Formula of Charge: Q = It and Q = ne, Unit Coulomb, Examples

The basic formula of charge is $Q = It$ : multiply a steady current in amperes by the time in seconds and you get the charge in coulombs that has passed a point. A current of 1 A running for 1 s moves exactly 1 C.

Physics uses a few other charge formulas, each suited to a different kind of question. Counting electrons gives $Q = ne$ . A capacitor holds $Q = CV$ . This page sets out all of them, shows when to use which, and ties them to the current formula and the wider set of electricity formulas.

Quick facts

Main formula
$Q = It$
Quantised form
$Q = ne$ , n a whole number
Capacitor
$Q = CV$
SI unit
coulomb (C) = ampere second
Dimensional formula
[M⁰ L⁰ T¹ I¹]
Type
Scalar; can be positive or negative
Elementary charge
$e = 1.602 \times 10^{-19}$ C

Charge formula in physics and its symbols

Symbols for Q = It and Q = ne
Symbol	Meaning	SI unit
$Q$ or $q$	Electric charge	C
$I$	Electric current, assumed steady	A
$t$	Time interval	s
$n$	Number of electrons or protons	no unit
$e$	Elementary charge, $1.602 \times 10^{-19}$ C	C

Current measures how quickly charge moves past a point, $I = Q/t$ . The charge formula is that definition turned round. If the current changes with time, plain multiplication fails; the charge is then the area under the current time graph, $Q = \int I\,dt$ . For a straight sloping graph that area is a triangle or trapezium you can work out by geometry.

Which charge formula to use

Picking a formula from the data
You are given	Formula	Typical question
Current and time	$Q = It$	Charge drawn by a heater or a battery
Number of particles	$Q = ne$	Charge on a rubbed balloon
Capacitance and voltage	$Q = CV$	Charge stored on a capacitor plate
Energy and voltage	$Q = W/V$	Charge moved through a potential difference
Changing current graph	Area under I against t	Charge in a pulse

The energy row comes from the definition of voltage, $V = W/Q$ . The capacitor row is covered in depth on the capacitance formula page.

Solving problems with the formula of charge

Problem 1: topping up a phone

A phone draws a steady 2.0 A for 30 minutes. How much charge flows into it?

Convert: t = 30 × 60 = 1800 s.

$Q = It = 2.0 \times 1800 = 3600\ \text{C}$

A battery rating of 1 mAh equals 3.6 C, so 3600 C is 1000 mAh.

Problem 2: how many electrons is that

How many electrons make up that 3600 C?

$n = \frac{Q}{e} = \frac{3600}{1.602 \times 10^{-19}} \approx 2.25 \times 10^{22}$

Problem 3: a sphere stripped of electrons

A metal sphere loses $5.0 \times 10^{13}$ electrons. Find its charge.

$Q = ne = (5.0 \times 10^{13})(1.602 \times 10^{-19}) = 8.0 \times 10^{-6}\ \text{C}$

Losing electrons leaves the sphere positive, so Q = +8.0 μC.

Quantisation and conservation of charge

Free charge always comes in whole multiples of e. You can have 3e or −7e on a drop of oil, never 2.5e. That is why $Q = ne$ uses a whole number n. A question that gives a charge of $2.4 \times 10^{-19}$ C on an object should make you suspicious, since 2.4 divided by 1.602 is not a whole number.

Charge is also conserved. Rubbing a glass rod with silk does not create charge. Electrons move from the glass to the silk, so the rod ends up positive and the silk negative by the same amount. In every circuit the charge leaving a battery terminal equals the charge returning to the other one. Charges of the same sign push apart and opposite signs pull together, with a strength given by the electrostatic force formula.

Coulomb, dimensions and small units

Because charge is current times time, its unit is the ampere second, given the special name coulomb. In base dimensions that is [M⁰ L⁰ T¹ I¹]: no mass, no length, one power of time and one of current. The full derivation sits on the dimensional formula of charge page.

Common fractions of a coulomb
Unit	In coulombs	Where you meet it
millicoulomb (mC)	10⁻³ C	Large capacitors
microcoulomb (μC)	10⁻⁶ C	Charged spheres in Coulomb's law problems
nanocoulomb (nC)	10⁻⁹ C	Dipoles and small rods
milliampere hour (mAh)	3.6 C	Battery capacity labels

Mistakes that cost marks

Leaving time in minutes or hours. Q = It needs seconds. One hour is 3600 s.
Writing e as negative in Q = ne. Use the size of e and decide the sign from whether electrons were gained or lost.
Using Q = It for a changing current. Find the area enclosed by the I against t graph.
Confusing charge with current. Charge is an amount, in C. Current is a flow rate, in C/s or A.

Gaining electrons makes an object negative. Losing them makes it positive. Protons do not move in ordinary charging.

Frequently asked questions

What is the formula of charge?

The main formula is Q = It, current times time. For a counted number of electrons use Q = ne, and for a capacitor use Q = CV.

Which SI unit is used for electric charge?

Charge is measured in coulombs, symbol C. A steady 1 A flowing for 1 s delivers exactly 1 C, which is why the coulomb is also written as the ampere second.

How many electrons are in one coulomb?

Divide 1 C by the elementary charge: 1 / (1.602 × 10⁻¹⁹) ≈ 6.24 × 10¹⁸ electrons.

Does electric charge have a direction?

No, charge is a scalar quantity. A charge carries a plus or minus sign, yet it does not point anywhere, so you combine charges with simple addition and subtraction.

What is the difference between charge and current?

Charge is how much electricity there is, measured in coulombs. Current is how fast that charge flows past a point, measured in amperes, and I = Q / t.