What is Kirchhoff's Voltage Law?

KVL states that the sum of all voltage rises and drops around any closed loop in a circuit equals zero. Voltage rises (EMFs, charged capacitors) are positive; voltage drops (resistors, diodes) are negative.

What sign convention should I use?

Use positive values for voltage rises (e.g. battery EMF in the direction of traversal) and negative values for voltage drops (e.g. resistor voltage in the direction of current). The calculator enforces ΣV = 0.

Can I use this for AC circuits?

KVL applies to AC circuits as well, but this calculator works with magnitudes only. For AC phasor analysis you need complex arithmetic.

What if I get a negative unknown?

A negative result is valid — it means the element's actual polarity is opposite to what you assumed. Simply reverse the element's assumed direction.

How many elements can I add?

You can add up to 10 elements per loop, which covers most textbook and practical circuit problems.

Kirchhoff Voltage Law Calculator

Name: Kirchhoff Voltage Law Calculator
Availability: InStock
Author: Nham Vu

Add voltages and EMFs around a closed loop — the calculator solves for the single unknown using KVL.

Loop Elements

Enter each voltage/EMF element. Mark one as Unknown.

Sign Convention

+ Voltage rise — EMF source traversed from − to +, capacitor charge.

− Voltage drop — resistor drop in current direction, forward diode.

Result

Enter loop elements and click Calculate.

Unknown Voltage

— V

KVL Equation (ΣV = 0)

Element Breakdown

Label	Voltage (V)

Sum 0 V

Summary

Add voltages and EMFs around a closed loop — the calculator solves for the single unknown using KVL.

How it works

KVL states that the algebraic sum of all voltages around a closed loop equals zero.
Enter each known voltage or EMF element with its sign (positive for voltage rises, negative for drops).
Add as many elements as your loop has — use the "Add Element" button.
Mark exactly one element as "unknown" — the calculator solves for it.
Click Calculate to see the unknown voltage and the full KVL equation.

Use cases

Find an unknown resistor voltage drop in a series circuit.
Verify Kirchhoff's Voltage Law for a given loop in homework problems.
Solve multi-element DC loop circuits in electronics coursework.
Check battery EMF against known resistor drops.
Quickly validate hand-calculated KVL results.

Frequently Asked Questions

Last updated: 2026-06-11 · Reviewed by Nham Vu