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Calculate series and parallel resistance

Enter the values of the resistors and choose how they are connected. The calculator finds the total resistance and shows the working.

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The value of each resistor.

Ω

Separate the values with semicolons or spaces, for example 10; 20; 30.

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Worked example
  • Connection: Series
  • Resistances: 10 Ω; 20 Ω; 30 Ω

Result

Resistance

60 Ω

Working

  1. R = R₁ + R₂ + …
    10 Ω + 20 Ω + 30 Ω = 60 Ω

The connection determines how the resistors add up

In a series connection, the resistors are placed one after the other. In a parallel connection, they are spread over branches between the same two points. The same set of resistors therefore gives different results depending on the connection.

Enter the values in Ω separated by semicolons or spaces. Then choose series or parallel. The calculator finds the total resistance for the chosen connection.

Formulas for series and parallel

In series the values are added: R = R₁ + R₂ + …. The result gets larger when a positive resistance is added to the series.

In parallel, R = 1 / (1/R₁ + 1/R₂ + …) is used. First the reciprocal of each resistance is found, then they are added, and finally the reciprocal of the sum is taken. For positive resistances, the result is smaller than the smallest single resistance.

Examples of both connections

10 Ω, 20 Ω and 30 Ω in series give 10 + 20 + 30 = 60 Ω.

For two 10 Ω resistors in parallel, the working is 1 / (1/10 + 1/10) = 1 / (0.1 + 0.1) = 1 / 0.2 = 5 Ω.