ElectroHub

Series and Parallel Resistance Calculator

Add as many components as you like and get the equivalent value. Resistors and capacitors follow opposite rules, which is the detail exams test and the one most often reversed under pressure.

Series / Parallel

Resistors: series adds (R₁ + R₂ + …), parallel is 1 / (1/R₁ + 1/R₂ + …).

Series
Parallel
  1. 1.Given: 100 Ω, 220 Ω
  2. 2.FormulaSeries adds: Rₛ = R₁ + R₂ + …SubstituteRₛ = 100 + 220ResultRₛ = 320 Ω
  3. 3.FormulaParallel uses reciprocals: 1/Rₚ = 1/R₁ + 1/R₂ + …Substitute1/Rₚ = 1/100 + 1/220ResultRₚ = 68.75 Ω
Common trap: Adding a resistor in parallel always lowers the total resistance — every extra branch is another path for current. The combined value is always smaller than the smallest branch.

The formula

Series: R = R₁ + R₂ + … | Parallel: 1/R = 1/R₁ + 1/R₂ + … (capacitors are the reverse)

Rₙ
each resistance in the group (ohms)
Cₙ
each capacitance in the group (farads)
R, C
the single equivalent component

Worked example

100 Ω, 220 Ω and 330 Ω.

  1. In series: R = 100 + 220 + 330 = 650 Ω
  2. In parallel: 1/R = 1/100 + 1/220 + 1/330
  3. 1/R = 0.01 + 0.004545 + 0.003030 = 0.017576

650 Ω in series, 56.9 Ω in parallel — always below the smallest resistor.

Where you'll use it

Reducing a network before applying Ohm's law, and the sanity check that catches arithmetic slips: a parallel result larger than the smallest resistor is always wrong.

The laws behind it

Parts this applies to

Resistor (fixed)Potentiometer / Rheostat / TrimmerResistor Array / NetworkThermistor (NTC / PTC)Varistor / MOVSupercapacitorLED (light-emitting diode)MOSFET

Related calculators

Circuit SolverR_series = R₁ + R₂ + …Ohm's Law CalculatorV = I × RStar-Delta Transformation CalculatorΔ→Y: R_a = (R_ab × R_ca) / (R_ab + R_bc + R_ca)Thévenin and Norton Equivalent CalculatorV_th = open-circuit voltage