Series and parallel calculator
Resistors, capacitors or inductors, in series or in parallel. Capacitors are the other way round from resistors, which is the commonest mistake in the subject. Nothing you type here leaves your browser — it is worked out on your own device, so there is nothing to send and nothing to log.
Capacitors are the other way round
This is the single most common mistake in the subject, and it is easy to see why once you know the reason.
| Resistors in series | Add. The current goes through both, so the opposition adds. |
|---|---|
| Resistors in parallel | Reciprocal sum. The current splits, so the total is always less than the smallest one. |
| Capacitors in parallel | Add. You are making the plates bigger. |
| Capacitors in series | Reciprocal sum. You are making the gap wider. |
| Inductors | Same way round as resistors. |
Parallel resistance is always less than the smallest one
Always, with no exceptions, and it is the fastest sanity check there is. Put 1 Ω in parallel with 1 MΩ and you get 0.999999 Ω, not something in the middle. If a parallel answer comes out bigger than any of the parts, the arithmetic is wrong.
Two equal resistors in parallel are exactly half one of them; three equal are a third. That is worth remembering because it covers most of what people actually do.
Tolerance does not cancel out
Combine two 5% resistors and the result is still roughly 5%, not 2.5% — the errors are independent, so they partly cancel on average and the worst case does not improve at all. If you need a value more accurate than you can buy, the answer is a more accurate part or a trimmer, not more parts.
Parallel is how you make a value that does not exist
This is what the combination is mostly for. Resistors are only made at preferred values — the E series — so E24 gives you twenty-four per decade and nothing in between. Need 1,200 Ω and you can buy it; need 1,850 Ω and you cannot.
Two in parallel will get you there. 3.9 kΩ beside 3.6 kΩ is 1,872 Ω; 2 kΩ beside 27 kΩ is 1,862 Ω. Two in series is the other way. Neither is free: two 5% parts in parallel are still about 5%, so you have bought a value you could not otherwise have, not an accuracy you could not otherwise have.
In parallel, the smallest resistor does most of the work
The voltage across them is the same, so the current through each goes as 1/R and the power as V²/R. Put a 10 Ω beside a 1 kΩ and the 10 Ω dissipates a hundred times as much. The tool above gives the split, because a resistor that gets hot is the one that fails.
What it will not do
- It will not handle networks that are neither series nor parallel. A bridge circuit — five resistors in a diamond — cannot be reduced this way at all; it needs a delta-star transform or a matrix.
- It will not account for magnetic coupling between inductors sat near each other, which changes the answer and is a real effect.
- It will not include equivalent series resistance, lead inductance, or any of the other ways a real component is not the ideal one.