circuit model. In ordinary circuit problems that is the standard assumption, but the condition is still worth stating.

Using KCL where a loop rule is needed

KCL is a node rule. If you need to relate voltage rises and drops around a closed path, that is a loop rule, not a node rule.

Assuming all branch currents must be equal

Currents only have to balance at the node. KCL does not say that every branch current has the same value.

When Kirchhoff's Current Law is used

KCL is used whenever a circuit has junctions and you need to relate branch currents. It is a foundation of node-voltage analysis, current-divider reasoning, transistor bias networks, and power-distribution circuits.

In practice, KCL is usually combined with a component relationship such as Ohm's law, $V = IR$, because KCL gives the current balance but not every branch value by itself.

How to check a KCL equation quickly

After solving a circuit, add the currents entering a node and compare them with the currents leaving. If the two sides do not match, something in the setup or sign convention is wrong.

Try a similar KCL problem

Change the example so that only one current enters and two leave, or assume the unknown current enters instead of leaves and see how the sign changes. If you want a quick check after solving it by hand, try your own version in GPAI Solver.