Capacitance

Q: Does a capacitor store charge or energy?

Both. The charge is $Q = C V$, and the energy stored is $\frac{1}{2} C V^2$, where $V^2$ means $V$ times $V$. The energy formula is a separate rule with its own page.

In one sentence: Capacitance tells you how much electric charge a capacitor stores for each volt across it.

$Q = C V$

Read it out loud: “Q equals C times V. Read Q as Q, the charge stored on one plate, in coulombs. C is the capacitance, the charge stored per volt, in farads. V is the voltage across the capacitor, in volts. Charge equals capacitance times voltage.”

Before you start

The ideas and signs this page uses, explained from zero. For powers of ten, Greek letters and other notation in general, see Math basics.

A capacitor and its plates: A capacitor is a component made of two conductors, usually metal plates, separated by an insulator, a material that does not let charge flow through it. When a voltage is applied, one plate gathers positive charge and the other gathers an equal amount of negative charge. A capacitor stores charge between its plates, and no charge passes through the gap.
The coulomb (C) and electric charge: Electric charge is an amount of electricity, and its unit is the coulomb, written C. One coulomb is a large amount, about $6.24 \times 10^{18}$ electrons’ worth of charge. Charge is like water held in a tank: it is an amount that can be stored or moved, measured in coulombs.
Powers of ten, like $10^{-4}$: A power of ten is 10 multiplied by itself a set number of times. A negative power means divide by 10 that many times, so $10^{-4} = 0.0001$ . The exponent says how many places to move the decimal point. Multiplying powers of ten adds their exponents, and dividing subtracts them.
The farad (F), microfarad ( $\mu$ F), nanofarad (nF) and picofarad (pF): The farad, written F, is the unit of capacitance: one coulomb of charge per volt. It is very large, so capacitors are rated in smaller units. The prefix micro, written $\mu$ , the Greek letter mu, means one millionth, so $1\ \mu\text{F} = 10^{-6}$ F. The prefix nano, written n, means one billionth, and pico, written p, means one trillionth.
The volt (V) as a push: A volt, written V, is the unit of voltage. It is the push that moves electric charge across a gap. One volt means one joule of energy is given to each coulomb of charge that passes. A USB port supplies a push of about 5 V.
Charge and current are different: Charge is an amount of electricity, measured in coulombs, and it can be stored. Current is the rate at which charge flows, measured in amperes, and one ampere is one coulomb per second. A capacitor holds charge; a current is the flow that moves charge from place to place.

What each symbol means

Symbol	Meaning
$Q$	The charge stored on one plate of the capacitor, measured in coulombs (C). The other plate holds the same amount with the opposite sign. In the example, Q is 500 microcoulombs, which is $5 \times 10^{-4}$ C.
$C$	The capacitance, the charge stored per volt, measured in farads (F). A bigger value means the capacitor holds more charge at the same voltage. The example uses 100 $\mu$ F, which is $10^{-4}$ F. The same letter also names the coulomb unit, so the context tells you which is meant.
$V$	The voltage across the capacitor, measured in volts (V). It is the push applied across the two plates. The example uses 5 V, a common low voltage in small electronics and USB devices.

The formula piece by piece

$C$: Start with the capacitance, the size of the storage. It tells you how much charge each volt can push onto the plates. It is set by how the capacitor is built, not by the voltage applied to it.
$V$: The voltage applied across the capacitor, the push that drives charge onto the plates. It is measured in volts. Doubling the voltage doubles the charge, as long as the capacitance stays the same.
$C V$: Capacitance multiplied by voltage. One farad is one coulomb per volt, so farads times volts leaves coulombs, because the volts cancel. Multiplying the two therefore gives the amount of charge stored on each plate, in coulombs.
$Q = C V$: The charge on each plate equals the capacitance multiplied by the voltage across the capacitor. For a fixed capacitance, the charge is directly proportional to the voltage, so doubling one doubles the other.

What the formula is doing, and why

A capacitor is two conductors close together, separated by an insulator. When a voltage is applied, one plate collects positive charge and the other collects an equal amount of negative charge. The charge $Q$ on each plate depends on the voltage $V$ and on how large the capacitor is. The number that links them is the capacitance $C$ .

Why multiply? The rule is $Q = C V$ . If the capacitance stays the same, doubling the voltage doubles the stored charge, because each volt pushes the same amount of charge onto the plates. A capacitor with a larger $C$ holds more charge at the same voltage. Solving for $C$ gives $C = \frac{Q}{V}$ , which is why capacitance is measured in charge per volt.

What the farad means. One farad is one coulomb per volt. That is a very large amount, so practical capacitors are usually rated in microfarads, $1\ \mu\text{F} = 10^{-6}$ F, or picofarads, $1\ \text{pF} = 10^{-12}$ F. The unit is named after Michael Faraday, the English scientist who studied electricity and magnetism.

What sets the value. The value of $C$ comes from the size, spacing and material of the capacitor. The voltage does not change it. Changing the voltage changes only the charge, while the capacitance stays fixed by the build. The next page, on the parallel-plate formula, shows how the size and the spacing set the value.

When the rule needs care. The rule describes an ideal capacitor. A real capacitor can leak a little charge over time, so the stored charge slowly falls even when nothing is connected to it. The rule still gives the charge at the moment the voltage is applied.

An everyday picture

Think of a capacitor as a tank whose water level is the voltage. The capacitance is how much water the tank holds for each unit of level. A wide tank needs more water to raise its level by one unit, so a wide tank has a large capacitance. The water in the tank is the charge.

Worked example: Charge on a 100 microfarad capacitor

A capacitor with $C = 100\ \mu\text{F}$ is charged to $5\ \text{V}$ , the voltage of a USB port. How much charge is stored on each plate? Give the answer in coulombs and in microcoulombs.

Write the rule and the known values. The rule is $Q = C V$ , so the charge equals the capacitance times the voltage. We know $C = 100\ \mu\text{F}$ and $V = 5\ \text{V}$ . Before multiplying, the capacitance must be in farads, because the rule works in the base units of coulombs, farads and volts.
Convert the capacitance to farads. The micro prefix, written $\mu$ , means one millionth, so $100\ \mu\text{F} = 100 \times 10^{-6}\ \text{F}$ . Multiplying by $10^{-6}$ moves the decimal point six places to the left: $100 \times 10^{-6} = 1 \times 10^{-4}\ \text{F}$ , which is 0.0001 F. A mistake of a factor of a million is easy to make here, so check the prefix first.
Multiply the capacitance by the voltage. Put in the numbers: $Q = 1 \times 10^{-4}\ \text{F} \times 5\ \text{V}$ . The front numbers multiply to 5, and the power of ten stays as $10^{-4}$ , so $Q = 5 \times 10^{-4}$ . The units are farads times volts. One farad is one coulomb per volt, so the volts cancel and leave coulombs: $Q = 5 \times 10^{-4}\ \text{C}$ .
Convert to microcoulombs. One microcoulomb is one millionth of a coulomb, $10^{-6}$ C. To count in microcoulombs, divide by $10^{-6}$ . Dividing by $10^{-6}$ is the same as multiplying by $10^{6}$ , so the exponent $-4$ rises by six to $+2$ : $5 \times 10^{-4}\ \text{C} = 5 \times 10^{2}\ \mu\text{C} = 500\ \mu\text{C}$ .
Check the size of the answer. The charge is 500 microcoulombs, or 0.0005 coulombs. One coulomb is about $6.24 \times 10^{18}$ electrons’ worth of charge, so this small capacitor holds only a tiny fraction of a coulomb, which fits a small gadget.
Note the other plate. The opposite plate holds the same amount of charge with the opposite sign. So the two plates together have zero net charge. The capacitor stores charge by separating it onto the two plates, not by creating it.

Answer: The capacitor stores 0.0005 C, which is 500 microcoulombs, on one plate. The opposite plate holds the same amount with the opposite sign.

The numbers in this example are recomputed by script every time the site is built.

Common mistakes

Forgetting the micro prefix. $100\ \mu\text{F}$ is $10^{-4}$ F, not 100 F. A factor of a million is easy to miss.
Mixing up the letters. The symbol $C$ stands for capacitance, and it is also the symbol for the coulomb unit. $Q$ is the charge in coulombs, so read the context to tell which one is meant.
Thinking a higher voltage changes the capacitance. Voltage changes the charge, while capacitance depends on the build of the capacitor.
Treating charge as current. Charge is an amount stored, in coulombs. Current is the rate at which charge flows, in amperes.

Where you will meet it

Camera flashes and power supplies, which store charge in capacitors and release it in a short burst.
Touch screens and some proximity sensors, which detect a finger by measuring a small change in capacitance.
Variable capacitors in radio tuners, where changing the capacitance selects a station.
Circuit board design, where each decoupling capacitor, which steadies the voltage near a chip, is specified by its capacitance in microfarads or nanofarads.

Questions people ask

What is a farad?

A farad (F) is one coulomb of charge per volt. It is named after Michael Faraday. Most real capacitors are much smaller, so microfarads and picofarads are common.

Does a capacitor store charge or energy?

Both. The charge is $Q = C V$ , and the energy stored is $\frac{1}{2} C V^2$ , where $V^2$ means $V$ times $V$ . The energy formula is a separate rule with its own page.

Does the capacitance change when the voltage changes?

No. The capacitance is set by the size, spacing and material of the capacitor. A change in voltage changes only the charge on the plates.

Is charge the same as current?

No. Charge is an amount, measured in coulombs. Current is the flow of charge per second, measured in amperes.

Parallel-Plate Capacitor: The parallel-plate formula says a capacitor holds more charge per volt when its plates are bigger, closer together, or separated by a material with a higher permittivity.
Capacitors in Series and Parallel: Capacitors connected side by side add their capacitances together, while capacitors connected in a chain give a smaller total that you find with a special rule.
Energy Stored in a Capacitor: A charged capacitor holds energy in the electric field between its two plates, and doubling the voltage across it makes the stored energy four times bigger.