Series & Parallel Resistor Calculator
Combine up to six resistors and see the equivalent resistance, currents, voltages and which part runs hottest.
Step-by-step
- Enter valid values to begin.
Ideal resistors at DC or low frequency; no tolerance, temperature coefficient or lead inductance. Leave a field blank to leave that resistor out; an entered 0 is treated as a short. With a current source and several shorted branches the current is assumed to split equally between them (real wiring resistance would decide). Pairs mode groups used resistors in order; an odd last resistor sits alone in its branch. The 50% utilisation band is a common derating practice, not a standard; use the manufacturer power-versus-temperature derating curve for the real limit.
Series and Parallel Resistors: Where the Current and the Heat Actually Go
Core Engineering Principles
Series resistors share one current, so the voltage divides in proportion to resistance and the biggest resistor dissipates the most heat. Parallel resistors share one voltage, so the current divides in inverse proportion and the smallest resistor takes the largest current and the largest slice of power. It decides what burns. We see it often: someone builds a 100 Ω dummy load from four 400 Ω parts in parallel and assumes each carries a quarter of the power. It does, but only because the values match. Swap in one 390 Ω part and it quietly runs hottest.
Parallel equivalent resistance is always smaller than the smallest branch, and a 0 Ω branch makes it exactly zero, which on a voltage source is a fault, not a calculation. Real parts also come in E-series preferred values (IEC 60063), so we use series-parallel pairs to hit a target the catalogue lacks and tolerance then stacks. Rating is per part, too. A network that needs 0.63 W in total still fails if one 1/4 W resistor takes 0.31 W of it.
Two in parallel: Req = R1R2 / (R1 + R2) • Power: P = I²R = V²/R
NEC & Standard References
IEC 60063 defines the E-series preferred values (E6, E12, E24, E96 and so on) that fixed resistors are made in. IEC 60115-1 is the generic specification for fixed resistors for electronic equipment, covering rated power, rated temperature and the derating curve above it. Read the datasheet for the power-versus-ambient curve and maximum working voltage, because a high-value resistor can hit its voltage limit before its power limit.1. Branch A = 100 + 220 = 320 Ω; branch B = 470 + 330 = 800 Ω.
2. Req = 320 × 800 / 1120 = 228.6 Ω.
3. IA = 12 / 320 = 37.5 mA and IB = 12 / 800 = 15 mA, so the total is 52.5 mA.
4. Power: R1 = 0.141 W, R2 = 0.309 W, R3 = 0.106 W, R4 = 0.074 W; the total is 0.63 W, which matches 12 V × 52.5 mA.
5. R2 runs at 62% of its 1/2 W rating, above our usual 50% derating target. We move R2 to a 1 W part, which brings it to 31%.
- Rating is per resistor, not per network. Check the hottest part, which is usually the largest value in a series branch.
- Derate for heat. Rated power applies at a stated ambient, and on a crowded board the allowed dissipation falls well below the headline figure.
- A shorted or open part changes the sharing. If one parallel branch opens, the survivors take more current than you designed for.
- Watch the voltage rating. Each part must stay under its own maximum working voltage.
- Pulse loads need a pulse rating. A part safe at average power can still fail on a short energy burst.