Series & Parallel Resistor Calculator
- Series total
- 1.47 kΩ
- Parallel total
- 319.728 Ω
- Resistors
- 2 values
How to Use the Series & Parallel Resistor Calculator
Combining resistors in series and parallel is foundational circuit analysis. Series strings add resistance for voltage division and current limiting; parallel groups reduce resistance to increase current capacity or create precise non-standard values from stock parts. Every breadboard prototype, LED current set resistor, and input termination network starts with these two formulas.
Series total resistance:
Rtotal = R1 + R2 + … + Rn
Parallel total resistance:
1/Rtotal = 1/R1 + 1/R2 + … + 1/Rn
For two parallel resistors the shortcut is Rtotal = (R1 × R2) / (R1 + R2). All values must be positive; zero-ohm jumpers in series add nothing, but parallel branches with one zero ohm dominate the network (short circuit).
Standard E12 resistor values cover most needs, but parallel combinations hit awkward targets — two 10 kΩ in parallel give 5 kΩ; 1 kΩ parallel with 4.7 kΩ yields 823 Ω, close to an unavailable E12 value. Power dissipation splits in parallel: each branch carries current inversely proportional to its resistance.
Worked example: An LED needs 20 mA from a 5 V supply with 2 V forward drop. Required resistor R = (5−2)/0.02 = 150 Ω. No 150 Ω in the kit — use 100 Ω + 47 Ω in series = 147 Ω (19.7 mA, acceptable). Alternatively 220 Ω parallel with 470 Ω: R = (220×470)/(220+470) = 150 Ω exactly. Power in the 220 Ω leg: I²R = 0.02² × 220 × (470/(220+470))² — verify each resistor stays below its ¼ W rating.
Feed results into the voltage divider calculator when the network forms a tap point, or the RC time constant calculator when a capacitor sits across the equivalent resistance.
E12 standard resistor values (subset)
| Decade | Values (Ω) | Example pair | Parallel result |
|---|---|---|---|
| 1–8 Ω | 10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82 | 47 ∥ 56 | 25.5 Ω |
| 10–82 Ω | 100, 120, 150, 180, 220, 270, 330, 390, 470, 560, 680, 820 | 220 ∥ 470 | 150 Ω |
| 100–820 Ω | 1k, 1.2k, 1.5k, 1.8k, 2.2k, 2.7k, 3.3k, 3.9k, 4.7k, 5.6k, 6.8k, 8.2k | 1k ∥ 4.7k | 826 Ω |
| 1k–8.2k Ω | Same ratios ×1k | 2.2k + 1k series | 3.2 kΩ |
| 10k–82k Ω | Same ratios ×10k | 10k ∥ 10k | 5 kΩ |
| 100k–820k Ω | Same ratios ×100k | 100k + 22k series | 122 kΩ |
Frequently asked questions
This tool handles pure series or pure parallel groups. Complex networks require reducing one section at a time or using nodal analysis.
Try two E12 resistors in parallel or series. Standard pairs often land within 1–2% of target values.
Total power splits among branches. Each resistor dissipates I²R for its branch current — size each part for its share.