Capacitor Calculator

What a capacitor stores

A capacitor is two metal plates separated by an insulator. Connect it to a battery and electrons pile up on one plate while the other plate runs short, creating an electric field in the gap. The device never lets current flow through; it holds a separated charge that can be released later. That is the whole trick, and it makes capacitors the shock absorbers of electronics: they smooth power supplies, time the blinks of indicators, and fire the flash in a camera.

Capacity is measured in farads. A one farad capacitor holds one coulomb of charge for every volt across it, which is an enormous amount for everyday parts. Real components are rated in microfarads (millionths of a farad) or picofarads (trillionths), the prefixes the NIST SI unit pages tabulate. An electrolytic capacitor marked 1000 microfarads is 0.001 farad, and a small ceramic marked 104 holds about 0.0000001 farad. The calculator above works in farads internally so the unit prefixes never contaminate the math.

Charge: how much electricity fits in

Charge follows one line: Q = C x V. Multiply capacitance in farads by voltage in volts and the result is coulombs. A 1,000 microfarad capacitor charged to 12 volts holds 0.001 x 12 = 0.012 coulombs, which is 12,000 microcoulombs. Double the voltage to 24 and the charge doubles to 0.024 coulombs; the relationship is straight.

A coulomb sounds abstract, so put it in faucet terms: one ampere is one coulomb per second, so 0.012 coulombs could feed a 12 milliamp LED for one second if it drained at that rate. Camera flash capacitors run bigger. A 200 microfarad unit charged to 300 volts holds 0.0002 x 300 = 0.06 coulombs, and it dumps that charge in about a millisecond, which is why the flash is blinding for an instant and the capacitor takes seconds to recharge from the battery.

One habit worth building: write the capacitance in farads before multiplying. Doing 1000 x 12 and calling the answer something in microcoulombs is the classic slip, off by a factor of a thousand. The widget handles the conversion, but on paper the farad-first rule saves you every time.

Energy: the half C V squared rule

Stored energy is E = 0.5 x C x V x V, in joules when C is farads and V is volts. The 1,000 microfarad part at 12 volts holds 0.5 x 0.001 x 144 = 0.072 joules. Notice the voltage appears twice: energy grows with the square of voltage, so the same capacitor at 24 volts holds 0.5 x 0.001 x 576 = 0.288 joules, four times as much, from only twice the charge.

That square is why high-voltage capacitors demand respect. The 200 microfarad camera flash unit at 300 volts stores 0.5 x 0.0002 x 90,000 = 9 joules, more than a hundred times the little 12-volt part, and it can deliver the lot in a blink. For comparison, a AA battery holds roughly 10,000 joules, so no capacitor replaces a battery; what capacitors do is deliver their modest energy almost instantly, then refill.

Reactance: how capacitors treat AC frequencies

Feed a capacitor direct current and it charges up, then blocks. Feed it alternating current and it continually charges and discharges, so current keeps flowing; how easily depends on frequency. Capacitive reactance measures that opposition in ohms, the unit the SI brochure from the BIPM defines alongside the farad: Xc = 1 / (2 x pi x f x C), where f is frequency in hertz. Twice the frequency, half the reactance.

Run the numbers for a 100 microfarad capacitor on a 60 Hz line: 2 x 3.14159 x 60 x 0.0001 = 0.0377, and 1 / 0.0377 = 26.53 ohms. Drop the frequency to 6 Hz and the reactance rises tenfold to about 265 ohms. At zero frequency, plain DC, the formula blows up: reactance is limitless, which is the mathematical way of saying a capacitor blocks DC completely.

This is the basis of coupling and filtering. A series capacitor passes audio but blocks the DC offset behind it. A capacitor to ground shunts high-frequency noise away from a power rail while leaving the DC untouched. Pick the value by working the reactance formula backward: decide the ohms you need at the frequency you care about, and the calculator solves for what that implies.

The RC time constant

Put a resistor between a voltage source and a capacitor and the voltage across the capacitor climbs on a curve, not a straight line. The pace is set by the time constant tau = R x C. With a 10,000 ohm resistor and a 100 microfarad capacitor, tau is 10,000 x 0.0001 = 1 second. After one tau the capacitor sits at 63.2 percent of the supply voltage; after five tau it is at 99.3 percent, close enough to call full.

The same curve runs in reverse on discharge: after one tau the capacitor has fallen to 36.8 percent, which is 100 minus 63.2. Designers use this to time things without a clock chip: a 555 timer's blink rate, a power-on reset delay, a soft-start ramp. Pick the product R x C for the delay you want, then choose standard component values that land near it.

Series and parallel combinations

Capacitors combine opposite to resistors. In parallel, capacitance adds: 100 microfarads beside 220 microfarads gives 320 microfarads, and the voltage rating stays that of the lowest-rated part. In series, capacitance shrinks and the reciprocals add, the same formula resistors use in parallel.

Series has a second payoff: voltage ratings add. Two 100 microfarad capacitors rated at 50 volts in series behave like 50 microfarads rated at 100 volts, which is how old radio rebuilds reach voltages no single modern part survives. The catch is charge sharing; real parts leak differently, so balanced bleeders or balancing resistors keep the split honest.

Reading the label: codes, tolerance and voltage

Small capacitors are too tiny for words, so they carry a three-digit code. The first two digits are the value and the third is the number of zeros, in picofarads. A marking of 104 means 10 followed by 4 zeros, so 100,000 picofarads, which is 0.1 microfarad, the most common decoupling value in electronics.

A letter after the code is tolerance: J means plus or minus 5 percent, K means 10 percent, M means 20 percent. Electrolytic capacitors print plain values and often a wide tolerance, minus 20 to plus 80 percent on some cheap grades, so never count on an electrolytic for timing precision. The voltage marking is a ceiling, not a suggestion; running an electrolytic at half its rating extends its life, while running it at or past the mark cooks it.

Safety: the charge outlives the plug

A capacitor holds its charge after the power is gone. The 1,000 microfarad supply filter that made your device work stores 0.072 joules at 12 volts, startling at worst. But mains-powered gear is another matter: switch-mode supplies keep 200 to 400 volt bus capacitors charged, and a microwave oven's capacitor can hold a lethal charge minutes after the cord leaves the wall. The occupational safety rules on OSHA's electrical pages exist because stored energy injures people who assumed off means empty.

Discharge before touching. A resistor from terminal to terminal, sized so the current stays modest, bleeds the charge in a few time constants; a 10,000 ohm resistor across that microwave capacitor empties it in seconds without a spark. Shorting terminals with a screwdriver works but pits the tip and stresses the part. Treat every capacitor above about 50 volts as live until you have measured it, and the measurement and all the calculations on this page stay in your browser: nothing you enter is uploaded anywhere.