Resistor Parallel / Series Calculator
Enter between two and eight resistor values to instantly see the total series resistance (R = R₁ + R₂ + …) and parallel resistance (1/R = Σ 1/Rᵢ). Each row has its own unit (mΩ / Ω / kΩ / MΩ / GΩ), blanks are skipped, so you can prototype a circuit, pick a substitute for an out-of-stock value, or sanity-check a physics-class problem.
Resistor values cannot be negative.
Series total
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Parallel total
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Resistors used: —
Min / max: —
Formula
Series: R = R₁ + R₂ + … + Rₙ Parallel: 1/R = 1/R₁ + 1/R₂ + … + 1/Rₙ
Blank rows are skipped automatically. The parallel total is always ≤ the smallest resistor; the series total is always ≥ the largest. A 0 Ω resistor (a short) forces the parallel total to 0.
Formula
Series: R_total = R₁ + R₂ + … + Rₙ Parallel: 1 / R_total = 1/R₁ + 1/R₂ + … + 1/Rₙ → R_total = 1 / Σᵢ (1/Rᵢ)
- · Unit shortcuts: mΩ = 0.001 Ω, kΩ = 1,000 Ω, MΩ = 1,000,000 Ω, GΩ = 10⁹ Ω. Each row can use a different unit.
- · Bounds: all resistor values must be ≥ 0 — negatives trip a rose error banner immediately.
- · Invariants: the parallel total is always ≤ the smallest resistor; the series total is always ≥ the largest. Use this as a free sanity check.
- · Short-circuit case: a 0 Ω resistor in parallel forces the total to 0 Ω (1/0 is handled explicitly so the result stays well-defined).
- · Scope: this tool computes the equivalent total only — it does not split voltage / current. For power dissipated in each resistor (P = I²R or V²/R), use a separate Ohm-law calculator.
- · Common E12 (5 %) preferred values: 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 — pick from these if you want a buildable real-world combination.
Frequently asked
Two identical resistors in parallel — what is the total?
Half. R || R = 1 / (1/R + 1/R) = 1 / (2/R) = R/2. So two 100 Ω in parallel → 50 Ω, two 1 kΩ in parallel → 500 Ω. More generally, N identical R in parallel = R/N. This is one of the most useful shortcuts in practical electronics — handy when you need a 500 Ω with only 1 kΩ in your parts bin.
Why is 6 Ω in parallel with 3 Ω not 4.5 Ω?
Because in parallel it is the conductances (1/R) that add, not the resistances themselves. 1/R_total = 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2, so R_total = 2 Ω — smaller than the smallest of the two (3 Ω). Parallel totals are always strictly less than the smallest resistor; that is the quickest way to spot-check an answer.
What happens if I leave some rows blank?
Blank rows are skipped — they are not treated as 0 Ω shorts. This lets you keep up to eight slots reserved while comparing different combinations (e.g. "3 resistors" vs "4 resistors") without adding and removing rows each time. If you actually want a short, type 0 explicitly.
Can it work backwards — pick standard values to hit a target?
There is no automatic solver, but iterating is fast: look up where your target sits among the E12 preferred values (10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 × 10ⁿ); if you need something smaller than a standard value, parallel two larger ones (parallel always goes smaller); if larger, series two smaller ones. Adjust the rows and watch the totals plus the min / max range update live — you usually converge in a few tries. Example: to hit 1.5 kΩ, try 2.2 kΩ ∥ 4.7 kΩ ≈ 1.50 kΩ.
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