Norton equivalent calculator

This calculator performs that source transformation directly: it divides the signed source voltage by the positive series resistance to obtain Norton current, then carries the same resistance into the parallel branch. The result is useful when writing node-voltage equations, combining current sources, or simplifying a linear resistive network before further analysis.

Enter the source using a consistent reference polarity

Start with the voltage-source form of the two-terminal network: an ideal source voltage in series with a resistance. Enter the source voltage in volts and the series resistance in ohms. The resistance must be finite and greater than zero because the conversion divides by it, and because a zero-ohm ideal voltage source does not have a finite Norton current. Voltage may be positive, zero, or negative. Its sign records the polarity you chose for the original source and therefore controls the sign of the resulting current. Before entering a negative voltage, keep the same terminal labels and reference direction throughout your schematic; changing both the polarity labels and the numeric sign would reverse the source twice. The calculator accepts ordinary decimal or scientific-notation values and returns amperes and ohms. The optional precision setting controls displayed rounding without changing the underlying relationship. Unit prefixes are not inferred, so convert millivolts, kilohms, or megohms to volts and ohms first, or scale every quantity carefully before interpreting the amperes in the result.

Understand the Norton transformation

The conversion uses two equations: I_N = V_S / R_S and R_N = R_S. Norton current is the short-circuit current that the original voltage source and series resistor would deliver at the selected output terminals. The resistance does not receive a reciprocal or any other numerical transformation; it simply moves from a series position in the voltage-source representation to a parallel position in the current-source representation. These two networks have the same terminal voltage for every external load in a linear resistive circuit. You can verify the result by connecting a load resistance to either form and comparing the load voltage or current. With the Norton form, current division gives the load current. With the original form, the series circuit gives the same value. A negative Norton current is valid and means the actual source current points opposite to the positive reference direction described by your source-voltage polarity. The formula text included in the output makes the convention explicit and helps preserve calculation context in reports or automated node-analysis pipelines.

Use the result in node-based circuit analysis

Norton form is especially convenient for nodal analysis because current sources enter Kirchhoff current equations directly and parallel conductances combine cleanly. Place the returned current source between the same two terminals as the original branch, orient its positive reference consistently, and place the returned resistance in parallel with it. If several transformed branches meet at one node, sum their signed source currents according to your chosen current convention and add their conductances, where each conductance is 1/R. The transformation applies to ideal independent sources with linear series resistance and also to a larger linear two-terminal network after you have found its open-circuit voltage and equivalent resistance. It does not by itself determine the equivalent resistance of a network containing dependent sources, nonlinear devices, frequency-dependent impedance, or active operating-point effects. For AC phasor circuits, the same structural idea uses complex impedance rather than a single real resistance, which is outside this calculator’s real-number input contract. Treat rounded output as presentation data; retain enough precision when the value will feed another calculation, particularly when nearly cancelling signed currents are combined.