Add as many resistors as you need, switch between series and parallel wiring, and get the combined resistance instantly.
Combining resistors is one of the most fundamental skills in circuit design — whether you're building a voltage divider, adjusting an LED's brightness, or creating a specific resistance value from parts you have on hand. The equivalent (total) resistance of a network depends entirely on whether the resistors are wired in series, in parallel, or in some combination of both.
For resistors in series (connected end-to-end in a single path), the total resistance is simply the sum of all individual resistances: Rtotal = R1 + R2 + R3 + …. The same current flows through every resistor in the chain, since there's only one path for it to take. Adding resistors in series always increases total resistance.
For resistors in parallel (connected across the same two points, forming multiple paths), the reciprocal of total resistance equals the sum of reciprocals: 1/Rtotal = 1/R1 + 1/R2 + 1/R3 + …. The same voltage appears across every branch, but current splits between them based on each branch's resistance. Adding resistors in parallel always decreases total resistance — the result is always lower than the smallest individual resistor in the group.
For exactly two resistors in parallel, there's a simpler shortcut: Rtotal = (R1 × R2) / (R1 + R2) — this avoids dealing with reciprocals directly.
Two resistors of 220Ω and 330Ω: In series, Rtotal = 220 + 330 = 550Ω. In parallel, using the two-resistor shortcut: Rtotal = (220 × 330) / (220 + 330) = 72,600 / 550 = 132Ω. Notice the parallel result (132Ω) is lower than even the smallest resistor (220Ω) — this is always true for parallel combinations.
For three or more resistors, say 100Ω, 220Ω, and 330Ω in parallel: 1/Rtotal = 1/100 + 1/220 + 1/330 = 0.01 + 0.00455 + 0.00303 = 0.01758. So Rtotal = 1/0.01758 ≈ 56.9Ω.
Combining standard resistor values lets you create resistances that aren't available as single off-the-shelf parts. Standard resistors follow the E12 or E24 series (12 or 24 values per decade), so if your circuit needs an odd value like 175Ω, combining two standard-series resistors (like 150Ω + 27Ω in series ≈ 177Ω) gets you close without needing a custom part. It's also common in power distribution — splitting current across multiple parallel resistors to divide the heat load, since each resistor only handles a fraction of the total power.
Real circuits often combine both — some resistors in series, feeding into a parallel group, or vice versa. The standard approach is to reduce the network step by step: identify a purely series or purely parallel sub-group, calculate its equivalent resistance, replace those resistors with a single equivalent value, and repeat until you're down to one resistor. For networks that can't be reduced this way (bridges, meshes with multiple sources), you need full nodal analysis — see our Resistor Network Solver for those cases.
Equivalent resistance is only one part of a real design. Before finalizing your resistor selection, also check: power rating (each resistor must dissipate its actual power without overheating — see our LED Resistor Calculator for a worked power calculation example), voltage rating (especially relevant for series combinations across high voltage), tolerance (±1% to ±20% depending on resistor type — tighter tolerance costs more but matters for precision circuits), and temperature coefficient (how much resistance drifts with heat, more significant in tightly-toleranced precision applications).
Is parallel resistance always lower? Yes — for any set of positive resistor values, the equivalent parallel resistance is always lower than the smallest individual resistor in the group.
Does series resistance always increase? Yes — series resistances add directly, so the total is always at least as large as the largest individual resistor.
What happens if I put a 0Ω resistor in parallel with anything? The combined resistance becomes 0Ω (a short circuit) — the 0Ω path completely dominates since current always takes the path of least resistance.
Can I use this for capacitors or inductors instead? No — capacitors combine with the opposite logic (parallel capacitors add directly, series capacitors use the reciprocal formula), and inductors follow the same rules as resistors. This calculator is resistor-specific.
Why does my parallel calculation give a very small number? That's expected behavior — parallel resistance is always smaller than any individual resistor, sometimes dramatically so if the values are very different (a 10Ω resistor in parallel with a 10,000Ω resistor gives a result very close to 10Ω, not an average of the two).
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