Vth is the open-circuit voltage measured at the output terminals with no load connected. Remove the load, then calculate or measure the voltage between the terminals.

Turn off all independent sources (replace voltage sources with shorts, current sources with opens). Then calculate the resistance seen looking into the terminals. This is Rth.

What is the maximum power transfer theorem?

Maximum power is delivered to the load when RL = Rth. At this point, Pmax = Vth²/(4Rth). However, efficiency is only 50% at maximum power transfer — half the power is lost in Rth.

Thevenin Equivalent Calculator

This calculator requires JavaScript. I_L = V_th / (R_th + R_L) | V_L = V_th × R_L / (R_th + R_L)

I_L = V_th / (R_th + R_L)

V_L = V_th × R_L / (R_th + R_L)

P_max when R_L = R_th

Thevenin Equivalent — Enter V_th, R_th and R_L

V_th Thevenin Voltage

Open-circuit voltage at the terminals

R_th Thevenin Resistance

Equivalent resistance seen from terminals

R_L Load Resistance

Load connected to Thevenin equivalent

Enter V_th, R_th and R_L

Thevenin Load Analysis

Norton Equivalent

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Max Power Transfer

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Load Current IL
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A

Load Voltage V_L

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Load Power P_L

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V_th (open cct)

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R_th

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I_sc (Norton)

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P_max (at R_L=R_th)

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Efficiency

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R_th Power Loss

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Figure 1: Any linear circuit can be replaced by a Thevenin equivalent: a voltage source V_th in series with resistance R_th. This simplifies load analysis to a single voltage divider.

Table of Contents

Fundamentals

What Is Thevenin’s Theorem?
How to Find V_th and R_th

Worked Examples

Simple Voltage Divider Source
Maximum Power Transfer
Thevenin to Norton Conversion

Deep Dive

Maximum Power Transfer Theorem
Thevenin vs Norton

Reference

Frequently Asked Questions
Related Circuit Analysis Calculators

What Is Thevenin’s Theorem?

Thevenin’s theorem states that any linear two-terminal circuit can be replaced by an equivalent circuit consisting of a single voltage source (V_th) in series with a single resistance (R_th). This is enormously useful because it reduces complex networks to a simple series circuit for load analysis — you only need two numbers to fully characterise the source.

Named after Léon Charles Thévenin (1857–1926), the theorem applies to any circuit containing only linear components: resistors, voltage sources, current sources, and controlled sources. The Norton Equivalent Calculator provides the dual representation using a current source in parallel with a resistance.

How to Find V_th and R_th

Step 1 — V_th: Remove the load. Calculate or measure the open-circuit voltage at the terminals. This is V_th.
Step 2 — R_th: Turn off all independent sources (replace voltage sources with short circuits, current sources with open circuits). Calculate the resistance seen looking into the terminals. This is R_th.

Once you have V_th and R_th, any load analysis becomes a simple voltage divider: V_L = V_th × R_L / (R_th + R_L).

Worked Example — Simple Voltage Divider Source

Given: 12 V source, R₁ = 1 kΩ in series, R₂ = 2.2 kΩ to ground, load across R₂

V_th = 12 × 2200/(1000+2200) = 8.25 V

R_th = 1000 ∥ 2200 = (1000×2200)/(1000+2200) = 687.5 Ω

With a 220 Ω load: I_L = 8.25/(687.5+220) = 9.09 mA, V_L = 9.09m × 220 = 2.0 V. The Series Circuit Calculator can verify the voltage divider portion of this analysis.

Worked Example — Maximum Power Transfer

Given: V_th = 5 V, R_th = 50 Ω

R_L for max power = R_th = 50 Ω

P_max = 5²/(4×50) = 125 mW

Efficiency at max power = 50% (half the power is lost in R_th)

Worked Example — Thevenin to Norton Conversion

Given: V_th = 12 V, R_th = 100 Ω

I_N = V_th / R_th = 12/100 = 120 mA

R_N = R_th = 100 Ω (same resistance)

The Norton equivalent is a 120 mA current source in parallel with 100 Ω. Both representations are mathematically identical — they produce the same voltage and current for any load. The Current Divider Calculator analyses the Norton equivalent with a load.

Maximum Power Transfer Theorem

Maximum power is delivered to the load when R_L = R_th. At this point P_max = V_th²/(4R_th). However, the efficiency is only 50% — equal power is wasted in R_th. In practice, power systems operate at high efficiency (R_L >> R_th), while communication systems operate at matched impedance for maximum signal power.

Thevenin vs Norton

Thevenin (voltage source + series R) and Norton (current source + parallel R) are equivalent. Convert between them with I_N = V_th/R_th and R_N = R_th. Use Thevenin when analysing voltage-driven circuits and Norton when analysing current-driven circuits. The KCL Circuit Calculator often benefits from Norton form for nodal analysis.

Frequently Asked Questions

Does Thevenin work for non-linear circuits?

No. Thevenin’s theorem applies only to linear circuits (components that obey a linear V-I relationship). Diodes, transistors, and other non-linear components cannot be directly Thevenised, though you can linearise them at a specific operating point for small-signal analysis.

Can a circuit have multiple Thevenin equivalents?

A circuit has one Thevenin equivalent for each pair of terminals. If you look at different terminals, you get different V_th and R_th values. The equivalent depends on where you “cut” the circuit.

What about dependent sources?

Dependent (controlled) sources cannot be turned off when finding R_th. Instead, apply a test voltage or current at the terminals and calculate R_th = V_test/I_test.

Is 50% efficiency at max power always bad?

Not necessarily. In RF and audio systems, the priority is maximum signal power to the load, not efficiency. In power systems, efficiency matters more, so loads are designed with R_L >> R_th to minimise source losses.

How does this relate to source impedance?

R_th is the source impedance (or output impedance). A low R_th means the source can deliver high current with little voltage sag — a “stiff” source. A high R_th means the voltage drops significantly under load.

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Last updated: March 2026