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Resistors in Series and Parallel Calculator

Physics

How are they connected?

Conductances add, so the result is always smaller than the smallest member. Every resistor sees the full supply voltage, and the smallest one carries the most current and burns the most power.

Optional. Leave blank for the equivalent resistance alone.

Resistor values

brown · black · brown · gold

red · black · brown · gold

orange · black · brown · gold

Paste a list instead

Separate values with commas, spaces or new lines. Each may carry its own suffix — 4k7, 4.7k, 1M2 and 220R all work, and m means milliohm where M means megaohm.

Equivalent resistance
54.545 Ω

54.545 Ω exactly

Conductance
18.333 mS

G = 1 / R_eq

Total current
220.000 mA

I = V / R_eq

Total power
2.640 W

P = V² / R_eq

Sanity check

Smaller than the smallest resistor (100.000 Ω) — parallel always reduces resistance. The same parts in series would give 600.000 Ω.

0 to 10. Exports use the same setting.

Circuit diagram

12.000 VR1100.000 Ω120.000 mAR2200.000 Ω60.000 mAR3300.000 Ω40.000 mA

One pair of nodes, one voltage: the labels under each branch are the branch currents.

Shown working

Formula

1/R_eq = 1/R₁ + 1/R₂ + … + 1/Rₙ

Substitute

1/R_eq = 1/(100.000 Ω) + 1/(200.000 Ω) + 1/(300.000 Ω)

Add the conductances

1/R_eq = 10.000 mS + 5.000 mS + 3.333 mS = 18.333 mS

Invert

R_eq = 1 / 18.333 mS = 54.545 Ω

Result

R_eq = 54.545 Ω

Total current

I = V / R_eq = 12.000 V / 54.545 Ω = 220.000 mA

Total power

P = V² / R_eq = (12.000 V)² / 54.545 Ω = 2.640 W

Conductance

G = 1 / R_eq = 18.333 mS

Step-by-step reduction chain

1

100.000 Ω ‖ 200.000 Ω = 66.667 Ω

2

66.667 Ω ‖ 300.000 Ω = 54.545 Ω

Per-resistor breakdown

ResistorResistanceCurrentVoltage dropPower% of ΣRRating
R1100.000 Ω120.000 mA12.000 V1.440 W16.7 %

—

R2200.000 Ω60.000 mA12.000 V720.000 mW33.3 %

—

R3300.000 Ω40.000 mA12.000 V480.000 mW50.0 %

—

Share of the total power dissipated — the bar length is the heat, and the caption is the share of ΣR.

R1

1.440 W · 16.7 % of ΣR

R2

720.000 mW · 33.3 % of ΣR

R3

480.000 mW · 50.0 % of ΣR

Wattage recommendation

The hardest-worked part is R1 at 1.440 W.

Minimum 2 WWith 50 % derating 3 W

The minimum figure only just covers the dissipation. Fitting the derated part keeps the resistor cool enough that its value does not drift with self-heating.

Tolerance range

51.818 Ω

54.545 Ω

57.273 Ω

Worst case across the entered tolerances — a spread of 10.0 % of nominal. Both rules rise monotonically with every member, so these corners really are the extremes.

Nearest standard value to R_eq

E24: 56.000 Ω (+2.67 %)E96: 54.900 Ω (+0.65 %)

If a single stock resistor lands close enough, use it instead of the network. The Design tab searches for two-resistor combinations when it does not.

Check the wattage before you build it

R1 dissipates 1.440 W, so it needs at least a 2 W part — or a 3 W one if you want the usual 50 % derating.

Why the two rules point opposite ways

In series there is one loop, so the same current crosses every resistor and the drops add: R_eq = R₁ + R₂ + … + Rₙ. In parallel there is one pair of nodes, so every branch sees the same voltage and the branch currents add — which means the conductances add, 1/R_eq = 1/R₁ + 1/R₂ + … + 1/Rₙ. That is why a parallel result can never exceed the smallest branch: adding a path can only make it easier for current to get through.

Note that this is the exact mirror of how capacitors behave — capacitances add in parallel and combine reciprocally in series, because capacitance rises with plate area and falls with plate separation.

Conductance in the results panel is measured in siemens, with 1 S = 1/Ω. It is the natural quantity for a parallel bank because it is the thing that adds: a 1 kΩ resistor contributes exactly 1 mS, so three of them make 3 mS and therefore 333.33 Ω.

About This Tool

Resistors in Series and Parallel – Equivalent Resistance, Current and Power

Combining resistors is the first piece of circuit analysis anyone learns, and the two rules point in opposite directions. In series the resistances add, R_eq = R₁ + R₂ + … + Rₙ, because the same current has to push through every drop in turn. In parallel the conductances add, 1/R_eq = 1/R₁ + 1/R₂ + … + 1/Rₙ, because each branch offers the current another route. This resistors in series and parallel calculator evaluates either rule for any number of resistors, mixes units freely, and then works out how current, voltage and dissipated power divide across the network.

Why parallel resistance is always below the smallest branch

Adding a parallel branch never removes an existing path, so the total conductance can only rise — and its reciprocal, the resistance, can only fall. That gives a free sanity check on every parallel answer: it must come out below the smallest member. Three resistors of 100 Ω, 200 Ω and 300 Ω in parallel sum to 18.333 mS of conductance and therefore 54.545 Ω, comfortably under the 100 Ω branch. Series obeys the mirror-image rule: 220 + 330 + 1000 = 1550 Ω, always above the largest member. For exactly two in parallel the reciprocal identity collapses into the familiar product over sum shortcut, R_eq = R₁·R₂ / (R₁ + R₂), and for N identical parts it reduces further to N·R in series and R/N in parallel.

How current, voltage and power divide

This is where the two topologies genuinely behave differently. In a series string the current is common — one loop, one current — so I = V/R_eq and the supply divides in proportion to resistance, Vᵢ = I·Rᵢ. The biggest resistor drops the most voltage and burns the most power. In a parallel bank the voltage is common, so Iᵢ = V/Rᵢ and the current divides inversely with resistance: the smallest branch carries the most current and runs the hottest. Either way Pᵢ = Vᵢ·Iᵢ = Iᵢ²·Rᵢ = Vᵢ²/Rᵢ, and the per-resistor figures must sum back to P = V²/R_eq for the whole network.

Worked example

A 220 Ω and a 330 Ω resistor in series across 12 V give R_eq = 550 Ω, so I = 21.818 mA. The 220 Ω part drops 4.8 V and dissipates 104.7 mW; the 330 Ω part drops 7.2 V and dissipates 157.1 mW. An ordinary 1/4 W part covers both with room to spare.

Choosing a wattage rating

Equivalent resistance alone will not tell you whether a circuit is safe to build. Once a supply voltage is entered, the calculator reports the power dissipation of every resistor and names the smallest catalogue rating — 1/8 W, 1/4 W, 1/2 W, 1 W, 2 W, 5 W — that covers the worst one. Common practice is to derate: pick a part rated at roughly twice the calculated dissipation, so it runs warm rather than hot. Paralleling is also a legitimate way to raise the power budget, because four 4.7 Ω 1 W resistors share the heat and handle 4 W between them while presenting 1.175 Ω.

A 0 Ω entry in parallel is a short

A zero-ohm branch shorts out the whole bank: the equivalent resistance collapses to 0 Ω and the branch current is unbounded. The calculator rejects it with an explanation rather than printing Infinity.

Standard values, tolerance and reverse solving

Real resistors come only in the IEC 60063 preferred series — E6, E12, E24, E48, E96 and E192 — whose steps are spaced so that neighbouring values just overlap at the series’ nominal tolerance (E24 with ±5 %, E96 with ±1 %). The standard value matcher snaps any target to its nearest stock part and searches for the best two-resistor series or parallel combination, which is how awkward values such as 750 Ω get built from parts you already own. Reverse solve answers the same question from the other end: given a target and one resistor in hand, R₂ = R_target − R₁ for a series partner and R₂ = R₁·R_target / (R₁ − R_target) for a parallel one — so a 1 kΩ resistor reaches 750 Ω with a 3 kΩ part in parallel.

The tolerance range recomputes the network with every component at its low extreme and again at its high extreme. Both combination rules increase monotonically with each individual value, so those corners really are the worst cases: two 1 kΩ ±5 % resistors in parallel give 500 Ω nominal with a true 475 Ω – 525 Ω envelope. Combining parts does not average tolerance away — plan for the band, or trim after assembly.

Frequently Asked Questions

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How does this resistors in series and parallel calculator work?

Enter your resistor values in whatever units they came in — mΩ, Ω, kΩ, MΩ and GΩ can be mixed freely in one network — and pick series or parallel. Every value is normalised to ohms before any arithmetic runs, resistances are added directly for series or reciprocally for parallel, and the single unrounded equivalent resistance then drives the current, voltage-drop, power and conductance outputs. Because nothing is rebuilt from a rounded intermediate, the displayed voltage drops still sum to the supply in series and the branch currents still sum to the total in parallel.

Why is parallel resistance always smaller than the smallest resistor?

Because adding a parallel branch adds another path for current without removing any existing one. Conductances add, 1/R_eq = 1/R₁ + 1/R₂ + …, so the total conductance is necessarily larger than any single branch's, and its reciprocal is necessarily smaller than any single resistance. Two 1 kΩ resistors in parallel give 500 Ω, and 100 Ω ‖ 200 Ω ‖ 300 Ω gives 54.545 Ω — below the 100 Ω branch. Series works the other way: the drops add, so R_eq is always above the largest member.

How do I know what wattage resistor to fit?

Enter a supply voltage and the calculator reports the dissipation of every resistor from P = V×I, then names the smallest catalogue rating that covers the worst one. In a series string the largest resistor drops the most voltage and so burns the most power; in a parallel bank it is the smallest resistor, because it carries the most current. Common practice is to derate — pick a part rated at roughly twice the calculated dissipation — so the tool suggests that figure as well. A resistor run at its limit drifts high, discolours, and eventually goes open circuit.

What are E6, E12, E24, E48, E96 and E192 series?

They are the IEC 60063 preferred-value tables that real resistors are manufactured to. Each series divides a decade into equally spaced logarithmic steps — 6, 12, 24, 48, 96 or 192 of them — sized so that consecutive values just overlap at the series' nominal tolerance: E24 pairs with ±5 % parts, E96 with ±1 %, E192 with ±0.5 %. The calculator snaps any target to its nearest preferred value and also searches for the best two-resistor series or parallel pair, which is how odd values such as 750 Ω or 3.6 kΩ get built from stock parts.

Does the tolerance range assume the worst case?

Yes, and it is genuinely the worst case rather than an estimate. Both combination rules increase monotonically with every individual resistance, so the extreme equivalent resistances fall out of the all-low and all-high corners — no interior combination can land outside them. Two 1 kΩ ±5 % resistors in parallel give 500 Ω nominal with a true 475 Ω to 525 Ω envelope. Note that combining parts does not average their tolerance away: the network keeps roughly the tolerance of its members.

How accurate is this for a real circuit?

The network arithmetic is exact for the values you enter, but real resistors are not ideal. Manufacturing tolerance, the temperature coefficient (which shifts the value as the part self-heats), lead and PCB-trace resistance in the milliohms, and contact resistance at connectors and breadboards all move the measured figure away from the calculated one. Treat the result as accurate for the nominal values entered, and expect a measured network to land somewhere inside the tolerance band rather than exactly on the nominal figure.