calculator
Series and parallel resistor calculator
Two or three resistors, wired end-to-end or side-by-side, act like a single resistor. This works out the equivalent value, the current the battery ends up pushing, and the heat in each part — with the exact circuit running below.
The answer
Req = 1.02 kΩ
R1 + R2 + R3 = 220 Ω + 330 Ω + 470 Ω = 1.02 kΩ
- Series adds up: 220 Ω + 330 Ω + 470 Ω = 1.02 kΩ
- Total current (Ohm's law, I = V ÷ R): 4.5 V ÷ 1.02 kΩ = 4.41 mA
- Total heat (P = V × I): 4.5 V × 4.41 mA = 19.9 mW
- Nearest single E12 resistor: 1 kΩ
Each resistor
| Resistor | Voltage across | Current through | Heat |
|---|---|---|---|
| R1 = 220 Ω | 0.97 V | 4.41 mA | 4.28 mW |
| R2 = 330 Ω | 1.46 V | 4.41 mA | 6.42 mW |
| R3 = 470 Ω | 2.07 V | 4.41 mA | 9.15 mW |
In series, the same current flows through every resistor and each takes a share of the battery voltage in proportion to its size.
simulating…
Series: one path, same current
Two resistors in series are like two toll booths on a one-lane road — every electron has to pay both. The equivalent resistance is the sum: Req = R1 + R2 (+ R3…). Because it's a single loop, the same current flows through every resistor. Each one takes a share of the battery voltage in proportion to its size, which is exactly what a voltage divider is.
Parallel: two paths, more current
Two resistors in parallel are two lanes on a wider road — each electron picks a lane. Every resistor sees the full battery voltage on its own, but the battery has to supply all the currents added together. The equivalent resistance is smaller than the smallest one: 1 / Req = 1/R1 + 1/R2 (+ 1/R3…). Two equal resistors in parallel come out as half the value; three equal ones, a third; and so on.
Why you'd ever do this
Real resistors come in fixed E12 steps (…100, 120, 150, 180, 220, 270…). If you need 150 Ω but only have 220s, two 220 Ω in parallel give 110 Ω — close enough for many circuits, and their combined heat rating is doubled too, which matters for a resistor sizing calculation that's pushing a single part over ¼ W. Series is the other direction: two 470 Ω in series make 940 Ω when your box only stops at 470.
The pizza mnemonic
Series adds up. Parallel is one-over-the-sum-of-one-over. If it ever looks wrong, sanity check the answer: series should always be bigger than any single resistor; parallel should always be smaller. If not, one of the numbers is off.
Common questions
What about mixed circuits — some series, some parallel? Simplify from the inside out. Combine the two resistors that are clearly in parallel first, then treat the result as one resistor and keep going. Any resistor network reduces to a single number this way.
What if one branch of a parallel pair is a wire (0 Ω)? The current takes the free lane and ignores the other resistor: Req = 0. That's a short circuit, and on a battery it drains fast. The "why is my LED so dim?" troubleshooter has an example.
Do the resistor's power ratings add? In series they see the same current, so heat splits by resistance. In parallel they see the same voltage, so heat splits by 1/R — the smallest resistor gets the most heat. Either way, the total heat is V × I from the battery.
See resistor combinations in Traffic Light (three LED branches in parallel) and Two Greens (two LEDs and their resistors in series), or read the Ohm's law skill for the underlying formula.