Thévenin ⇄ Norton & Max Power Transfer Calculator

Understanding the Thévenin and Norton equivalent calculator — concept and principle

Any linear circuit seen from two terminals can be replaced by a single voltage source with a series resistance (Thévenin) or a single current source with a parallel resistance (Norton). This calculator converts a Thévenin equivalent into its Norton form, finds the current and power delivered to a chosen load, the maximum power the source could deliver, and the efficiency. It is used to match loads to amplifiers, sensors, batteries and solar cells, and to simplify circuit analysis.

A matched 4 Ω load gets the most power, 9 W, but only half of what the source supplies.

How it is calculated

Norton current: I_N = V_th / R_th (the Norton resistance equals R_th)
Load current: I_L = V_th / (R_th + R_L)
Load power: P_L = I_L² · R_L
Maximum power: P_max = V_th² / (4 · R_th), reached when R_L = R_th
Efficiency: η = R_L / (R_th + R_L) × 100%

Voltages are in volts, resistances in ohms, currents in amperes and power in watts.

The principle

Thévenin (1883) and Norton (1926) showed that the two equivalents are interchangeable: short-circuiting the Thévenin source gives the current V_th / R_th, which is exactly the Norton current. The load and R_th form a series loop, so the load current follows from Ohm's law. Writing load power as V_th² · R_L / (R_th + R_L)² and differentiating with respect to R_L shows that it peaks when R_L = R_th. At that point half the energy is lost in R_th, so efficiency is 50%. This is the maximum power transfer theorem.

Worked example

Inputs: V_th = 12 V, R_th = 4 Ω, R_L = 4 Ω.
Norton current = 12 / 4 = 3 A.
Load current = 12 / (4 + 4) = 1.5 A.
Load power = 1.5² × 4 = 2.25 × 4 = 9 W.
Maximum power = 12² / (4 × 4) = 144 / 16 = 9 W, the same because R_L = R_th.
Efficiency = 4 / 8 × 100 = 50%.

Each point is the calculator re-run with only “Thévenin resistance (Ω)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Thévenin resistance (Ω)	Norton current (A)
1	12
2	6
3	4
4	3
5	2.4
6	2
8	1.5

How to read the result

If the load power equals the maximum power, the load is matched. A larger load resistance raises efficiency but delivers less power; a smaller one draws more current but wastes more in the source. Matching is the goal in radio-frequency and audio-signal links, where getting the most power is what matters. Power distribution and batteries aim for R_L much larger than R_th, so that efficiency is high and the source does not overheat.

Common mistakes

Believing that maximum power transfer means maximum efficiency; at the matched point it is only 50%.
Changing R_th to match a fixed load; the theorem is about choosing the load for a given source.
Applying the equivalents to non-linear circuits, such as diodes, without linearizing first.

Keep in mind: The model is valid only for linear circuits and DC or resistive AC loads. With reactive impedances, maximum power requires the load to be the complex conjugate of the source impedance.

Frequently asked questions

How do I find V_th and R_th of a real circuit?

V_th is the open-circuit voltage at the terminals. R_th is V_th divided by the short-circuit current, or the resistance seen with all independent sources turned off.

Why aren't power stations matched to their loads?

Matching would waste half the generated power in the source. Grids are designed for high efficiency instead.

Sources: L. Thévenin, "Extension de la loi d'Ohm aux circuits électromoteurs complexes", Annales Télégraphiques (1883) · J. W. Nilsson and S. A. Riedel, Electric Circuits, Pearson

Checked 8 Nov 2026. Standard textbook formulas in SI units, computed in your browser. For learning and estimates — real designs must follow your local codes and be checked by a qualified engineer.

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