One bank, both rules, live arithmetic. Enter each capacitor with its own unit, flip between series and parallel, and watch the total, the working and the equal-value shortcuts update on every keystroke — no calculate button, no unit conversions by hand.
Up to 12 capacitors, each with its own unit. Live on every keystroke.
Design arithmetic rarely lands on a shelf value. The ripple calculation asks for 680 µF while the drawer holds 470 µF parts, the motor nameplate calls for 45 µF while the catalog sells 30 µF and 15 µF, and the bus in front of you sits at 600 V while the highest-rated capacitor in the bin survives 250 V. Combining capacitors is how real designs close that gap: two or more parts wired to behave as one capacitor with the value, the voltage rating or the footprint the circuit actually needs. The two wiring rules behind every bank — series and parallel — are simple, exact, and opposite in what they trade away.
The reasons to combine are practical, not exotic. Bulk capacitance: parallel banks add capacity beyond what any single affordable part reaches — a 5 000 µF rail is easier to build from ten 500 µF cans than to buy as one part. Ripple-current sharing: in a parallel bank the AC ripple current divides between members, so each capacitor heats less than a lone part carrying the whole load would. Voltage: series strings stack ratings, letting 200 V film capacitors sit across a 600 V bus that would destroy any single part you own. Physical size: a low, wide spread of SMD parts sometimes fits under a shield where one tall radial can cannot.
Each direction has a price. Series cuts the capacitance by more than half the moment two parts are involved, and makes every member a shareholder in the string voltage, which must be divided fairly. Parallel multiplies capacitance but keeps the voltage rating of the weakest part in the bank. The calculator above applies both rules at once so the trade stays visible while you type: the total, the working behind it, and the shortcuts that appear the moment your values repeat.
Two rules govern every bankPhoto: UnsplashParallel is the forgiving direction. Wire the capacitors side by side — every lead of one polarity tied together — and each part sees the full bank voltage while the stored charges simply add. The rule is the one everyone hopes for: C_total = C₁ + C₂ + …, with no reciprocals and no surprises. Ten microfarads wired next to twenty-two is thirty-two, every time, in any units, for any number of parts.
Three consequences matter in practice. The voltage rating of a parallel bank is the lowest rating among its members — one 25 V part in a bank of 50 V parts makes it a 25 V bank. The equivalent ESR falls the way parallel resistors do, so a bank of ordinary parts can behave like one low-ESR part, and ripple current divides between members roughly in inverse proportion to their impedance. And tolerance behaves gently: a ±20% error on one small member of a large bank moves the total far less than 20%, because its share of the total is small.
Three parts, one equivalent: 79 µF at the rating of the weakest member. Try it in the calculator above — the three default rows are exactly this bank, and switching to parallel shows 79 µF with the sum written out underneath.
Mixed units are legitimate as long as every value lands in one base before the rule applies: 100 nF is 0.1 µF, and 0.1 + 0.22 = 0.32 µF. The per-row unit selectors in the calculator perform exactly this conversion on the fly.
Series is the strict direction. Connect capacitors end to end and the same charge must pass through every part, so the voltages add while the effective plate spacing — the stack of dielectrics — grows. A larger gap stores less charge per volt, and the rule that captures it is the resistor-parallel form: 1/C_total = 1/C₁ + 1/C₂ + … . Add the reciprocals of every member, then invert the sum. That is the whole rule; everything else is consequences.
Two consequences cover most bench work. First, the equal-value shortcut: N identical capacitors in series give exactly C/N — two 47 µF parts make 23.5 µF, four 100 V parts make one part worth a quarter of the capacitance at four times the voltage. Second, the floor: the series total is always smaller than the smallest capacitor in the string. A 1 µF in series with a 0.1 µF gives 0.0909 µF — just below the small part, because the small part owns the dominant reciprocal term and no amount of extra capacitance can push the total back up.
Two equal parts always halve; N equal parts give C/N. The voltage rating doubles as the capacitance halves — the trade that makes series strings useful, and the reason every member must now survive its share of the string voltage.
The total came out below the smallest member — always. The 0.1 µF part contributes ten times the reciprocal of the 1 µF part, so it dominates the sum. Series wiring can shrink a bank toward zero; it can never grow it.
In a series string the same charge Q sits on every capacitor, and the voltage across each part is Q divided by its own capacitance. Small capacitor, large share: voltage divides in inverse proportion to capacitance. For two parts the sharing is V₁ = V_total × C₂ / (C₁ + C₂) — the partner value appears on top, which is why the smaller capacitor always takes the larger slice of the voltage.
An example makes it concrete. Put a 1 µF and a 2 µF capacitor in series across a 300 V supply. The string capacitance is (1 × 2) / (1 + 2) = 0.667 µF, so the common charge is 0.667 µF × 300 V = 200 µC. The 1 µF member then sees 200 µC ÷ 1 µF = 200 V and the 2 µF member sees 100 V. Two-thirds of the supply landed on the smaller part — exactly the inverse-capacitance rule at work, and the reason the comfortable assumption that a string shares equally between unequal parts ends careers and capacitors.
With film or ceramic capacitors, whose leakage currents are tiny and similar, the ideal division is close to reality. Aluminium electrolytics are another matter: leakage differs widely from part to part and drifts with age and temperature, so the DC voltage across a bare electrolytic string migrates until the leakiest, lowest-value member sits above its rating and begins to fail first. That is why high-voltage electrolytic banks get a balancing resistor across each capacitor — equal-value resistors, often 100 kΩ to 470 kΩ at modest rail voltages, sized to pass several times the worst leakage so the division stays pinned near equal. The resistors bleed a little power continuously and add their own tolerance to the error budget, which is one more reason practical strings carry voltage margin rather than running the parts at their bare ratings.
Series strings earn their complexity where no single part exists: DC link banks above 450 V, vacuum-tube power supplies, supercapacitor stacks that additionally need active balancing, and legacy CRT-era equipment still on the bench. If the target voltage is reachable with one part, one part is nearly always the better answer — fewer failure points, no balancing network, and the full capacitance of every farad you paid for.
The one-line takeaway: in a series string the smallest capacitor takes the largest voltage. Check every member against its rating before powering the bank — and treat electrolytic strings as unbalanced until balancing resistors prove otherwise.
Series strings trade capacitance for voltagePhoto: UnsplashA bank of identical parts is easy to reason about; real bins rarely cooperate. Mixing values is electrically harmless — the rules do not care where the numbers come from — but the bookkeeping is where errors hide, because a schematic that says 100 nF beside one that says 0.22 µF must land in a single unit before any rule applies. Convert everything to one base (µF is the usual working unit), then either add the values or add the reciprocals. The calculator above keeps a unit selector on every row precisely so this conversion never happens on a napkin.
Tolerance behaves differently by direction. In a parallel bank the total is the sum, so each part error contributes in proportion to its share of the total: independent errors partially cancel in aggregate, and the bank usually measures closer to nominal than its worst member. In a series string the smallest part dominates the sum of reciprocals, so its tolerance nearly becomes the tolerance of the whole string — one member reading 10% low pulls the total visibly low. Designers who need a precise equivalent either buy the value outright or trim the bank with a small adjustable member.
Ripple current deserves its own look in parallel banks. The bank as a whole presents a lower ESR, which is the point, but the sharing of ripple between members follows impedance, not wishful thinking: parts with similar ESR share fairly, while a single low-ESR member can quietly take most of the current and run hot anyway. Mixing families — a ceramic beside an electrolytic — is normal and healthy for decoupling, because each part handles the frequency band it is best at. For heavy ripple duty at one frequency, keep the bank members similar in type, value and age so the load actually divides.
| Bank | Parallel total | Series total | Note |
|---|---|---|---|
| 2 × 47 µF | 94 µF | 23.5 µF | Equal parts: ×N and C/N shortcuts |
| 10 µF + 22 µF + 47 µF | 79 µF | 6.00 µF | Series total sits below the smallest part |
| 100 nF + 0.22 µF | 0.32 µF | 68.8 nF | Mixed units — convert to one base first |
| 3 × 100 µF · 200 V | 300 µF · 200 V | 33.3 µF · 600 V* | *Electrolytics need balancing resistors |
The rules are two lines long; the judgment lives in the application. These three recipes cover the situations that send people to a bank calculator in the first place, with the arithmetic shown the way it looks on the bench.
A 3.3 V microcontroller rail wants bulk storage and fast high-frequency charge delivery, and no single part does both. One 47 µF electrolytic plus a 100 nF ceramic at each of two ICs gives a parallel bank whose arithmetic barely moves the headline — but the impedance curve moves a lot. The electrolytic carries the low-frequency load transients; the ceramics cover the megahertz region where the electrolytic has already run out of inductance. Parallel banks in decoupling are about impedance shape, not the total on the label.
The number stays flat; the impedance profile is the real product.
The bin holds 100 µF / 200 V electrolytics; the DC bus is 400 V. Two in series halve the capacitance and stack the rating to 400 V — with zero margin, which is not a design. Good practice adds balancing resistors across each part, sized to pass several times the worst-case leakage, and often builds the string with three members for headroom instead. Three 100 µF parts in series give 33.3 µF while the rail divides into about 133 V per part — a comfortable third below every rating, with the resistors holding the division fair as the parts age.
Margin comes from a third part plus balancing resistors, not from the label.
The nameplate asks for 45 µF at 370 V; the shelf has 30 µF and 15 µF, both at 440 V. Parallel wiring gives 30 + 15 = 45 µF exactly, and the higher voltage rating is always safe — voltage rating can only go up in a substitution. This direction is legitimate for run capacitors because the capacitance value is what sets motor torque and winding current. Never substitute downward and never try to reach 45 µF by series-wiring larger parts: series reduces capacitance, and a run capacitor sitting even 10% low already shortens compressor life. Keep any substitution within about ±5% of the nameplate and at equal-or-higher voltage.
Parallel is the only legal direction here; series would starve the motor.
Every bank starts with the values printed on the parts, and those values hide behind 3-digit codes: 104, 473, 225. The main calculator on the home page decodes any marking into pF, nF and µF with its tolerance range, and the capacitance converter translates between all five units when a bank mixes dialects. Once the bank is designed, the guide library covers what the two rules quietly assume — ESR, ripple sharing, balancing and the rest.
The workflow is short: decode the parts, convert the units, combine the bank here, then verify the finished build with a meter before it carries real voltage.
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Open calculatorYes — parallel is the additive direction: C_total = C₁ + C₂ + …, exactly, for any number of parts. Each member sees the full applied voltage, so the bank voltage rating is the lowest rating among its members. The trade is size and cost, not performance: the bank also presents a lower ESR than any single member and divides ripple current between the parts. A bank of two 22 µF capacitors is a genuine 44 µF capacitor as far as the rest of the circuit can tell.
Up to a point. N identical capacitors in series share the string voltage roughly equally, so the rating scales toward N × V — but the sharing is only as fair as the parts allow. Leakage differences, especially in aluminium electrolytics, let the DC division drift until one member carries more than its share. Film and ceramic strings track the ideal well; electrolytic strings need balancing resistors. Practical designs also leave margin: a three-part string of 200 V capacitors across 400 V, not a two-part string at exactly the limit.
In parallel, freely — the values simply add, and mixed units are fine once everything is converted to a common base. In series, mixing works mathematically but shifts the voltage division: the smaller capacitor takes the larger share of the voltage, and its tolerance then dominates the total. Mixed series banks are legal and sometimes necessary; they just need the per-part voltage check that equal banks get almost for free.
In a parallel bank, the error of the total is the share-weighted blend of the member errors — independent ±10% parts partially cancel, and the bank usually measures tighter than its worst member. In a series string, the smallest capacitor dominates the sum of reciprocals, so its tolerance nearly becomes the tolerance of the whole string. Direction of the errors matters too: in series, one part reading low pulls the total low out of proportion to its size.
Because series wiring stacks dielectrics: the effective plate separation grows while the charge on every part stays identical. The reciprocal rule expresses it — the smallest part contributes the largest 1/C term, so the sum of reciprocals is always greater than 1/C of the smallest member, and inverting a bigger number yields a smaller capacitance. Adding more parts in series can only push the total toward zero, never toward any member value.
For film and ceramic capacitors, usually not — their leakage is tiny and similar, so the ideal division holds within ratings. For aluminium electrolytics, yes in anything permanent: leakage varies part to part and drifts over life, letting the DC sharing walk until the wrong member is overloaded. Equal resistors across each capacitor, sized to pass a few times the worst-case leakage, pull the division back toward equal. Supercapacitor stacks go further and use active balancing boards instead.
There is no electrical limit — the rules extend to any count — and the calculator on this page takes twelve, which covers nearly every practical bank. Beyond a handful, other limits take over first: layout inductance starts to matter for decoupling banks, current sharing becomes uneven as members differ, and cost usually says a bigger single part wins. Ten small parts in parallel is a design decision; fifty is a pallet.
Yes, and the method is reduction: collapse each pure group into its equivalent, then combine the equivalents one rule at a time. A two-by-two bank of 100 µF parts — two in series making 50 µF, those pairs doubled in parallel — lands back at 100 µF with a doubled voltage rating. Work any network series group first or parallel group first, whichever isolates cleanly, then fold the results together. The twelve-slot calculator handles one rule per pass; a large network is simply several passes.
Read the values off the parts, set a unit on each row, and flip between series and parallel until the bank matches the circuit. The total, the working and the shortcuts update as you type — free, private, and instant.