Series & parallel resistance calculator
Combine two to six resistor values as one explicit all-series or all-parallel network and see the equivalent resistance, formula and sanity check.
The equivalent series resistance is greater than the largest entered resistor, as expected for a series chain.
All-series or all-parallel positive ideal resistors only. No mixed topology, tolerance, rating, frequency or temperature effects.
Included
- Two to six positive resistor values
- One explicit all-series or all-parallel arrangement
- A shared mΩ, Ω, kΩ or MΩ input unit
- Equivalent resistance, base ohms, substitution and magnitude check
Not included
- Mixed series-parallel or bridge networks
- Tolerance, power rating, frequency and temperature effects
- Component or circuit design advice
What this means
In a series chain, the same current passes through every resistor and the equivalent resistance is their sum. It must therefore be greater than the largest component value.
In parallel, every branch has the same voltage and conductances add. The equivalent resistance is the reciprocal of the summed reciprocals and must be below the smallest branch resistance.
All entered values share one unit and are converted to ohms before the equation runs. Empty optional rows are omitted rather than treated as physical zero-ohm branches.
Formula & worked example
series: Rₑq = R₁ + R₂ + … + Rₙ parallel: 1 ÷ Rₑq = 1 ÷ R₁ + 1 ÷ R₂ + … + 1 ÷ Rₙ
100 Ω and 200 Ω
- Series
- 100 Ω + 200 Ω = 300 Ω
- Parallel
- 1 ÷ (1/100 + 1/200) = 66.6667 Ω
The series result exceeds both components; the parallel result is lower than either component.
How this calculation works
The calculation follows the formulas, definitions and assumptions explained on this page. The references below support the method and any stated boundaries.
Official sources
- OpenStax Physics — electrical key equations — Equivalent resistance for N series resistors and N parallel resistors
- NIST — SI units for electric current — The ohm definition and its relationship to volts and amperes
- NIST — metric SI prefixes — Milli, kilo and mega factors used by the shared resistance unit control