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Maximum Power Transfer Calculator

Enter the source voltage and source resistance.

How it is calculated

Enter the source voltage V in volts (the open-circuit, or Thevenin, voltage) and the source's internal resistance R in ohms. The maximum power transfer theorem says the load takes the most power when its resistance equals the source resistance, so R_load = R. With that load, the circuit has total resistance 2R, so the current is I = V ÷ (2R) in amperes. The power in the load is P_max = I² × R = V² ÷ (4R) in watts. The tool shows the matched load in ohms, the maximum power to four decimals and the current to four decimals. The resistance must be above zero. The same amount of power, P_max, is lost inside the source, so efficiency at this point is 50%.

Worked example

A source has an open-circuit voltage of 12 V and an internal resistance of 8 Ω. The best load is equal to the source resistance: 8.00 Ω. Total resistance is 8 + 8 = 16 Ω, so the current is 12 ÷ 16 = 0.7500 A. Power in the load: 0.75² × 8 = 4.5 W, which matches V² ÷ (4R) = 144 ÷ 32 = 4.5000 W. The source resistance burns another 4.5 W internally, so only half of the 9 W produced reaches the load.

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Common mistakes

  • Entering the voltage across a load that is already connected. The input is the open-circuit source voltage; a measured voltage under load is lower because of the voltage drop in the source resistance.
  • Using the load resistance as the input. The field is the source's own internal (Thevenin) resistance, and the tool returns the load value that matches it.
  • Treating the result as the most efficient design. Matching gives the most power but only 50% efficiency, so power systems keep the source resistance much smaller than the load.
  • Entering the resistance in kilohms or milliohms without converting. The calculation assumes ohms, so a 4 kΩ source must be typed as 4000.
  • Applying it to an AC circuit with reactance as if it were plain resistance. This tool handles resistive sources only.

About this calculator

The maximum power transfer theorem states that a load draws the greatest possible power from a source when the load resistance equals the source's internal resistance (its Thevenin equivalent resistance). This calculator takes a source's voltage and internal resistance and computes both the optimal load resistance and the maximum power that can actually be delivered to it at that matched condition.

This principle guides circuit and audio engineers when matching a speaker's impedance to an amplifier's output impedance, sizing antenna-to-transmitter interfaces in RF design, and designing power-transfer stages generally — though it's worth noting the theorem maximizes delivered power, not efficiency: at the matched point exactly half the source's power is dissipated inside the source itself, which is why power-distribution systems deliberately use a low source impedance relative to the load instead.

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