Capacitance

What capacitance measures

Capacitance says how much electric charge a component can hold for each volt you put across it. Double the capacitance and the same voltage pushes twice the charge onto its plates. The unit is the farad, defined as one coulomb of charge per volt of potential difference. A full farad is enormous by electronics standards, so practical parts are rated in microfarads (millionths of a farad), nanofarads or picofarads. The farad appears among the derived units of the International System in the NIST SI units page and in NIST SP 330, the US edition of the SI brochure.

Every pair of conductors separated by an insulator has some capacitance: two wires routed side by side, a circuit board trace over a ground plane, even your body relative to the floor. Designers usually fight stray capacitance because it slows signals and bleeds charge, while power supply and flash circuits buy large capacitors on purpose so there is a reservoir of charge to draw from.

The formulas: charge, voltage and energy

One multiplication covers charge. A capacitor charged to V volts with capacitance C farads holds a charge of Q = C x V coulombs. Work in microfarads and the arithmetic stays friendly: charge comes out in microcoulombs, because a microfarad times a volt is a microcoulomb.

For the 470 microfarad capacitor at 12 volts from the top of this page, Q = 470 x 12 = 5,640 microcoulombs, which is 5.64 millicoulombs. Energy needs one more factor of voltage: E = C x V x V / 2, so E = 0.5 x 470 x 12 x 12 = 33,840 microjoules, or 33.84 millijoules. The same number comes out of the shortcut E = Q x V / 2, since half the charge times the voltage is exactly the energy the charging source delivered and the capacitor kept.

The square in the energy formula matters in practice. Holding capacitance fixed and doubling the voltage quadruples the stored energy, which is why a capacitor rated for 25 volts sees heavy duty if you run it near its limit, and why flash circuits charge small capacitors to a few hundred volts instead of using a big part at low voltage.

Worked example: a camera flash capacitor

Camera flashes and stun-gun style circuits push a small capacitor to a few hundred volts. Take a typical 200 microfarad photoflash part charged to 330 volts. Q = 200 x 330 = 66,000 microcoulombs of charge, and E = 0.5 x 200 x 108,900 = 10,890,000 microjoules, which is 10.89 joules. That is roughly the mechanical work of lifting a one kilogram mass a bit over a meter, released in the fraction of a second the tube fires.

The same arithmetic explains the safety rule with big capacitors: they keep their charge after the power is off. A charged 330 volt flash capacitor has no way to warn you, and 10.89 joules delivered through a finger is a real shock. Meter the voltage and discharge the part through a resistor before touching a circuit that contained one.

Notice the supercapacitor: a full farad at 5 volts stores less energy than the tiny 200 microfarad part at 330 volts, because voltage enters the energy formula squared. Capacitance alone does not tell you how much work a part can do.

Parallel plates: why geometry sets the limit

For the simplest capacitor, two flat plates facing each other across a thin gap, capacitance follows straight from geometry: C = er x e0 x A / d, where A is the plate area, d the gap, er the relative permittivity of the material in the gap, and e0 the permittivity of empty space, 8.854 x 10 to the minus 12 farads per meter, which is 8.854 picofarads per meter.

A worked example with air in the gap: plates of 25 square centimeters (0.0025 square meters) held 0.1 millimeters (0.0001 meters) apart. The area to gap ratio is 0.0025 / 0.0001 = 25, so C = 8.854 x 25 = 221.4 picofarads. Slide a ceramic dielectric with er of 4.7 into the same gap and C = 4.7 x 8.854 x 25 = 1,040 picofarads, five times the capacitance from the same physical size.

This formula explains the shape of every capacitor you have handled: films rolled into tight cylinders to stack area, electrolytics with an oxide layer just atoms thick to shrink the gap, and multilayer ceramic chips that alternate dozens of plate and dielectric layers.

Dielectric constants vary with temperature and manufacturing lot, so treat the table as typical textbook values rather than guaranteed ratings.

Series and parallel combinations

Capacitors combine in the opposite way from resistors. In parallel, the plates effectively add area, so capacitance adds: two 470 microfarad parts in parallel give 470 + 470 = 940 microfarads at the same voltage rating. In series, the effective gap grows, so reciprocals add and the total shrinks: two equal parts give 470 / 2 = 235 microfarads.

Series banks earn their keep when no single part can stand off the voltage. Two 200 volt capacitors in series share the stress and handle up to about 400 volts, though real parts never share perfectly, so designers add balancing resistors across each one to even out the leakage currents.

The energy bookkeeping looks odd at first: two capacitors in parallel store four times the energy of one at the same voltage, twice the capacitance times the same squared voltage. Two in series at the doubled voltage store exactly what the pair stores in parallel. Geometry fixes the charge, and the voltage rating fixes how far you can push it.

Time constants: how fast a capacitor charges

Through a resistor, a capacitor fills at a predictable pace. The product R x C sets the time constant tau, measured in seconds: ohms times farads. A 10,000 ohm resistor charging a 100 microfarad capacitor (0.0001 farads) gives a time constant of exactly 1 second. After one time constant the capacitor has reached about 63.2 percent of the supply voltage; after five, about 99.3 percent, close enough that circuit designers call it full.

The same constant runs the discharge in reverse, which is why bleeders are sized by their resistance: a bleeder resistor across a big capacitor sets how long the part stays dangerous after power off. Halve the resistance and the wait halves too, at the cost of continuous drain while the equipment runs.

The calculator on this page does not model the resistor, but the energy and charge it reports are the endpoints that the exponential curve approaches. For timing work, pick the resistor from the time constant first, then check the energy figures here against what the part can tolerate.

Real capacitors: ratings, tolerances and safety

The number printed on a capacitor is a nominal value with a tolerance band. Aluminum electrolytics commonly wander 20 percent either way and lose capacitance as they age and dry out. Standard ceramics are tighter, while high-K ceramics trade stability for size and can shed a large share of their capacitance under the DC bias you run them at. Treat marked values as a center, not a promise.

Voltage ratings deserve margin. Running a 25 volt part at 24 volts leaves nothing for spikes and shortens its life; the usual rule of thumb is to double the expected working voltage when choosing the rating. The energy figures from this page are stored regardless of rating, so a part run near its limit holds the same joules and has less headroom to survive them.

Three habits cover most capacitor safety. First, discharge before touching: meter the voltage, then bleed it through a resistor rather than a screwdriver. Second, respect the big ones, since values above a few hundred microfarads at more than 50 volts can hold a dangerous shock for minutes. Third, mind polarity on electrolytics, because reverse voltage heats them and vents them. The OSHA guidance on electrical hazards treats stored capacitive charge as a lockout concern for exactly this reason. For charge and energy at any operating point, the solver at the top of this page gives the numbers in one step.