Kirchhoff Laws Calculator

Kirchhoff published his two circuit laws in 1845 at age 21. Together they let you analyze any DC resistor network, no matter how complex.

Kirchhoff’s Voltage Law (KVL): The sum of all voltages around any closed loop equals zero. In a series circuit, this means the supply voltage equals the sum of voltage drops across each resistor: V = V1 + V2 + V3 + …

Kirchhoff’s Current Law (KCL): The current entering any node equals the current leaving it. In a parallel circuit, total current splits across branches: I = I1 + I2 + I3 + …

For a series circuit: total resistance R_total = R1 + R2 + … because the same current flows through each resistor. Voltage across each resistor: Vn = I × Rn. The resistor with the largest resistance gets the most voltage.

For a parallel circuit: 1/R_total = 1/R1 + 1/R2 + … The total resistance is always less than the smallest individual resistor. The same voltage appears across each branch. Current through each branch: In = V/Rn. The smallest resistor carries the most current.

A practical note: most real circuits are neither pure series nor pure parallel — they’re combinations. You apply KVL to loops and KCL to nodes and solve the resulting simultaneous equations. For simple two-mesh or three-mesh circuits, that approach is fast. For more complex networks, matrix methods (nodal analysis) are more efficient.

Power dissipated per resistor: P = V² / R = I² × R. In a series circuit, the largest resistor dissipates the most power. In parallel, the smallest resistor dissipates the most.