Norton Equivalent Calculator

Norton Equivalent Calculator
IL = IN × RN/(RN+RL)
Vth = IN × RN
RN = Rth
Norton Equivalent — Enter IN, RN and RL
IN Norton Current
Short-circuit current at terminals
RN Norton Resistance
Same as Rth
RL Load Resistance
Enter IN, RN and RL
Norton Load Analysis
Thevenin Equivalent
—
Max Power at RL=RN
—
Load Current IL
—
A
Load Voltage VL
—
V
Load Power PL
—
W
IN (short cct)
—
A
RN
—
Ω
Vth = IN×RN
—
V
Norton Equivalent Circuit IN RN RL IL = IN × RN / (RN + RL) — current divider

Figure 1: The Norton equivalent is a current source IN in parallel with resistance RN. It is the dual of the Thevenin equivalent and produces identical load behaviour. Load current follows the current divider rule.

Table of Contents
Fundamentals
  1. What Is Norton’s Theorem?
  2. How to Find IN and RN
Worked Examples
  1. Current Source with Load
  2. Norton to Thevenin Conversion
  3. Parallel Source Analysis
Deep Dive
  1. Norton vs Thevenin
  2. Applications
Reference
  1. Frequently Asked Questions
  2. Related Circuit Analysis Calculators

What Is Norton’s Theorem?

Norton’s theorem states that any linear two-terminal circuit can be replaced by an equivalent circuit consisting of a current source (IN) in parallel with a resistance (RN). It is the dual of Thevenin’s theorem — where Thevenin uses a voltage source in series, Norton uses a current source in parallel.

The Norton current IN is the short-circuit current at the terminals (the current that flows when the terminals are directly connected). The Norton resistance RN is identical to the Thevenin resistance Rth — the resistance seen looking into the terminals with all independent sources turned off.

How to Find IN and RN

Step 1 — IN: Short-circuit the output terminals. Calculate the current flowing through the short. This is IN.
Step 2 — RN: Turn off all independent sources. Calculate the resistance seen from the terminals. RN = Rth.
Convert: Vth = IN × RN and IN = Vth / Rth

Worked Example — Current Source with Load

Given: IN = 120 mA, RN = 100 Ω, RL = 220 Ω

IL = 0.12 × 100/(100+220) = 37.5 mA (current divider)

VL = 0.0375 × 220 = 8.25 V

PL = 8.25 × 0.0375 = 309 mW

The load current follows the current divider rule: the total Norton current splits between RN and RL inversely proportional to their resistance.

Worked Example — Norton to Thevenin Conversion

Given: IN = 50 mA, RN = 1 kΩ

Vth = 0.05 × 1000 = 50 V

Rth = RN = 1 kΩ

The Thevenin equivalent is a 50 V source in series with 1 kΩ. Both representations produce identical behaviour for any load.

Worked Example — Parallel Source Analysis

Given: Two Norton sources in parallel: IN1 = 100 mA with RN1 = 200 Ω, IN2 = 50 mA with RN2 = 400 Ω

IN(total) = 100 + 50 = 150 mA

RN(total) = 200 ∥ 400 = 133.3 Ω

Norton equivalents in parallel simply add their currents and combine their resistances in parallel — much simpler than combining Thevenin equivalents. This is why Norton form is preferred for parallel source combination. The Parallel Circuit Calculator handles the resistance combination.

Norton vs Thevenin

Both theorems produce equivalent circuits that behave identically at the terminals. Norton is preferred for parallel circuits, current-mode analysis, and when combining multiple sources. Thevenin is preferred for series circuits, voltage-mode analysis, and amplifier modelling. The KVL Circuit Calculator naturally uses Thevenin (voltage) form, while the KCL Circuit Calculator naturally uses Norton (current) form.

Applications

Norton equivalents appear in transistor small-signal models (the output is a current source with output resistance), operational amplifier analysis, current mirror circuits, and any situation where current sources simplify the analysis. The Power Dissipation Calculator helps verify component ratings in the final design.

Frequently Asked Questions

Is Norton the same as Thevenin?
They are equivalent — both produce the same terminal voltage and current for any load. The difference is representation: Thevenin uses a voltage source in series with R, Norton uses a current source in parallel with R. Convert with Vth = IN × RN.
What if RN is zero?
If RN = 0, the Norton equivalent is an ideal current source (infinite output impedance in the Thevenin sense is not applicable). The load always receives exactly IN regardless of RL. Vth = 0 in this case, which is not useful in Thevenin form.
When is Norton better than Thevenin?
When combining parallel sources, when working with current-mode circuits (like current mirrors), when doing nodal analysis, or when the source naturally behaves as a current source (like a transistor collector or a photodiode).
Can I measure IN directly?
In principle, yes — short the terminals and measure the current. In practice, this may damage the circuit if the short-circuit current is too high. It is safer to calculate IN from Vth and Rth.
Series Circuit Calculator Circuit Current Calculator Voltage Drop Calculator Induced Current Calculator Wheatstone Bridge Calculator Magnetic Force Between Wires Calculator Magnetic Force on Wire Calculator

Browse all Electronics Calculators →

Last updated: March 2026