What this calculator does
Resistors wired end to end in series simply add up, which is the easy case. Wired side by side in parallel they do the opposite: the total drops below the smallest resistor in the group, because every extra path gives current another route to take.
This calculator works out both arrangements at once from the same set of values, so the difference between wiring a pair one way and the other is visible on a single screen. Leave the third and fourth boxes at zero to work with just two resistors.
The formula
For series, add the resistances together. For parallel, add the reciprocals of each resistance and take the reciprocal of that total. The current figures apply Ohm's law at 12 volts to each result, as a quick check on what the arrangement would actually draw.
| Term | Meaning |
|---|---|
| Series | Resistors connected one after another, so the same current passes through each in turn and the resistances add. |
| Parallel | Resistors connected across the same two points, so the current splits between them and the total resistance falls. |
| Ohm (Ω) | The unit of resistance. One ohm passes one amp when one volt is applied across it. |
The inputs explained
| Field | What to enter |
|---|---|
| R₁ (Ω) | The first resistance, in ohms. |
| R₂ (Ω) | The second resistance, in ohms. |
| R₃ (0 to ignore) (Ω) | A third resistance, if there is one. Leave at zero to ignore it. |
| R₄ (0 to ignore) (Ω) | A fourth resistance, if there is one. Leave at zero to ignore it. |
When to use it
Making up a value you do not have
Two common resistors in series or parallel will often land close to an awkward value that is not in the drawer, and this shows which combination gets nearest.
Checking a divider or load
Knowing the combined resistance tells you the current the arrangement will draw, which is what determines whether the parts are within their power rating.
Understanding an existing circuit
Working out the equivalent resistance of a group is usually the first step in simplifying a circuit down to something that can be analysed by hand.
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 do series and parallel totals compare for a 100 Ω resistor paired with another?
A 100 ohm resistor paired with a range of second values.
| R₂ | Series total | Parallel total |
|---|---|---|
| 100 Ω | 200.000 Ω | 50.000 Ω |
| 220 Ω | 320.000 Ω | 68.750 Ω |
| 470 Ω | 570.000 Ω | 82.456 Ω |
| 1000 Ω | 1,100.00 Ω | 90.909 Ω |
Questions
Why is the parallel total always smaller than the smallest resistor?
Because adding another path can only make it easier for current to flow, never harder. Every resistor added in parallel increases the total current at a given voltage, which by Ohm's law means the equivalent resistance has fallen.
What happens with two equal resistors in parallel?
The total is exactly half of one of them. Three equal resistors give a third, four give a quarter, and so on, which is a useful shortcut worth remembering.
Does the order of the resistors matter?
No. Series resistances add and parallel reciprocals add, and addition does not care about order. Physically rearranging the same resistors in the same configuration gives the same total.
What about power ratings?
This calculates resistance and current, not the power each individual resistor dissipates. In a series chain the same current passes through all of them, so the largest resistance dissipates the most power, which is worth checking against the parts' ratings.
For voltage and current from resistance directly, see the Ohm's law calculator. For the same series and parallel question applied to capacitors, where the rules are reversed, see the capacitors in series and parallel calculator.