Series & Parallel Resistor Calculator
Total resistance of resistors in series or parallel, and the best standard pair for a target value
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Finds the equivalent resistance of resistors in series or in parallel, and the pair of standard values that comes closest to a target. Capacitors and inductors work on the same page.
How to use
- Under "Component", choose "Resistors", "Capacitors" or "Inductors".
- On "Series & parallel", type the values separated by commas or spaces, such as 4k7 or 2.2M. The series and parallel totals and the working appear at once.
- For a mixed circuit, open "Mixed circuit" and type an expression such as (100+220)||470: + means series, || means parallel.
- On "Find a pair", enter the "Target value" and choose the "Standard series". Pairs are listed from the smallest error.
How it works
- Resistors in series: R = R₁ + R₂ + …. In parallel: 1/R = 1/R₁ + 1/R₂ + …. For exactly two in parallel, R = R₁ × R₂ ÷ (R₁ + R₂).
- Capacitors work the opposite way: parallel values add, series reciprocals add. Inductors follow the resistor rules, assuming no magnetic coupling.
- The standard series are the IEC 60063 E series: E12, E24 and E96 for resistors, E6, E12 and E24 for capacitors and inductors. The error uses nominal values; real parts have their own tolerance.
- For learning and low-voltage electronics, not for mains wiring.
Questions and answers
- What is the formula for resistors in parallel?
- Add the reciprocals, then take the reciprocal of the sum: 1/R = 1/R₁ + 1/R₂ + …. For n equal resistors it is R ÷ n, so two 10 kΩ resistors give 5 kΩ.
- Why is parallel resistance smaller than the smallest resistor?
- Each extra resistor adds another path for the current. A 100 Ω and a 1 kΩ resistor in parallel give about 90.9 Ω, which is less than 100 Ω.
- How do I make 5k ohms from standard resistors?
- Type 5k into "Find a pair" to see the closest pairs. In E24, for example, two 10 kΩ resistors in parallel give exactly 5 kΩ.
- How do capacitors in series differ from resistors?
- The formulas swap. Capacitors in parallel give C = C₁ + C₂, and in series 1/C = 1/C₁ + 1/C₂. Choose "Capacitors" under "Component" to use these rules.