Thevenin Equivalent Calculator

A Thevenin equivalent reduces a linear electrical network at a pair of load terminals to two values: Thevenin voltage and Thevenin resistance. With a resistive load connected, the circuit behaves as a voltage source in series with an equivalent source resistance feeding the Load resistance.

The Thevenin Equivalent Calculator produces the connected-load values needed to review source loading and voltage division:

• Load current
• Load voltage
• Load power
• Source resistance loss
• Total series resistance

These results are useful when checking whether a simplified source can support a connected resistive device, estimating terminal voltage under load, or comparing the effect of alternate load resistances. In practical electrical troubleshooting, the calculation can represent a measured source that shows normal open-circuit voltage but loses voltage when connected to a load.

Thevenin Source at the Load Terminals

The calculator does not derive a Thevenin equivalent from an arbitrary circuit diagram. The upstream circuit must first be analyzed or measured to obtain the values at the intended load terminals.

Thevenin voltage is the open-circuit voltage measured or derived across the load terminals with the load disconnected.

Thevenin resistance is the equivalent resistance seen looking back into the source network from those same terminals. It represents the source’s internal resistance or the combined resistance of the linear network supplying the load.

Load resistance is the connected linear resistive load. The calculator treats the source resistance and load resistance as series resistance.

The resulting circuit is:

\(\displaystyle V_{th} \rightarrow R_{th} \rightarrow R_L\)

where:

• \(V_{th}\) = Thevenin voltage
• \(R_{th}\) = Thevenin resistance
• \(R_L\) = Load resistance

Calculation Method

The calculator first adds the source and load resistances:

\(\displaystyle R_{total} = R_{th} + R_L\)

The connected Load current is then:

\(\displaystyle I_L = \frac{V_{th}}{R_{th} + R_L}\)

The voltage delivered to the load is:

\(\displaystyle V_L = I_L \times R_L\)

Load wattage is:

\(\displaystyle P_L = I_L^2 \times R_L\)

The power dissipated in the equivalent source resistance is:

\(\displaystyle P_{source} = I_L^2 \times R_{th}\)

The voltage drop across the equivalent source resistance is not displayed as a separate result, but it can be determined from:

\(\displaystyle V_{drop} = I_L \times R_{th}\)

The Thevenin voltage equals the load voltage plus this source-resistance voltage drop:

\(\displaystyle V_{th} = V_L + V_{drop}\)

Calculation Example

Enter the following values:

Input	Value
Thevenin voltage	12 V
Thevenin resistance	4 ohm
Load resistance	8 ohm

First, calculate Total series resistance:

\(\displaystyle R_{total} = 4\ \text{ohm} + 8\ \text{ohm} = 12\ \text{ohm}\)

Next, calculate Load current:

\(\displaystyle I_L = \frac{12\ \text{V}}{12\ \text{ohm}} = 1\ \text{A}\)

Then calculate Load voltage:

\(\displaystyle V_L = 1\ \text{A} \times 8\ \text{ohm} = 8\ \text{V}\)

The load power is:

\(\displaystyle P_L = 1^2 \times 8 = 8\ \text{W}\)

The source resistance loss is:

\(\displaystyle P_{source} = 1^2 \times 4 = 4\ \text{W}\)

Result	Value
Load current	1 A
Load voltage	8 V
Load power	8 W
Source resistance loss	4 W
Total series resistance	12 ohm

The 12 V open-circuit source delivers only 8 V to the 8-ohm load because 4 V is dropped across the 4-ohm Thevenin resistance. One-third of the total source power is dissipated in the equivalent source resistance.

Load Voltage and Source Loading

A low Thevenin resistance relative to the Load resistance produces less voltage drop and delivers a larger share of the source voltage to the load. A high Thevenin resistance limits load current and increases source resistance loss.

For a resistive load, maximum load power occurs when:

\(\displaystyle R_L = R_{th}\)

At that condition, the load receives one-half of the Thevenin voltage and the source resistance dissipates the same power as the load. Maximum power transfer is not necessarily an efficient operating condition because half of the available power is lost in the equivalent source resistance.

In distribution work, a source or feeder is normally selected to minimize voltage drop and unwanted heating rather than to operate at maximum power-transfer conditions. Thevenin analysis can help identify why a load terminal voltage collapses when current rises, but it does not replace a conductor ampacity, voltage-drop, overcurrent protection, or equipment-duty calculation.

Field Limits

The calculator applies to an entered linear resistive load after Thevenin voltage and Thevenin resistance have already been established. It does not model nonlinear loads, changing impedance, inrush current, motor starting, power factor, inductive or capacitive reactance, harmonics, electronic power supplies, battery discharge behavior, transformer regulation, or fault-current behavior.

Do not use the result alone to select AWG or kcmil conductors, determine ampacity, apply an adjustment factor or correction factor, establish raceway fill, verify branch-circuit or feeder protection, or approve an installation. Those decisions require the actual load characteristics, conductor insulation temperature rating, terminal rating, installation conditions, voltage-drop criteria, equipment instructions, and applicable AHJ requirements.