Maximum Power Transfer Calculator
Find Pmax, VTH or RTH for any Thévenin source, test any load RL, and watch the circuit, power curve and efficiency respond live.
The theorem in one minute
A source with Thévenin voltage VTH and resistance RTH delivers PL = VTH²·RL / (RL+RTH)² to a load. Setting dPL/dRL = 0 gives (RTH−RL) = 0, so power peaks when RL = RTH. Substituting back gives Pmax = VTH² / (4RTH).
At the match
I = VTH/(2RTH), VL = VTH/2, and the load gets exactly half of the total source power.
Efficiency η = RL/(RL+RTH)
Only 50 % at the match. Power utilities run RL ≫ RTH for high efficiency; signal circuits (audio, RF, sensors) match for maximum signal power.
Norton view & AC
With IN = VTH/RTH, Pmax = IN²·RTH/4. For AC, the load must be the complex conjugate: ZL = ZTH*, and Pmax = |VTH|²/(8RTH) for peak phasors.
Worked example
RL = RTH = 4 Ω
Pmax = 12² / (4 × 4) = 144 / 16 = 9 W
I = 12 / 8 = 1.5 A, VL = 6 V, η = 50 %
Load ratio reference table
How much power the load receives as RL departs from RTH. The amber row is the maximum-power point. It is independent of VTH.
| RL/RTH | PL/Pmax | Efficiency | VL/VTH |
|---|
FAQ
No. Power transfer peaks at RL = RTH with 50 % efficiency; efficiency keeps rising toward 100 % as RL grows, while delivered power falls.
Remove the load. VTH is the open-circuit voltage across the terminals. RTH is the resistance seen from the terminals with independent sources turned off (voltage sources shorted, current sources opened), or VOC/ISC.
Use the Advanced test-load slider: it shows how far you are from the peak. Matching networks, transformers or impedance converters are used to make the load look equal to RTH.
The theorem assumes RL is variable and RTH is fixed. If RL is fixed and RTH can vary, power is maximised by making RTH as small as possible (zero).
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| P_max | Maximum power transferred | W |
| R_L | Load resistance | Ω |
| R_TH | Thevenin equivalent resistance | Ω |
| V_TH | Thevenin equivalent voltage | V |
What it means
The maximum power transfer theorem states that a load receives maximum power when its resistance equals the Thévenin resistance of the source network. This condition is known as impedance matching. At this point, the load voltage is V_TH/2, and the power delivered to the load is P_max = V_TH² / (4*R_TH). The efficiency at maximum power transfer is only 50% because the source internal resistance dissipates an equal amount of power. This theorem is applied in communication systems (e.g., matching antenna to receiver), audio systems (matching speakers to amplifiers), and transmission lines. In power systems, it is not used for transmission because high efficiency is more important than maximum power; instead, load impedance is kept much higher than source impedance. The theorem also extends to AC circuits, where matching requires both resistance and reactance to be conjugately matched (Z_L = Z_TH*). Example: If a source has R_TH = 5Ω, the load should be R_L = 5Ω for maximum power transfer, yielding P_max = V_TH² / (4*5).
Worked example
Maximum Power Transfer – Practical Example
Real‑World| Parameter | Value |
|---|---|
| VTH | 12 V |
| RTH | 6 Ω |
| Condition | RL = RTH |
Common mistakes
- Condition: R_L = R_TH (the Thevenin resistance) – not the load voltage or current.
- Efficiency: At maximum power transfer, the efficiency is only 50% (half the power is lost in the source).
- AC case: For AC, match the complex impedance (Z_L = Z_TH*) for maximum power transfer.
- Practical: In power systems, we avoid maximum power transfer (inefficient) – we aim for high efficiency.
- Non‑linear: The theorem applies to linear circuits only.
Applications
The maximum power transfer theorem states that a load receives maximum power when its resistance equals the Thévenin resistance of the source. This principle is crucial for matching loads to sources in audio systems, communication circuits, and power electronics. Engineers use it to design impedance‑matching networks, to select speakers for amplifiers, and to optimise antenna–transmitter interfaces. While the theorem ensures maximum power delivery, it does so at 50% efficiency, which is acceptable in low‑power signal applications. In power systems, however, efficiency is prioritised, so the theorem is less applicable. By understanding this theorem, professionals can balance power delivery and efficiency. It is a fundamental concept in circuit design and impedance matching.
- Impedance matching for audio and communication systems
- Speaker‑amplifier matching for maximum sound power
- Antenna design and transmission line matching
- Power supply output impedance optimisation
- Educational understanding of load‑source interaction
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