What this calculator does
Wiring resistors in parallel always gives a total resistance lower than any single resistor in the group, because each extra branch gives current another path to flow through. This parallel resistor calculator adds up to four resistors at once and returns the combined resistance, using the standard reciprocal-sum formula rather than the shortcut that only works for exactly two.
The two-resistor shortcut, R1×R2÷(R1+R2), is quick but stops working the moment a third resistor joins the circuit. The general formula, 1/Rtotal = 1/R1 + 1/R2 + 1/R3 + 1/R4, handles any of those cases the same way, which is why it is what this calculator uses throughout, whether two, three or four resistors are entered.
The formula
Take the reciprocal of each resistor value, add those reciprocals together, then take the reciprocal of that sum to get the total. Leave a resistor at 0 to exclude it: only positive values are included in the calculation.
| Term | Meaning |
|---|---|
| R1, R2, R3, R4 | The resistance of each resistor in the parallel group, in ohms. |
| Rtotal | The combined resistance of the whole parallel group, always smaller than the smallest individual resistor. |
The inputs explained
| Field | What to enter |
|---|---|
| Resistor 1 (Ω) | The first resistor in the parallel group. |
| Resistor 2 (Ω) | The second resistor in the parallel group. |
| Resistor 3 (0 = not used) (Ω) | A third resistor, if there is one. Leave at 0 to use only two resistors. |
| Resistor 4 (0 = not used) (Ω) | A fourth resistor, if there is one. Leave at 0 to use only two or three resistors. |
When to use it
Combining stock resistor values
The exact resistance a circuit needs is rarely a value that comes off the shelf. Wiring two or more standard resistors in parallel is a common way to land closer to an odd target value.
Working out a load bank or heater array
Multiple identical heating elements or resistive loads wired in parallel present the supply with a combined resistance well below any single element, which matters for sizing the supply and its wiring.
Checking a measured resistance against a design
If a multimeter reading across a parallel network does not match what the reciprocal-sum formula predicts, one of the resistors is likely open, shorted or reading outside its tolerance.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How total resistance changes as a second resistor is added
One 100 Ω resistor in parallel with a second resistor of varying size.
| Second resistor | Total parallel resistance |
|---|---|
| 50 Ω | 33.333 Ω |
| 100 Ω | 50.000 Ω |
| 150 Ω | 60.000 Ω |
| 220 Ω | 68.750 Ω |
| 330 Ω | 76.744 Ω |
| 470 Ω | 82.456 Ω |
Total resistance of several identical resistors in parallel
The same 100 Ω resistor value, with a third identical resistor added to the group.
| Third resistor | Total parallel resistance |
|---|---|
| Not used (2 resistors) | 50.000 Ω |
| 100 Ω added (3 resistors) | 33.333 Ω |
Questions
What is the parallel resistor formula?
1/Rtotal = 1/R1 + 1/R2 + 1/R3 + ... for however many resistors are in the group. Take the reciprocal of the final sum to get the total resistance, which this calculator does for up to four resistors at once.
Is total resistance in parallel always lower than each resistor?
Yes. Adding a parallel path always gives current an extra route, so the combined resistance is always lower than the smallest individual resistor in the group, never higher and never in between.
Can I use this for just two resistors?
Yes. Leave the third and fourth fields at 0 and the calculator treats the group as two resistors, which also matches the simpler R1×R2÷(R1+R2) shortcut that only applies to exactly two resistors.
What about resistors in series instead?
Series resistance is simpler: it is just the sum of the individual values, R1+R2+R3+..., with no reciprocals involved. This calculator is specifically for the parallel case.
To solve for voltage, current or power in a single resistor rather than a combined network, see the Ohm's law calculator. To read a resistor's value from its colour bands, see the resistor colour code calculator.