What is the difference between series and parallel resistor connections?

In series, resistances add directly (Req = R1 + R2 + ...). In parallel, reciprocals add (1/Req = 1/R1 + 1/R2 + ...), making the equivalent lower than the smallest branch.

Can I mix units like Ω, kΩ, and MΩ?

Yes. The calculator converts all inputs to ohms internally, so you can mix units freely.

Does the tool round to preferred E-series values?

Optionally, yes. You can round the equivalent resistance to the nearest E6, E12, or E24 preferred value.

How accurate are the results?

Results are mathematically exact given your inputs. Real-world components have tolerances, temperature coefficients, and loading effects that can shift actual values.

Series and Parallel Resistor Calculator

Q: How many resistors can I add?

Practically as many as you need for a calculation. For usability we recommend up to 50 per network.

Q: Why can’t I enter 0 Ω?

A 0 Ω branch in parallel collapses the equivalent to 0 Ω and is uncommon in practical design. To avoid undefined or unsafe results, this calculator requires strictly positive values.

Quickly compute the equivalent resistance of any number of resistors connected in series or in parallel. Built for engineers, students, and makers, this mobile-first tool supports mixed units (Ω, kΩ, MΩ), inline validation, E-series rounding, and shareable deep links.

Calculator

Connection type

Series Parallel

Decimal precision

Optional rounding to preferred E-series

Resistors

Results

Equivalent resistance (auto unit) —

Equivalent resistance (Ω) —

Equivalent conductance (S) —

Nearest preferred value —

Enter at least one valid resistor value to see results.

Data Source and Methodology

Authoritative reference: “Resistors in Series and Parallel”, All About Circuits Textbook, Volume I — Direct Current (DC), Chapter 5, accessed 2025-09-14. Direct link to source. All calculations are strictly based on the formulas and data provided by this source.

Preferred-number series: IEC 60063: Preferred number series for resistors and capacitors (E6, E12, E24). Used here to provide optional rounding to standard values.

The Formula Explained

Series: \\( R_{eq} = \sum_{i=1}^{n} R_i \\)

Parallel: \\( \\dfrac{1}{R_{eq}} = \\sum_{i=1}^{n} \\dfrac{1}{R_i} \\quad \\Rightarrow \\quad R_{eq} = \\left(\\sum_{i=1}^{n} \\dfrac{1}{R_i}\\right)^{-1} \\)

Conductance relation: \\( G = \\dfrac{1}{R} \\), where \\(G\\) is in siemens (S).

Two-resistor parallel shortcut: \\( R_{eq} = \\dfrac{R_1 R_2}{R_1 + R_2} \\)

Glossary of Variables

Rᵢ (Ω, kΩ, MΩ): Value of the i-th resistor entered in the list.
Connection type: Series or Parallel configuration across all listed resistors.
R_eq: Equivalent resistance of the network.
G_eq: Equivalent conductance (1/R_eq), expressed in siemens (S).
Precision: Display formatting for decimal places (does not affect internal math precision).
Preferred series: Optional rounding of R_eq to the nearest IEC 60063 value (E6/E12/E24).

How It Works: A Step-by-Step Example

Suppose you have three resistors in parallel: 220 Ω, 330 Ω, and 1 kΩ. Select “Parallel” and enter the values. The calculator evaluates:

\\[ \\frac{1}{R_{eq}} = \\frac{1}{220} + \\frac{1}{330} + \\frac{1}{1000} \\;\\Rightarrow\\; R_{eq} = \\left(\\frac{1}{220} + \\frac{1}{330} + \\frac{1}{1000}\\right)^{-1} \\approx 132.5\\,\\Omega \\]

If you enable E12 rounding, the nearest preferred value is 130 Ω. You can copy the results or generate a shareable link to revisit the same setup later.

Frequently Asked Questions (FAQ)

What’s the practical difference between series and parallel?

In series, resistances add directly and the same current flows through each element. In parallel, each branch sees the same voltage and the equivalent resistance becomes lower than any individual branch.

How many resistors can I add?

You can add as many as you need. For usability and performance we suggest keeping it under 50.

Can I mix Ω, kΩ, and MΩ?

Yes. The tool converts every input to ohms internally, so mixed units are handled seamlessly.

Why can’t I enter 0 Ω or negative values?

Mathematically, 0 Ω in parallel forces the equivalent to 0 Ω, and negative resistances are non-physical for passive components. To maintain robust results and prevent undefined states, only positive values are accepted.

Does rounding to E-series change the main result?

No. The primary calculation remains exact. The E-series value is shown as a convenience for selecting a nearby standard component.

Will tolerances and temperature affect the result?

Component tolerances (e.g., ±1%, ±5%) and temperature coefficients shift real-world values. This calculator provides the nominal equivalent based on your inputs.

Tool developed by Ugo Candido. Content verified by CalcDomain Engineering Editorial.
Last reviewed for accuracy on: September 14, 2025.