Series and Parallel Calculator
Total resistance, capacitance or inductance for parts in series or parallel, plus network expressions like (1k + 2k) || 3k with k, µ, n and p prefixes.
The interactive tool loads here when JavaScript runs.
About this toolWhat is the Series and Parallel Calculator?
Type a list of values and this series and parallel calculator gives the total for all of them in series and all of them in parallel. Switch between resistors, capacitors and inductors and the rules change with it: resistors and inductors add in series, capacitors add in parallel.
For anything more tangled than one string or one bank, use the network expression box. Write + for "in series with" and || (or //) for "in parallel with", group with brackets, and the calculator works out the total. (1k + 2k) || 3k is 1.5 kΩ; 4k7 + (2k2 || 2k2) is 5.8 kΩ. Values take engineering prefixes, so 4.7k, 4k7, 100n, 10u, 10µ and 22p all work.
The list mode also shows how a parallel bank shares the load: the percentage of current each resistor or inductor carries, or the share of charge each capacitor stores.
- Resistors, capacitors and inductors with the right rule for each
- Network expressions with +, || and brackets
- Engineering prefixes and RKM codes (4k7, 2R2) accepted
- Current or charge share of each part in a parallel bank
- Clear errors that point at the value or bracket at fault
- Shareable link and copyable result
How to use the Series and Parallel Calculator
- Choose Resistors, Capacitors or Inductors.
- Type the values into the list, separated by commas or spaces. Use prefixes: k and M for resistors, p, n, u (or µ) and m for capacitors and inductors.
- Read the series and parallel totals. The table shows each part's share of current (or charge) in the parallel case.
- For a mixed network, type an expression such as (220 + 330) || (470 + 100) in the expression box, or click a sample to start.
- Copy the results or share a link to the network you entered.
Worked examples
Three resistors
Input
100, 220, 330 Ω
Output
Series 650 Ω; parallel 56.897 Ω
In parallel the 100 Ω resistor carries 56.9% of the current, the 330 Ω only 17.2%. The total is below the smallest resistor, as it always is.
Two strings in parallel
Input
(220 + 330) || (470 + 100)
Output
279.91 Ω
Each string totals 550 Ω and 570 Ω; in parallel they give a little under half of either. Handy for making an odd value from stock parts.
Electrolytic capacitors for a bulk supply rail
Input
Capacitors 10u, 22u, 47u
Output
Parallel 79 µF; series 5.9977 µF
Parallel is the normal way to add bulk capacitance. In series the total falls below the smallest part, and the voltage splits unevenly in proportion to 1/C.
Capacitor network
Input
(100n || 220n) + 470n
Output
190.38 nF
100 nF and 220 nF in parallel make 320 nF; 320 nF in series with 470 nF gives 1 ÷ (1/320 + 1/470) = 190.38 nF.
Background and insight
In series the same current flows through every part, so voltages add: for resistors R = R₁ + R₂ + …, and for inductors (with no magnetic coupling between them) L = L₁ + L₂ + …. In parallel the same voltage sits across every part, so currents add, which makes the conductances add: 1/R = 1/R₁ + 1/R₂ + …. Two equal resistors in parallel give half the value; n equal resistors give 1/n of it. A parallel total is always smaller than the smallest part in it.
Capacitors flip the rules because capacitance measures charge stored per volt. In parallel the charges add at the same voltage, so C = C₁ + C₂ + …. In series every capacitor carries the same charge and the voltages add, so 1/C = 1/C₁ + 1/C₂ + …. Two 10 µF capacitors in series make 5 µF, but each only sees half the voltage, which is why series capacitors are used to build up a voltage rating (with balancing resistors across each to share the DC voltage evenly).
The expression mode treats || like multiplication and + like addition, so || binds tighter: 1k + 2k || 2k means 1k + (2k || 2k) = 2 kΩ. Brackets override that, as in ordinary arithmetic. Every value must be greater than zero; a short circuit or open circuit is better reasoned about directly than typed in as 0 or infinity.
Common use cases
Making a value you do not have
Combine stock resistors or capacitors to get close to a calculated value, such as 5.8 kΩ from a 4.7 kΩ and two 2.2 kΩ.
Raising power or voltage ratings
Parallel resistors share dissipation; series capacitors share voltage. Check the total stays where you need it.
Circuit analysis homework
Reduce a resistor ladder or a capacitor network step by step and check the answer.
Speaker and heater wiring
Work out the impedance of speakers or heating elements wired in series, parallel or a mix of both.
Tips and limitations
- Parallel resistors share current inversely to resistance, so the smallest one dissipates the most power. Check its rating, not just the total.
- Capacitors in series do not share DC voltage equally once leakage is involved. Put a balancing resistor across each one when stacking electrolytics for voltage.
- Inductors close together couple magnetically. The simple sums assume no coupling; coupled coils add or subtract twice the mutual inductance.
- Tolerances carry through: a total built from 5% parts is still only good to about 5%.
- In the expression box, m is milli and M is mega. 1m of inductance is 1 mH; 1M of resistance is 1 MΩ.
Frequently asked questions
How do you calculate resistors in series and parallel?
In series, add them: 100 + 220 + 330 = 650 Ω. In parallel, add the reciprocals and invert: 1 ÷ (1/100 + 1/220 + 1/330) = 56.9 Ω. For two resistors the parallel value is also R₁ × R₂ ÷ (R₁ + R₂).
How do capacitors add in series and parallel?
The opposite way to resistors. In parallel capacitances add directly (10 µF + 22 µF = 32 µF). In series you add reciprocals: two 10 µF capacitors in series make 5 µF.
What does the || symbol mean in a circuit expression?
It means "in parallel with". R₁ || R₂ is the combined value of R₁ and R₂ connected in parallel. In this calculator, // means the same, and || is evaluated before + unless brackets say otherwise.
Why is parallel resistance less than the smallest resistor?
Each resistor in parallel is an extra path for current. Adding any path, however poor, lets more current flow at the same voltage, so the combined resistance must drop below that of the best single path.
How do inductors combine in series and parallel?
Like resistors: they add in series and combine reciprocally in parallel, as long as their magnetic fields do not interact. Coupled coils, such as two windings on one core, need the mutual inductance included.
How do I get 5k from standard resistors?
Two 10 kΩ resistors in parallel make exactly 5 kΩ. Other options are 4.7 kΩ + 300 Ω in series, or 5.1 kΩ (E24) as a single part at 2% high.
What is the total of two equal capacitors in series?
Half of one of them. Two 100 nF in series make 50 nF, and each sees half the applied voltage if they are well matched.
Is there an in-depth guide to the Series and Parallel Calculator?
Yes. “Series and Parallel Circuits: Resistors, Capacitors and Inductors” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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