Circuit Analysis & FundamentalsDesign workbench
Thévenin / Norton Equivalent Calculator
Thévenin voltage and resistance, and the Norton current, for the classic source-behind-R1-with-R2-across-the-terminals network — plus load power and the maximum-power-transfer point.
About this calculator
Thévenin's and Norton's theorems say that any linear two-terminal network, however complicated inside, behaves at its terminals exactly like one source behind one resistance. Thévenin's form is a voltage source V_th in series with a resistance R_th; Norton's form is a current source I_N in parallel with the same resistance. Reducing a network to one of these makes it trivial to see what any load will do.
This calculator works the canonical textbook configuration so the reduction is exact and easy to follow: an ideal source V_s behind a series resistor R1, with a resistor R2 bridging the output terminals, feeding a load R_L. It finds the open-circuit terminal voltage V_th = V_s·R2/(R1+R2), the resistance R_th = R1∥R2 seen from the terminals with the source zeroed, and the short-circuit (Norton) current I_N = V_th/R_th. It then attaches your load to the equivalent and reports the load voltage, current, and power — and the maximum-power-transfer point, R_L = R_th, where the load draws the most power the network can deliver.
The scope is deliberately bounded: this is the two-resistor case, not a general network solver. That keeps every step visible — find the open-circuit voltage, deactivate the source and look back for the resistance, convert to Norton — which is exactly the procedure you apply by hand to bigger networks. Use it to learn the method, to reduce a divider-with-source that feeds a load, and to reason about loading and power transfer; for arbitrary multi-loop networks, reduce them to this form first or use nodal/mesh analysis.
Design notes & common mistakes
- This tool is the canonical two-resistor case: source Vs behind R1, R2 across the terminals. Reduce a larger network to this form before comparing.
- R_th is found by deactivating sources — short ideal voltage sources, open ideal current sources — and looking back into the terminals.
- Thévenin and Norton are duals of the same network: R_N = R_th and I_N = V_th / R_th. Convert freely.
- Maximum power transfer (R_L = R_th) delivers the most power but only 50% efficiency — matched loads are for signal power, not for efficient energy delivery.
Assumptions
- The internal network is exactly one ideal source Vs in series with R1, with R2 across the terminals.
- All elements are linear and resistive; the source is ideal (zero internal resistance beyond R1).
- R_th is evaluated with independent sources deactivated (ideal voltage source shorted).
When to use this calculator
Appropriate for
- Reducing a source-with-divider that feeds a load to its Thévenin or Norton equivalent
- Predicting load voltage, current, and power from the equivalent
- Teaching the Thévenin/Norton reduction procedure and maximum power transfer
Not suitable for
- Arbitrary multi-loop networks (reduce to this form first, or use nodal/mesh analysis)
- Networks containing dependent sources or reactive elements
- Efficiency-critical power delivery, where a matched load wastes half the power as heat
What this calculator does not cover
- Restricted to the single-source, two-resistor terminal configuration; it is not a general multi-loop network solver.
- Independent DC sources only — no dependent (controlled) sources, which need the test-source method for R_th.
- Purely resistive and DC; it does not handle reactive elements or an AC Thévenin impedance.
- The maximum-power-transfer result assumes a purely resistive load matched to a resistive R_th.
- As with every calculator on this site: results are preliminary and educational, are not verified for any specific installation, and must be reviewed against the applicable code edition and stamped by a licensed Professional Engineer before real-world use.
Frequently asked questions
How do I find the Thévenin equivalent of a circuit?
Two steps. First, find the open-circuit voltage across the terminals with the load removed — that is V_th. Second, deactivate the independent sources (short ideal voltage sources, open ideal current sources) and find the resistance looking back into the terminals — that is R_th. The Thévenin equivalent is V_th in series with R_th.
What is the relationship between the Thévenin and Norton equivalents?
They are two views of the same network and share the same resistance: R_N = R_th. The Norton current is the short-circuit terminal current, I_N = V_th / R_th, and conversely V_th = I_N · R_th. You can convert between the two forms freely.
When does a load receive maximum power?
When the load resistance equals the Thévenin resistance, R_L = R_th. At that match the load power is P_max = V_th² / (4·R_th). Note that maximum power transfer is only 50% efficient — half the power is lost in R_th — so it is used for signal circuits, not for efficient power delivery.
References
- Irwin, J. D., Basic Engineering Circuit Analysis, 11th ed. (Thévenin and Norton theorems)
- Nilsson, J. & Riedel, S., Electric Circuits, 11th ed. (source transformations, maximum power transfer)
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