How to use it
- Choose Components: Resistors, Capacitors or Inductors.
- Type each value in Values, one per line, for example 4.7k, 10k and 2.2k. Clear the box and start again to try another list.
- Read Series total and Parallel total.
- Open Working, step by step to see the formula with every value in it.
The rules
Resistors in series add up, because the same current passes through each one. Resistors in parallel share the voltage, so the total conductance is the sum of the conductances: the parallel resistance is the reciprocal of the sum of the reciprocals. Two equal resistors in parallel give half of one of them.
Resistors and inductors:
series R = R1 + R2 + … + Rn
parallel R = 1 ÷ (1 ÷ R1 + 1 ÷ R2 + … + 1 ÷ Rn)
Capacitors (the rules are swapped):
series C = 1 ÷ (1 ÷ C1 + 1 ÷ C2 + … + 1 ÷ Cn)
parallel C = C1 + C2 + … + Cn- Capacitors in parallel add their capacitance; capacitors in series give a smaller total than the smallest one.
- The total of resistors in parallel is always smaller than the smallest of them.
- Inductors follow the resistor rules only when they do not couple magnetically (no shared core or nearby fields). Coupled inductors need the mutual inductance, which this calculator does not include.
What this calculator does not cover
- Series and parallel networks mixed together. Work out each group first, then combine the results.
- Tolerance, power rating and voltage rating of the parts. The total of a capacitor string also depends on how the voltage is shared between its parts.
- AC impedance of capacitors and inductors at a given frequency: the totals here are the component values, not the impedance.
Worked example: 4.7 kΩ, 10 kΩ and 2.2 kΩ
In series: R = 4.7 kΩ + 10 kΩ + 2.2 kΩ = 16.9 kΩ.
In parallel: 1 ÷ (1 ÷ 4.7 kΩ + 1 ÷ 10 kΩ + 1 ÷ 2.2 kΩ) = 1 ÷ 0.00076731 = 1.303 kΩ, which is smaller than the smallest resistor.
For capacitors of 100 nF and 47 nF the rules swap: in series C = 1 ÷ (1 ÷ 100 nF + 1 ÷ 47 nF) = 31.97 nF, and in parallel C = 100 nF + 47 nF = 147 nF.
Frequently asked questions
Why are capacitors in series the opposite of resistors?
Capacitors store charge, and a chain of capacitors shares one charge along the chain, so the voltages add and the total capacitance falls. Resistors in series share the current and add their resistance.
How do I combine two resistors in parallel quickly?
Multiply them and divide by their sum: R = R1 × R2 ÷ (R1 + R2). For 4.7 kΩ and 10 kΩ that is 47 ÷ 14.7 = 3.197 kΩ.
Can I enter the values with prefixes?
Yes. Type 4k7, 4.7k, 100n or 2µ2; the calculator reads the prefix and shows the total with the prefix that fits it best.
What happens if one value is zero?
A zero resistor in parallel shorts the whole group, so the parallel total is zero. A zero capacitor in series does the same for the series total. The calculator shows a note when this happens.
Do the same rules apply to inductors?
Yes, when the inductors are far enough apart that they do not couple magnetically. Coupled inductors need their mutual inductance.
Sources
Figures and text last checked on Tuesday, November 10, 2026.