The Series/Parallel Resistor Calculator combines the functionality of both a Series Circuit Calculator and a Parallel Resistor Calculator. It allows you to calculate the total resistance for circuits with resistors arranged in series or parallel configurations. This calculator supports up to 10 resistors, making it versatile for various circuit designs. Simply enter the resistor values in the provided fields, and the total resistance for a parallel or series circuit will be calculated instantly. You can input resistor values in ohms (Ω), kilohms (kΩ), or megohms (MΩ) for added convenience.

Parallel and Series Resistor Calculator

Resistor Calculator

Calculate the equivalent resistance for resistors in series or parallel.

* Enter resistor values (in Ω) separated by commas.

Step 1: Enter Resistor Values

Separate multiple values with commas

Formulas:

Series: $$R_{eq} = R_1 + R_2 + \dots + R_n$$
Parallel: $$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots + \frac{1}{R_n}$$
How the Series/Parallel Resistor Calculator Works

How the Series/Parallel Resistor Calculator Works

The Series/Parallel Resistor Calculator is designed to compute the total resistance of circuits with resistors in series, parallel, or mixed configurations. Understanding the underlying formulas can help you use this tool effectively.

Key Concepts

  • Resistors in Series: In a series configuration, resistors are connected end-to-end, and the total resistance is the sum of the individual resistances. 
    Total Resistance (Rtotal) = R₁ + R₂ + ... + Rₙ
  • Resistors in Parallel: In a parallel configuration, resistors are connected across the same two points, and the reciprocal of the total resistance is the sum of the reciprocals of the individual resistances. 
    1 / Rtotal = 1 / R₁ + 1 / R₂ + ... + 1 / Rₙ

How the Calculator Works

  1. Select the Configuration: Choose whether your circuit is a series, parallel, or mixed configuration.
  2. Input Resistor Values: Enter the resistance values for up to 10 resistors in the input boxes provided.
  3. Choose the Unit: Specify the unit for each resistor:
    • Ohms (Ω)
    • Kilohms (kΩ)
    • Megohms (MΩ)
  4. Calculation Process: The calculator uses the following logic based on your selected configuration:
    • For Series Circuits: The calculator adds all resistance values directly using the formula: 
      Rtotal = R₁ + R₂ + ... + Rₙ
    • For Parallel Circuits: The calculator computes the reciprocal of the total resistance using: 
      1 / Rtotal = 1 / R₁ + 1 / R₂ + ... + 1 / Rₙ
      Then, it inverts the result to find the total resistance: 
      Rtotal = 1 / (1 / R₁ + 1 / R₂ + ... + 1 / Rₙ)
  5. Instant Results: Once you enter the resistor values, the total resistance is displayed immediately. Results are provided in the unit you selected.

Worked Example

Example: Calculate the total resistance for a circuit with the following resistors:

  • Series: R₁ = 10Ω, R₂ = 20Ω, R₃ = 30Ω
  • Parallel: R₁ = 10Ω, R₂ = 20Ω, R₃ = 30Ω

Series Calculation:

Rtotal = 10 + 20 + 30 = 60Ω

Parallel Calculation:

1 / Rtotal = 1 / 10 + 1 / 20 + 1 / 30
1 / Rtotal = 0.1 + 0.05 + 0.0333 = 0.1833
Rtotal = 1 / 0.1833 ≈ 5.46Ω

The calculator performs these computations automatically and displays the results for your selected configuration.

Conclusion

The Series/Parallel Resistor Calculator simplifies complex resistance calculations for electrical circuits, making it a valuable tool for students, engineers, and hobbyists.