Enter the open-circuit voltage and short-circuit current to calculate the norton equivalent, or quickly converter Thevenin to Norton.

Norton’s Theorem Calculator

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Enter the open-circuit voltage and short-circuit current to find the Norton equivalent. Load resistance is optional.

Use either side below. Enter a complete pair, then calculate to convert instantly.

Thévenin to Norton
Norton to Thévenin

Norton’s Theorem Formula

The following formula is used to calculate the load current according to Norton’s Theorem. 

I_L = I_{SC}\,\frac{R_{TH}}{R_{TH}+R_L}

Variables:

  • I_L is the load current (Amps)
  • I_{SC} is the short circuit current (Amps)
  • R_{TH} is the Thévenin equivalent resistance (Ohms)
  • R_L is the load resistance (Ohms)

To calculate the load current using Norton’s Theorem, use current division: multiply the short circuit (Norton) current by the ratio of the equivalent resistance to the total parallel resistance, RTH/(RTH+RL).

What is Norton’s Theorem?

Norton’s Theorem is a simplification technique used in circuit analysis. According to the theorem, any linear two-terminal electrical network (including independent/dependent sources) can be replaced at terminals A-B by an equivalent current source (I_{SC}) in parallel with an equivalent resistance (R_{TH}). (For AC analysis, the same idea applies using impedances instead of resistances.) This theorem is used to simplify the analysis of circuits by reducing them to a basic equivalent circuit, making calculations easier to manage.

How to Calculate Load Current using Norton’s Theorem?

The following steps outline how to calculate the load current using Norton’s Theorem.

  1. First, determine the short circuit current (I_{SC}) in Amps.
  2. Next, determine the Thévenin equivalent resistance (R_{TH}) in Ohms.
  3. Next, determine the load resistance (R_L) in Ohms.
  4. Next, gather the formula from above: I_L = I_{SC} × R_{TH}/(R_{TH}+R_L).
  5. Finally, calculate the load current (I_L) in Amps.
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Short circuit current (I_{SC}) = 5 Amps

Thévenin equivalent resistance (R_{TH}) = 10 Ohms

Load resistance (R_L) = 20 Ohms