Kirchhoff’s Voltage Law (KVL) Calculator

Calculate an unknown voltage in a closed loop circuit based on KVL.

Unknown Voltage Drop (V_unknown)

Intermediate Values:

Voltage Breakdown in the Circuit Loop

Component	Voltage (V)	Type
Source (Vs)		Voltage Rise
Drop 1 (V1)		Voltage Drop
Drop 2 (V2)		Voltage Drop
Unknown (Vunknown)		Calculated Drop

What is Kirchhoff’s Voltage Law (KVL)?

Kirchhoff’s Voltage Law, also known as KVL or Kirchhoff’s second law, is a fundamental principle in electrical circuit analysis. It is based on the principle of conservation of energy and states that **the algebraic sum of all the potential differences (voltages) around any closed loop in a circuit is equal to zero.** In simpler terms, the total voltage supplied by sources (voltage rises) in a closed loop must equal the total voltage used by components (voltage drops). This law is essential for analyzing series circuits and understanding how voltage is distributed among different elements.

The Formula to Calculate Voltage Using Kirchhoff’s Law

The standard representation of Kirchhoff’s Voltage Law is:

ΣV = 0

This means the sum (Σ) of all voltages (V) in a closed loop is zero. When applying this to a simple circuit with one voltage source (V_s) and multiple voltage drops (V₁, V₂, V₃, …), the formula can be written as:

V_s – V₁ – V₂ – V₃ – … = 0

To find an unknown voltage drop, we can rearrange the formula. This calculator solves for an unknown voltage (V_unknown) in a loop with a source and two known drops:

V_unknown = V_s – V₁ – V₂

KVL Formula Variables

Variable	Meaning	Unit	Typical Range
Vs	Source Voltage	Volts (V)	1.5V (AA battery) to 480V (industrial)
V1, V2, …	Voltage Drop across a component	Volts (V)	Depends on component resistance and current
Vunknown	The calculated unknown voltage drop	Volts (V)	Calculated based on other values

Practical Examples

Example 1: Basic LED Circuit

Imagine a simple circuit with a 9V battery, a resistor with a 5V drop across it, and another resistor with a 2V drop. We want to find the voltage remaining for a third component (like an LED).

• Inputs: V_s = 9V, V₁ = 5V, V₂ = 2V
• Formula: V_unknown = 9V – 5V – 2V
• Result: The voltage drop across the third component is 2V.

Example 2: Verifying a Series Circuit

You have a 12V car battery powering a circuit with two known voltage drops of 4V and 6V. You need to calculate the voltage drop across a third, unknown component.

• Inputs: V_s = 12V, V₁ = 4V, V₂ = 6V
• Formula: V_unknown = 12V – 4V – 6V
• Result: The voltage drop across the unknown component is 2V.

How to Use This KVL Calculator

1. Enter Source Voltage: In the first field, input the total voltage supplied by your power source (e.g., a battery).
2. Enter Known Voltage Drops: Input the measured or known voltage drops across two components in the circuit loop. The unit for all inputs is Volts (V).
3. View the Result: The calculator automatically updates, showing the ‘Unknown Voltage Drop’ in the results area. This is the voltage available for the remaining component in the loop to satisfy KVL.
4. Analyze Breakdown: The table provides a clear summary of the voltage rise from the source and the subsequent drops across all components, including the calculated one.

Key Factors That Affect Voltage Calculations

• Component Tolerance: Resistors and other components have a manufacturing tolerance, meaning their actual values might differ slightly from their rated values, affecting the real voltage drop.
• Internal Resistance: Power sources like batteries have internal resistance, which can cause a small voltage drop within the source itself, especially under heavy load.
• Temperature: The resistance of most materials changes with temperature, which can alter voltage drops in a circuit.
• Measurement Accuracy: The precision of the multimeter or device used to measure the known voltage drops will directly impact the accuracy of the calculated result.
• Wire Resistance: While often considered negligible, long or very thin wires have resistance that can cause minor voltage drops.
• Circuit Complexity: KVL applies to any closed loop, but in complex circuits with multiple loops, you must apply the law to each loop independently. You may find our Ohm’s Law Calculator useful for this.

Frequently Asked Questions (FAQ)

1. What does it mean if the calculated voltage is negative?

A negative result means the sum of the known voltage drops is greater than the source voltage. In a real passive circuit, this is physically impossible. It indicates an error in one of the input measurements or that there’s another voltage source in the loop that was not accounted for.

2. Can I use this calculator for a circuit with more than 3 drops?

This specific tool is designed for one source and three total drops (two known, one unknown). To solve for a circuit with more components, you can sum your known drops. For example, if you have drops of 2V, 3V, and 4V, you could enter V₁=5V (2+3) and V₂=4V.

3. Does Kirchhoff’s Voltage Law apply to AC circuits?

Yes, but it becomes more complex. In AC circuits, you must use phasor sums to account for the phase differences between voltages across resistors, inductors, and capacitors. This calculator is intended for DC circuits or purely resistive AC circuits. For more advanced problems, you might need a complex circuit analyzer.

4. What is the difference between KVL and KCL?

Kirchhoff’s Voltage Law (KVL) deals with the conservation of energy and voltages in a closed loop. Kirchhoff’s Current Law (KCL) deals with the conservation of charge at a junction (or node), stating that the total current entering a node must equal the total current leaving it.

5. Is KVL always true?

KVL is based on the lumped-element model of circuits, which assumes that magnetic fields are confined to components (like inductors). In very high-frequency AC circuits, this assumption can break down, and the law may not strictly apply. However, for the vast majority of DC and low-frequency AC circuits, it is a highly reliable rule. Our guide to circuit limitations has more details.

6. What is a “voltage drop”?

A voltage drop is the reduction in electrical potential energy as electricity moves through a component that resists the flow of current, like a resistor or an LED. A voltage source, like a battery, provides a “voltage rise”.

7. Why is the sum of voltages zero?

It reflects the conservation of energy. Imagine walking around a mountain loop and returning to your starting point. The sum of your elevation gains must equal the sum of your elevation losses to end up at the same height. Similarly, in a circuit loop, all the energy (voltage) gained from sources must be lost (dropped) across components.

8. Can I calculate current with this tool?

Not directly. This tool only solves for voltage based on other voltages. To find the current, you would need to know the resistance of the components and use our Power & Ohm’s Law calculator.