Kirchhoff’s Laws Circuit Solver Online

Enter the circuit as branches (nodes, R, E, current sources) — the calculator writes Kirchhoff’s equations, solves them by mesh currents and node voltages, finds all branch currents and checks the power balance.

Describe the circuit as branches: the two nodes of each branch (any names: a, b, 1, 2…), resistance R and EMF E (acting from “from” to “to”). A current source J is a separate branch without R and E. Empty fields mean 0. “From → to” is the positive current direction; a negative answer means the current flows the other way.

№	From	To	R, Ω	E, V	J, A
1
2
3

Calculate

Kirchhoff’s laws

Current law: the algebraic sum of currents at a node is zero; a circuit with q nodes gives q − 1 independent equations.

Voltage law: around any closed loop the sum of I·R drops equals the sum of EMFs (signs follow the loop direction). There are p − q + 1 independent loops (p branches, current sources excluded).

Procedure

Number nodes and branches, pick current directions (a negative result just means the opposite direction).
Write q − 1 KCL and p − q + 1 KVL equations and solve.
Check the power balance ΣE·I + ΣU·J = ΣI²R.

Mesh current method

One loop current per independent loop: Z₁₁·I₁₁ + Z₁₂·I₂₂ + … = E₁₁, where Z₁₁ is the loop resistance, Z₁₂ the shared resistance (negative if the loop currents oppose), E₁₁ the loop EMF. A branch current is the sum of loop currents through it.

Nodal analysis

Set one node to zero potential; for the others G₁₁·φ₁ − G₁₂·φ₂ − … = J₁₁. Branch currents follow from I = (φ₁ − φ₂ + E)/R. Best when there are few nodes.

FAQ

How many Kirchhoff equations are needed?

As many as unknown currents: q − 1 by the current law and p − q + 1 by the voltage law.

What does a negative current mean?

The current flows opposite to the chosen direction; its magnitude is correct.

How do I check the solution?

With the power balance: source power ΣE·I + ΣU·J equals load power ΣI²R. Both sums are shown.

Why use mesh currents?

Fewer equations — one per independent loop instead of one per branch. Nodal analysis is even shorter with few nodes.

How do I enter a current source?

As a separate branch with only J (no R or E): the current J flows from “from” to “to”.