Kirchhoff Calculator
Kirchhoff's voltage law says the source voltage in a closed loop equals the sum of the voltage drops around that loop, and Kirchhoff's current law says one current flows through every component of a single series path. Combining these with Ohm's law lets you solve a series circuit completely. Enter the source voltage and up to three series resistances and this tool returns the loop current, the individual voltage drop across each resistor, and the total power delivered by the source, all from the defining laws of circuit analysis.
Kirchhoff loop formula
KVL: V_source = V_R1 + V_R2 + V_R3
Total resistance R_total = R1 + R2 + R3
KCL (series): one loop current I flows everywhere
Ohm's law: I = V_source / R_total
Drop across each resistor: V_n = I * R_n
Source power: P = V_source * I
Because the resistors are in series, the same current flows through all of them (KCL), and the source voltage divides among them in proportion to their resistance, summing exactly to the source voltage (KVL).
Circuit analysis context
- Kirchhoff's two laws, published by Gustav Kirchhoff in 1845, are exact consequences of charge conservation and energy conservation.
- In a series loop, the largest resistor always drops the largest share of the voltage.
- The voltage drops always add back up to the source voltage; that identity is a quick way to check your arithmetic.
- Power dissipated in a resistor equals its voltage drop times the current; the resistor powers always sum to the source power.
- Set a resistor to zero ohms to model only the resistors you actually have in the loop.
Kirchhoff calculator: frequently asked questions
What is Kirchhoff's voltage law?
Kirchhoff's voltage law (KVL) states that the algebraic sum of all voltages around any closed loop in a circuit equals zero. In a simple series loop, the source voltage equals the sum of the voltage drops across each resistor. This calculator uses KVL to solve for the loop current when a single voltage source drives resistors in series.
What is Kirchhoff's current law?
Kirchhoff's current law (KCL) states that the algebraic sum of currents entering a node equals the sum of currents leaving it. In a single series loop there is only one current path, so the same current flows through every component. This calculator reports that single loop current.
How do I find the voltage drop across each resistor?
By Ohm's law, the voltage drop across a resistor is the loop current multiplied by that resistor's resistance (V = I times R). Because the same current flows through each series resistor, larger resistors drop proportionally more voltage. The drops always sum to the source voltage, which is KVL.
What if I enter a resistance of zero?
If the total series resistance is zero, Ohm's law gives an undefined (infinite) current, so the calculator shows n/a. A real circuit always has some resistance, even if only the internal resistance of the source and wires. Enter at least one nonzero resistance to model a physical series loop.
Does this handle parallel resistors or multiple sources?
This calculator models a single closed loop with one source and up to three series resistors, the most common KVL teaching example. For parallel branches or multiple sources you would write one KVL equation per loop and one KCL equation per node, then solve the resulting linear system.
Official sources
- NIST: SI units of electric current.
- NASA Glenn Research Center: Ohm's law.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.