Resistor Formulas: Series, Parallel, Divider
Resistor formulas for series and parallel resistance, the voltage divider and power in a resistor, with worked examples and a table of parallel pairs.
The formulas
| To find | Formula |
|---|---|
| Resistors in series | R = R1 + R2 + R3 + … |
| Resistors in parallel | 1 / R = 1 / R1 + 1 / R2 + 1 / R3 + … |
| Two in parallel | R = R1 × R2 / (R1 + R2) |
| Voltage divider | Vout = Vin × R2 / (R1 + R2) |
| Power in a resistor | P = V² / R = I² × R = V × I |
R is in ohms, V in volts, I in amperes and P in watts. The divider formula holds when nothing loads the output. A load in parallel with R2 lowers Vout.
Worked example: series and parallel
- Series: 100 + 220 + 330 = 650 Ω
- Parallel, 100 Ω and 220 Ω: 100 × 220 / (100 + 220) = 68.75 Ω
Worked example: a voltage divider
R1 is 10 kΩ and R2 is 4.7 kΩ, from a 12 V supply.
- Vout = 12 × 4700 / (10000 + 4700) = 3.837 V
- Power in R2: P = 3.837² / 4700 = 3.132 mW
100 Ω in parallel with another resistor
| Pair | Combined |
|---|---|
| 100 Ω and 100 Ω | 50 Ω |
| 100 Ω and 220 Ω | 68.75 Ω |
| 100 Ω and 470 Ω | 82.46 Ω |
| 100 Ω and 1000 Ω | 90.91 Ω |
Frequently asked questions
Why is the parallel resistance smaller than the smallest resistor?
Each resistor adds another path for the current, so the total opposition falls.
How do I find the resistor power rating?
Calculate the power with P = V² / R, then choose a rating of at least twice that value so the resistor runs cool.
Does the divider formula work with a load?
Not directly. Put the load resistance in parallel with R2 first, then use the combined value.
What do the color bands mean?
They give the value and tolerance of the resistor. See the resistor color code page.
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