Enter the load resistance, source resistance, and source voltage into the calculator to determine the power delivered to the load. The transferred power is maximized when the load resistance equals the source resistance (for purely resistive circuits).

Maximum Power Transfer Calculator

Enter any 3 values to calculate the missing variable

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Maximum Power Transfer Formula

The following formula gives the power delivered to the load for a Thevenin-equivalent source voltage (V) in series with a source resistance (Rs) and a load resistance (RL). This delivered power is maximized when RL = Rs (for purely resistive circuits).

P_L = (V² / (R_s + R_L)²) * R_L
R_L = R_s \quad \Rightarrow \quad P_{max} = V^2 / (4 R_s)

Variables:

  • PL is the power delivered to the load
  • Pmax is the maximum power delivered to the load (when RL = Rs)
  • V is the (Thevenin) source voltage
  • Rs is the source (Thevenin) resistance
  • RL is the load resistance

To calculate the power delivered to the load, divide the square of the source voltage by the square of the sum of the source resistance and load resistance. Multiply the result by the load resistance to get the load power. To get the maximum power transfer for a resistive source, set RL = Rs and use Pmax = V² / (4Rs).

What is Maximum Power Transfer?

The maximum power transfer theorem states that to obtain maximum power in a resistive load from a source with a finite internal resistance (modeled by its Thevenin equivalent), the load resistance must equal the source (Thevenin) resistance as seen from its output terminals. In AC circuits with complex impedances, maximum power transfer occurs when the load impedance equals the complex conjugate of the source (Thevenin) impedance.

This principle is widely used in electrical engineering (for example, impedance matching in RF and some audio applications) to maximize the power delivered to a load. It generally does not maximize efficiency; for a purely resistive match (RL = Rs), the efficiency is 50% because half the power is dissipated in the source resistance.

How to Calculate Maximum Power Transfer?

The following steps outline how to calculate the Maximum Power Transfer.

  1. Determine the Thevenin/source voltage (V) and the source (Thevenin) resistance (Rs) seen at the load terminals.
  2. Set the load resistance equal to the source resistance: RL = Rs (for purely resistive circuits).
  3. Calculate the maximum load power using Pmax = V² / (4Rs).
  4. If you want the power for a specific (non-matched) load, use PL = (V² × RL) / (Rs + RL)².
  5. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Load Resistance (RL) = 10 Ω

Source Resistance (Rs) = 10 Ω

Source Voltage (V) = 20 V

Since RL = Rs, the maximum power transferred to the load is Pmax = 20² / (4 × 10) = 10 W.