Solve Kirchhoff’s voltage law (KVL) for an unknown loop voltage, series circuit current, voltage or resistance, or an LED resistor value.

One per line; drops positive, rises negative. Example: −12 V, 3 V, 4 V on separate lines. Up to 10 known terms.

Optional settings

Kirchhoff’s Voltage Law Formula

Σₖ₌₁ⁿ Vₖ = 0
  • Where Vk is the voltage rise or drop across the k-th element in the loop (with a consistent sign convention)
  • n is the number of voltage terms (elements) included in the loop equation

To calculate an unknown voltage using Kirchhoff’s Voltage Law, choose a loop direction and sign convention (for example, treat voltage drops as positive and voltage rises as negative), then solve so that the algebraic sum of voltages around the loop equals zero.

Kirchhoff’s Current Law: One Unknown Branch

For currents at a node, choose “KCL: unknown current.” Enter the known branch currents one per line, positive for current entering the node and negative for current leaving. Choose the direction of the unknown branch and the result unit.

Iunknown,signed = - Σ Iknown

KCL assumes no net charge accumulation at the node: the algebraic sum of all branch currents is zero. A negative answer reverses the selected direction. For example, 5 A entering and 2 A leaving require another 3 A leaving; the balance is 5 − 2 − 3 = 0 A.

Kirchhoff’s Voltage Law Definition

Kirchhoff’s Voltage Law (KVL) states that the algebraic sum of all voltage rises and drops around any closed loop in a circuit is zero. Equivalently, the total of the voltage rises equals the total of the voltage drops (using a consistent sign convention).

Example

How to calculate Kirchhoff’s voltage law?

  1. First, determine the voltages across each element.

    Choose a loop direction and measure (or calculate) the voltage across each component in that loop, keeping track of polarity/sign.

  2. Next, apply KVL and solve for the unknown.

    Sum the voltages algebraically around the loop so that their total equals 0, then rearrange to find the missing voltage.

FAQ

What is Kirchhoff’s voltage law?

Kirchhoff’s voltage law states that the algebraic sum of all voltages around any closed loop in a circuit equals 0.