Series & Parallel Resistance Calculator

In series the resistances simply add:

R = 100 + 220 + 330 = 650 Ω  →  I = 12/650 = 18.5 mA (the same through every resistor)

In parallel the conductances add:

1/R = 1/100 + 1/220 + 1/330 = 0.0175758 S  →  R = 56.897 Ω

Sanity check that always works: a parallel combination is always smaller than the smallest resistor in it. 56.9 Ω is below 100 Ω, so the result is plausible. If a parallel answer ever comes out larger than any single branch, the arithmetic is wrong.

Ohm's law mode is the same relation with two knowns: 12 V at 2 A gives R = 6 Ω and P = VI = 24 W.

Equivalent resistance tells you the current. What burns components is the power in each individual resistor, and series and parallel behave in opposite ways.

In series the largest resistor dissipates the most (it drops the most voltage at common current). In parallel the smallest does (it draws the most current at common voltage). The 100 Ω part goes from 34 mW to 1.44 W — a factor of 42 — purely by changing the topology.

That matters because a standard 0.25 W resistor is fine in the series case and will fail in the parallel one. And rated power assumes a specified ambient, typically 70 °C, with a derating curve above it: a part rated 0.25 W at 70 °C may be good for only half that at 100 °C inside an enclosure. Size on the derated figure at your actual ambient, and check voltage rating separately — a high-value resistor can exceed its maximum working voltage long before it reaches its power limit.

Ideal, purely resistive elements. Real resistors have parasitic inductance (significant in wirewound types) and shunt capacitance. Below a few hundred kilohertz this is irrelevant; at RF a resistor stops behaving like one, and the impedance — not the resistance — governs.

DC or low-frequency AC only. With capacitance or inductance in circuit, use impedance and phasors. The arithmetic here has no phase information.

Linear and ohmic. Diodes, transistors, lamps, thermistors and LEDs are not resistors and cannot be combined this way. An incandescent lamp's cold resistance can be a tenth of its hot value.

No temperature effect. Resistance drifts with temperature by the temperature coefficient, quoted in ppm/°C: around 50–100 ppm/°C for ordinary thick-film parts, under 25 ppm/°C for precision thin-film. Over a 100 °C rise a 100 ppm/°C part shifts 1%, which can exceed its stated tolerance. Self-heating causes this even at constant ambient.

Nominal values, not real ones. Standard resistors come from the IEC 60063 preferred series — E12 at ±10%, E24 at ±5%, E96 at ±1%. In series the absolute tolerances add, so three ±5% parts give a worst-case ±5% on 650 Ω, or roughly ±33 Ω. Where a ratio matters, as in a divider or an amplifier gain network, specify tolerance explicitly and consider that matched parts in one package track far better than two separate ones.

No wiring resistance. Contact resistance, track resistance and connector resistance are ignored. At low resistance and high current they stop being negligible — which is why four-wire measurement exists.

Preferred values: IEC 60063 defines the E3 to E192 series. Designing to an arbitrary value you cannot buy is a common beginner error — pick from the series, or make the value from a combination.

Marking: IEC 60062 covers the colour code and alphanumeric marking, including the tolerance band.

Component specification: IEC 60115 for fixed resistors for use in electronic equipment, covering rated power, rated voltage, the derating curve and endurance testing. MIL-PRF-55342 for high-reliability chip resistors.

Next steps: after finding the equivalent resistance, calculate the power in each resistor separately, then derate for your enclosure ambient rather than the datasheet's 70 °C. Check maximum working voltage on high-value parts. If the network sets a precision ratio, work out the tolerance stack rather than assuming nominal values, and check the temperature coefficient against the drift you can tolerate. For anything above audio frequency, move from resistance to impedance.