Series and parallel resistance calculator
Enter up to eight resistances in ohms. You get the total for the same resistors in series and in parallel — and if you add a supply voltage, the current, the branch currents and the voltage across each one.
| Resistor | Series: volts across | Parallel: branch amps |
|---|
Ideal resistors and an ideal supply: connection and wire resistance are left out.
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How it works
Series — one path, so the resistances simply add: RT = R1 + R2 + R3 … The same current flows through every one, and the supply voltage splits between them in proportion to their resistance.
Parallel — every resistor has the full supply voltage across it, and each branch draws its own current, V ÷ R. The currents add up to the total. The total resistance is the reciprocal of the sum of the reciprocals: 1 ÷ RT = 1 ÷ R1 + 1 ÷ R2 + … For just two, the shortcut is product over sum: RT = (R1 × R2) ÷ (R1 + R2).
Worked example
6 Ω and 3 Ω on a 12 V supply
- Series: 6 + 3 = 9 Ω. Current 12 ÷ 9 = 1.333 A. Volts across the 6 Ω: 1.333 × 6 = 8 V; across the 3 Ω: 4 V. 8 + 4 = 12 ✓.
- Parallel: product over sum, (6 × 3) ÷ (6 + 3) = 18 ÷ 9 = 2 Ω.
- Branch currents: 12 ÷ 6 = 2 A and 12 ÷ 3 = 4 A. Total 6 A — and 12 ÷ 2 Ω = 6 A ✓.
Three equal resistors
- Three 30 Ω resistors in parallel. Equal branches: divide one by how many there are.
- 30 ÷ 3 = 10 Ω. (The long way: 1/30 + 1/30 + 1/30 = 3/30 = 1/10, so 10 Ω.)
Questions people ask
Why is the parallel total smaller than the smallest resistor?
Every branch you add is another path for current. More paths means more total current for the same voltage, and more current for the same voltage is what less resistance means. So two 10 Ω resistors in parallel make 5 Ω, and adding a 1,000 Ω branch still lowers the total a little.
What about a combination circuit?
Reduce it in pieces. Work out each parallel group with this calculator, write the group down as one resistor, then add the groups and the single resistors in series. The combination circuits lesson walks through one step by step.
What if one resistance is 0 Ω?
In parallel, a 0 Ω branch is a dead short across all the others: the total is 0 Ω and, with a supply connected, the current is limited only by the supply and its protection. The calculator shows 0 Ω and no current figure for that case.
Related
- Series circuits — the lesson behind this tool.
- Parallel circuits — the lesson behind this tool.
- Combination circuits — the lesson behind this tool.
- Series / parallel practice drill — work them by hand, marked as you go.
- Series vs parallel lighting — the same idea on a lighting circuit.
- Ohm’s law calculator
- Resistor colour code calculator
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