Parallel Resistor Calculator

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Enter two or more resistor values to find the single resistor value that would act the same in a parallel circuit. This is sometimes called the “equivalent resistance”.

For two resistors: Req = (R1 x R2) / (R1 + R2)
For N resistors in parallel: 1 / Req = sum(1 / Ri)
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How to use the Parallel Resistor Calculator

Steps

  1. Enter Resistor 1 (R1) and choose the unit (ohm, kOhm, or MOhm).
  2. Enter Resistor 2 (R2) and choose the unit.
  3. Optional: Open “Advanced options” and enter R3, R4, and R5. Leave any of them blank to ignore.
  4. Click Calculate to get the equivalent resistance (Req).

Quick checks

  • Req is always lower than the smallest resistor in the set.
  • If all resistors are equal (value R) and you enter N of them, Req should be about R / N.

How this Parallel Resistor Calculator works

What “parallel” means

Resistors are in parallel when they share the same two nodes. Each resistor has the same voltage across it. The total current is the sum of the branch currents. Using Ohm’s law (I = V / R), this leads to a conductance sum.

General formula (N resistors in parallel)

The calculator uses the standard equivalent resistance equation for resistors in parallel: 1 / Req = (1 / R1) + (1 / R2) + … + (1 / RN). It computes the sum of reciprocals, then takes the reciprocal to get Req. See: Khan Academy (parallel resistors), Wikipedia (series and parallel circuits).

Two-resistor shortcut

When there are only two resistors, the calculator can check the result with the common shortcut: Req = (R1 x R2) / (R1 + R2). This is algebraically equivalent to 1 / Req = 1 / R1 + 1 / R2. See: All About Circuits (two-resistor form), Analog Devices wiki (parallel circuits defined).

Why Req is lower than the smallest resistor

Each added parallel resistor increases total conductance, so equivalent resistance decreases. That is why Req is always below the smallest branch resistance for a valid parallel set. See: Wikipedia (parallel resistance property).

Sources

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