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Resistor Network Calculator

Compare two different arrangements of the same three resistors. The series result assumes one current path through all three; the parallel result assumes every resistor connects across the same two nodes. These are alternatives, not two measurements of one unspecified network. Use the output that matches your circuit diagram. A series equivalent exceeds each positive input, while a parallel equivalent is below the smallest input.

Enter every field, including explicit zeros when permitted. Decimal and scientific notation are accepted; commas, fractions and blanks are rejected. Each input must be finite and no larger than 1 billion in absolute value. Observe the units and positive-value requirements below.

Series equivalent (Ω)600
Parallel equivalent (Ω)54.54545455

How to use this calculator

  1. Match your inputs to the stated circuit model and field labels.
  2. Convert your quantities to the units printed next to each field.
  3. Select Calculate, or press Enter, and read the labeled results.

Formula and method

Rseries = R1 + R2 + R3; Rparallel = 1/(1/R1 + 1/R2 + 1/R3).

The calculation runs in your browser. After changing an input, select Calculate again. Invalid inputs or undefined mathematical conditions hide the previous result so it cannot be mistaken for an answer to the new values.

Worked example

For 100 Ω, 200 Ω and 300 Ω, the series total is 600 Ω. The parallel equivalent is 600/11 ≈ 54.54545455 Ω.

Limitations and safety

Ideal-component calculation only. Component tolerance, heating, parasitic effects and frequency limits are not modeled. This output does not establish component ratings, wiring compliance or a safe circuit design. Have consequential designs checked by a qualified professional; do not use this tool as instructions for working on energized equipment. Mixed series-parallel networks and zero-resistance shorts are outside this three-component model.

The fields accept signed numerical input, but positive-only component values and nonnegative time or frequency requirements are enforced by the calculation. Read each error message before changing a value. Results use floating-point arithmetic and are shown to approximately 10 significant digits; component tolerances generally do not justify using all those digits in a physical design.

Frequently asked questions

Why is parallel resistance smaller than any input?

Parallel branches provide additional current paths. The reciprocal-sum formula gives an equivalent below the smallest positive branch resistance.

Why are my units important?

The calculator uses exactly the units printed in the input labels. For example, a micro-unit is one millionth of a base unit, and a milli-unit is one thousandth. Entering a base-unit value into a prefixed-unit field changes the meaning of the input.

Does the answer establish a safe component rating?

No. The formula evaluates an ideal model. Ratings, tolerances, transients, installation requirements and environmental limits need a separate design assessment.

Review notes and reference

Reviewed October 3, 2026. The default worked example and an additional boundary or scaling check were tested against expected values. Validation checks included blanks, nonnumeric text and inputs outside the supported range. OpenStax University Physics formula reference provides the circuit theory behind this model. The text and worked example on this page are original.

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