Thevenin Circuit Calculator

Enter the values for the source voltage and resistors to calculate the Thevenin equivalent voltage (V_th) and resistance (R_th) for the circuit shown below:

We are finding the Thevenin equivalent across terminals A and B.

Example Calculations

Vs (V)	R1 (Ω)	R2 (Ω)	Vth (V)	Rth (Ω)
10	100	100	5.00	50.00
12	50	50	6.00	25.00
9	200	100	3.00	66.67
24	1000	2000	16.00	666.67

Table showing example Thevenin equivalent values for different circuit parameters.

What is a Thevenin Circuit Calculator?

A Thevenin Circuit Calculator is a tool used to simplify a complex linear electrical circuit into a Thevenin equivalent circuit. This equivalent circuit consists of a single voltage source (V_th) in series with a single resistor (R_th), which behaves identically to the original circuit at two specified terminals. The Thevenin Circuit Calculator helps engineers and students quickly determine these two values, V_th and R_th, without manually solving complex circuit equations every time.

Anyone studying or working with electrical circuits, from students learning circuit analysis to engineers designing or analyzing electronic systems, can benefit from a Thevenin Circuit Calculator. It simplifies analysis, especially when you want to understand how a circuit behaves with different loads connected to it.

A common misconception is that Thevenin’s theorem can be applied to any circuit. However, it’s only applicable to linear circuits, meaning circuits composed of resistors, capacitors, inductors, and linear dependent and independent sources. Non-linear elements like diodes or transistors need to be linearized around an operating point for the theorem to be applied approximately.

Thevenin Circuit Calculator Formula and Mathematical Explanation

Thevenin’s theorem states that any linear electrical network containing only voltage sources, current sources, and resistances can be replaced at terminals A-B by an equivalent combination of a voltage source V_th in a series connection with a resistance R_th.

For the circuit shown in our Thevenin Circuit Calculator (V_s in series with R1, and R2 across terminals A-B):

1. Thevenin Voltage (V_th): This is the open-circuit voltage across the terminals A and B. With no load connected across A-B, R1 and R2 form a simple voltage divider.
   
   V_th = V_s * (R2 / (R1 + R2))
2. Thevenin Resistance (R_th): This is the equivalent resistance of the circuit looking back into terminals A and B, with all independent voltage sources short-circuited (replaced by a wire) and all independent current sources open-circuited. In our case, shorting V_s puts R1 and R2 in parallel.
   
   R_th = (R1 * R2) / (R1 + R2)

The Thevenin Circuit Calculator uses these formulas directly.

Variables used in the Thevenin Circuit Calculator.

Variable	Meaning	Unit	Typical Range
Vs	Source Voltage	Volts (V)	0.1 – 1000 V
R1	Resistor 1	Ohms (Ω)	1 – 1,000,000 Ω
R2	Resistor 2	Ohms (Ω)	1 – 1,000,000 Ω
Vth	Thevenin Voltage	Volts (V)	Calculated
Rth	Thevenin Resistance	Ohms (Ω)	Calculated

Practical Examples (Real-World Use Cases)

Example 1: Sensor Interface

Imagine a sensor that outputs a voltage but has some internal resistance, modeled as V_s=5V, R1=500Ω, and it’s connected to a circuit represented by R2=1kΩ before reaching an ADC. We want to find the Thevenin equivalent seen by the ADC if it were connected across R2.

• V_s = 5 V
• R1 = 500 Ω
• R2 = 1000 Ω

Using the Thevenin Circuit Calculator or formulas:
V_th = 5 * (1000 / (500 + 1000)) = 5 * (1000 / 1500) = 3.33 V
R_th = (500 * 1000) / (500 + 1000) = 500000 / 1500 = 333.33 Ω
The ADC effectively sees a 3.33V source with a 333.33Ω series resistance.

Example 2: Power Supply Output Stage

A simple power supply model might have an internal voltage V_s=12V, a series resistance R1=2Ω, and an internal shunt resistance R2=500Ω before the output terminals.

• V_s = 12 V
• R1 = 2 Ω
• R2 = 500 Ω

Using the Thevenin Circuit Calculator:
V_th = 12 * (500 / (2 + 500)) = 12 * (500 / 502) ≈ 11.95 V
R_th = (2 * 500) / (2 + 500) = 1000 / 502 ≈ 1.99 Ω
The output looks like an 11.95V source with a 1.99Ω internal resistance.

How to Use This Thevenin Circuit Calculator

1. Enter Source Voltage (V_s): Input the voltage of the independent voltage source in your circuit (in Volts).
2. Enter Resistor R1: Input the value of the resistor in series with the voltage source (in Ohms).
3. Enter Resistor R2: Input the value of the resistor across which the Thevenin equivalent is being found (in Ohms).
4. View Results: The Thevenin Circuit Calculator will instantly display the Thevenin Voltage (V_th) and Thevenin Resistance (R_th) in the “Results” section.
5. Analyze Chart: The chart shows how V_th and R_th change as R2 varies, giving you a visual understanding of the circuit’s behavior.

The results tell you that the original complex circuit, as viewed from terminals A-B, can be replaced by an ideal voltage source of V_th in series with a resistor R_th. This is useful when analyzing the effect of connecting different load resistances across A-B.

Key Factors That Affect Thevenin Circuit Calculator Results

• Source Voltage (V_s): V_th is directly proportional to V_s. Doubling V_s will double V_th, but R_th remains unchanged as it depends only on resistances.
• Resistance Values (R1, R2): Both V_th and R_th depend on the ratio and product of R1 and R2. Changes in either resistor will affect both the equivalent voltage and resistance.
• Circuit Linearity: Thevenin’s theorem and this Thevenin Circuit Calculator only apply to linear circuits. If there are non-linear components, the results are only valid if those components are operating in a linear region or are linearized.
• Frequency (for AC circuits): This calculator is for DC circuits or AC circuits with only resistances (impedances are purely real). For AC circuits with capacitors and inductors, impedances must be used, and V_th and Z_th (Thevenin Impedance) become complex numbers. Our calculator assumes DC/resistive circuits.
• Independent Sources Only: When calculating R_th, only independent sources are turned off (voltage sources shorted, current sources opened). Dependent sources remain active. This calculator assumes only one independent voltage source and resistors.
• Terminals of Interest: The Thevenin equivalent is always found with respect to two terminals in the original circuit. Changing the terminals will change the equivalent circuit. Our Thevenin Circuit Calculator finds it across R2.

Frequently Asked Questions (FAQ)

What is Thevenin’s Theorem?

Thevenin’s Theorem is a principle in electrical circuit theory that allows any linear two-terminal circuit to be replaced by an equivalent circuit consisting of a single voltage source (V_th) and a single series resistor (R_th).

How do you find Thevenin Voltage (V_th)?

V_th is the open-circuit voltage between the two terminals of interest. You calculate the voltage across these terminals as if no load is connected.

How do you find Thevenin Resistance (R_th)?

R_th is the equivalent resistance looking back into the terminals, with all independent voltage sources short-circuited and independent current sources open-circuited. Dependent sources are left as they are.

Can I use the Thevenin Circuit Calculator for AC circuits?

This specific Thevenin Circuit Calculator is designed for DC circuits with resistors. For AC circuits with capacitors and inductors, you need to use impedances (complex numbers), and the results (V_th and Z_th) will also be complex.

What if my circuit has more components?

For more complex circuits, you need to apply circuit analysis techniques (like mesh or nodal analysis, or source transformation) to find V_th and R_th or use a more advanced circuit analysis tool. This calculator handles a specific simple configuration.

Why is Thevenin’s theorem useful?

It simplifies complex circuits, making it easier to analyze the behavior of the circuit when different loads are connected across the terminals. It’s particularly useful for maximum power transfer analysis.

Is there a Norton equivalent?

Yes, Norton’s theorem is the dual of Thevenin’s theorem, where the equivalent circuit is a current source (I_N) in parallel with a resistance (R_N or R_th). You might find a Norton’s Theorem calculator useful too.

What are the limitations of this Thevenin Circuit Calculator?

This calculator is for a specific circuit configuration (V_s-R1-R2 voltage divider). It doesn’t handle dependent sources, multiple independent sources, or non-linear elements directly. See our guide on equivalent circuits for more.

Related Tools and Internal Resources

• Norton’s Theorem Calculator: Find the Norton equivalent of a circuit.
• Ohm’s Law Calculator: Calculate voltage, current, resistance, and power.
• Superposition Theorem Calculator: Analyze circuits with multiple sources using superposition.
• Circuit Analysis Tools: A collection of tools for analyzing electrical circuits.
• Equivalent Circuits Explained: Learn more about Thevenin, Norton, and other equivalent circuits.
• Maximum Power Transfer Theorem: Understand how R_th relates to maximum power delivery.