Resistors combine in two ways. In series the values simply add, raising resistance. In parallel the reciprocals add, lowering it — the total is always below the smallest branch. This calculator takes a list of resistor values and reports both the series and parallel totals.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: series & parallel resistance laws, recomputed in code.
The formulas
For exactly two resistors in parallel there's a handy shortcut — the product over the sum: Rt = R₁R₂ / (R₁ + R₂). With n equal resistors in parallel, the total is just one value divided by n. Series strings split voltage in proportion to resistance; parallel branches split current, with more current through lower-resistance paths.
Worked examples
10, 20, 30 Ω:
Four 4 Ω resistors:
10 Ω with 20 Ω (two-resistor shortcut):
A practical set like 1 kΩ, 2.2 kΩ and 4.7 kΩ totals 7,900 Ω in series but about 600 Ω in parallel — the parallel value sits just under the smallest resistor, as always.
Frequently Asked Questions
1/Rt = Σ(1/R). 10, 20, 30 Ω → ≈ 5.45 Ω, below the smallest.
Rt = ΣR. 10 + 20 + 30 = 60 Ω.
Product over sum: R₁R₂/(R₁+R₂). 10 ∥ 20 = 200/30 ≈ 6.67 Ω.
More paths for current lowers total R. n equal resistors give R/n.
Separate by commas, spaces or new lines, e.g. 10, 20, 30.