Capacitance Calculator
Combine capacitors in series or parallel, and calculate stored charge Q = CV, energy E = ½CV², and the RC time constant. Live SVG schematic, smart unit formatting.
- 1/Ctotal = 1/C1 + 1/C2 + … + 1/Cn
How It Works
- 1
Pick series/parallel or energy mode
Use the Series/Parallel tab to combine up to 10 capacitors. Use the Energy & Charge tab to compute Q = CV, E = half CV squared, and the RC time constant from a single capacitor, voltage, and optional resistance.
- 2
Enter capacitor values with units
Choose pF, nF, uF, mF, or F per row. In energy mode, enter capacitance, voltage, and optionally a resistance for the time constant. The calculator auto-formats results into the most readable unit.
- 3
Read the result and diagram
The total capacitance (network mode) or charge, energy, and time constant (energy mode) update live. The SVG schematic reflects the current configuration with IEC-style capacitor symbols.
Capacitors, charge storage, and the Leyden jar legacy
The first practical capacitor was the Leyden jar, built independently by Ewald Georg von Kleist and Pieter van Musschenbroek in 1745. It stored static charge between a glass wall and metal foils, and it shocked the experimenters who touched it. Nearly a century later, Michael Faraday quantified the relationship between charge and voltage on a conductor, and the unit of capacitance (the farad) was named in his honor. One farad stores one coulomb per volt, an enormous amount for most circuits. Typical values in electronics span twelve orders of magnitude: RF and microwave designs use 0.5 pF to 100 pF, general decoupling runs 100 nF to 10 uF, and bulk power-supply filtering reaches hundreds or thousands of microfarads in electrolytic or polymer aluminum cans. At the extreme end, supercapacitors (electric double-layer capacitors, first commercialized by NEC in 1978) reach 3000 F per cell at 2.5 to 2.7 V, storing enough energy to hold up a server through a 10-second power glitch. Capacitors in series follow the opposite rule from resistors: 1/C_total = 1/C1 + 1/C2 + ... + 1/Cn (because charge is conserved along the chain and voltages add). Capacitors in parallel simply add: C_total = C1 + C2 + ... + Cn (because the same voltage appears across each, and charges sum). The stored energy E = half C V squared determines how much work a charged capacitor can do, from firing a camera flash (about 36 J in a 400 V, 450 uF cap) to welding spots in a capacitor-discharge welder. Real capacitors also have ESR (Equivalent Series Resistance), which limits ripple current and causes self-heating in switch-mode power supplies.
Common pitfalls
Ignoring DC-bias derating on Class II ceramics. X7R, X5R, and Y5V MLCCs lose capacitance under applied DC voltage: a 10 µF 0805 X5R rated at 10 V typically drops to ~3 µF at 10 V DC, a 70% loss. Always check the manufacturer's DC-bias curve. Use C0G/NP0 (Class I) when the capacitance must hold; at a cost of volume.
Forgetting ESR and ripple-current rating. An electrolytic's ESR dissipates I²_ripple × ESR as heat. A 1000 µF cap with 0.1 Ω ESR carrying 2 A_rms ripple dissipates 400 mW, enough to raise its core temperature 20-30 °C in a small can. ESR rises sharply below 0 °C; a 'good' cap at 25 °C can look open at -20 °C.
Reversing polarity on electrolytics. An aluminum electrolytic reverse-biased by more than ~1.5 V electrolyzes its electrolyte into hydrogen gas. The pressure either vents the scored end or blows the can. Tantalum is worse; reverse voltage triggers a short circuit that can burst into flame.
Using the nominal ±20% tolerance for timing. General-purpose electrolytics are +50/-10% at 20 °C and drift another 20% over their temperature range. Use film or C0G for RC time constants that must hold; reserve bulk electrolytics for energy storage and decoupling.
Treating supercapacitors like batteries. They hold energy in an electric field, not electrochemistry, so voltage drops linearly with discharge (V = V0 - I·t/C). A 'fully charged' 2.7 V supercap delivering constant current reaches 1.35 V (half discharge) after releasing only 75% of its stored energy. You need a buck-boost converter to use all of it.
Frequently Asked Questions
Why do capacitors in series follow the opposite rule from resistors?
Capacitors store charge, and charge is conserved along a series chain. The same charge Q sits on every capacitor in the string, but the voltage across each one is Q/C. Voltages add in series, so 1/C_total = 1/C1 + 1/C2 + … + 1/Cn. Resistors in series share current, and their voltages add the same way, but voltage and resistance relate by V = IR, so resistance itself adds directly. The duality comes from capacitance being the inverse of elastance (S = 1/C), just as conductance is the inverse of resistance.
When would I put capacitors in series?
The most common reason is voltage rating. Two 25 V rated capacitors in series can handle up to 50 V across the pair (as long as a balancing resistor or active circuit keeps the voltage split even). High-voltage valve amps, CRT circuits, and Marx generators stack caps in series for exactly this reason. The trade-off is reduced total capacitance.
How does E = 1/2 CV squared relate to real circuits?
The formula gives the total electrostatic energy stored in the capacitor's electric field. It determines how much energy a capacitor bank can dump into a load (camera flash, defibrillator pulse, rail gun), how much energy a decoupling cap can supply during a transient, and how much damage a charged capacitor can cause if shorted. A 400 V, 450 uF photo flash capacitor stores about 36 joules, enough to cause a severe burn.
What is the RC time constant and why does it matter?
Tau = R times C gives the time in seconds for a charging or discharging capacitor to reach 63.2% of its final value (one time constant) through a resistor R. After 5 tau the cap is 99.3% charged and considered fully settled. RC time constants set the speed of analog filters, the debounce time of switch circuits, the hold time of sample-and-hold stages, and the decay rate of power supply droop after load steps.
What are typical capacitance values in electronics?
RF and microwave circuits use picofarads (pF), often 0.5 pF to 100 pF. General decoupling and bypass caps run 100 nF to 10 uF. Bulk filtering on power supply rails uses 100 uF to several thousand uF of electrolytic or polymer aluminum. Supercapacitors reach 1 F to 3000 F for energy storage and hold-up power, but their voltage rating is low (2.5 to 2.7 V per cell), so they are often stacked in series with active balancing.
How does ESR affect a real capacitor?
Equivalent Series Resistance (ESR) is the parasitic resistance inside the capacitor from leads, foil, and electrolyte. It causes power loss (P = I_rms squared times ESR), limits ripple current handling, and raises the effective impedance above the ideal 1/(2 pi f C) at high frequencies. Low-ESR capacitors (polymer aluminum, MLCC) are critical in switch-mode power supply output filtering where ripple currents are high.
Does this calculator handle mixed series-parallel capacitor banks?
Not directly. Work in stages: compute the series combination of one branch, then use that result as a single element in a parallel calculation (or vice versa). For arbitrarily connected networks, use mesh or nodal analysis with impedances Z = 1/(j omega C).
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