Series and parallel resistance
In series, current has one path and resistances simply add: Rtotal = R₁ + R₂ + … . The total is always larger than the largest resistor in the chain.
In parallel, current splits across the branches and the conductances add: 1/Rtotal = 1/R₁ + 1/R₂ + … . The total is always smaller than the smallest branch — a quick sanity check for any result. For exactly two resistors the familiar shortcut applies: Rtotal = (R₁ × R₂) / (R₁ + R₂), and N equal resistors in parallel give R/N.
Worked examples
Series: 1 kΩ + 2.2 kΩ + 470 Ω = 3.67 kΩ.
Parallel: 1 kΩ ∥ 2.2 kΩ: (1000 × 2200) / (1000 + 2200) = 687.5 Ω — smaller than 1 kΩ, as expected.
Why the reverse solver exists
Resistors only come in standard E-series values: E12 (±10%) has 12 values per decade, E24 (±5%) has 24, E96 (±1%) has 96. When your circuit calls for 3.5 kΩ, no single E24 part matches — but a 3.3 kΩ + 200 Ω series pair hits it exactly, and both are stock E24 values. Enter a target above and the solver searches every sensible combination for you.
Frequently asked questions
- Does the order of series resistors matter?
- Not for the total resistance — addition is addition. It can matter for other reasons (voltage rating across each part, tapping a midpoint as a divider).
- What about power ratings?
- Each resistor must handle its own dissipation: I²R in series (same current through all), V²/R in parallel (same voltage across all). In a parallel bank the smallest resistor runs hottest.
- Do tolerances add up?
- Worst case, yes — two 5% resistors in series can be off by 5% combined. Statistically errors partially cancel, but for precision work use E96 1% parts or better.
- Need volts and amps too?
- Once you have the total resistance, the Ohm's law calculator turns it into currents and power.