Dimensional Formula of Charge: [M⁰ L⁰ T¹ I¹] Derived

The dimensional formula of charge is [M⁰ L⁰ T¹ I¹], usually shortened to [IT] or [AT]. Charge carries no mass and no length dimension; it is electric current multiplied by time.

This follows from the fact that SI picks electric current, not charge, as its base electrical quantity. Current is the flow of charge per second, I = Q/t, so charge is current times the time it flows. One coulomb is the charge moved when one ampere flows for one second. For worked problems with Q = ne and Q = It, see the charge formula page.

Quick facts

Dimensional formula
[M⁰ L⁰ T¹ I¹], short form [IT]
Defining formula
$Q = I t$
SI unit
coulomb (C), equal to one ampere second
Other unit
ampere hour: 1 A h = 3600 C
Type
Scalar, can be positive or negative
Elementary charge
e = 1.602 × 10⁻¹⁹ C

How to derive the dimensional formula of charge

Current measures how many coulombs pass a point each second: $I = \frac{Q}{t}$ .
Rearrange for charge: $Q = I \times t$ .
Current is a base quantity with dimension [I], and time has [T].
So $[Q] = [I][T] = [TI]$ , which in the full form with zero powers reads [M⁰ L⁰ T¹ I¹].

You can also start from Coulomb's law if a question insists on it. Rearranged, $q_1 q_2 = 4\pi\varepsilon_0 F r^{2}$ , and with ε₀ written as [M⁻¹L⁻³T⁴I²], the right side collects to $[M^{-1+1}L^{-3+1+2}T^{4-2}I^{2}] = [T^{2}I^{2}]$ . Taking the square root for one charge gives [TI] again. The shorter route through current is the one examiners expect.

From [IT] to the coulomb and the ampere hour

Replace I with the ampere and T with the second and the bracket reads A s. That is the coulomb, so 1 C = 1 A s. Any unit made of a current unit times a time unit is therefore a unit of charge.

Example: a phone battery is rated 4000 mA h. How much charge can it deliver in coulombs?

Given: 4000 mA h = 4.000 A h.

1 A h = (1 A)(3600 s) = 3600 C.

$Q = 4.000 \times 3600 = 1.44 \times 10^{4}\ \text{C}$ .

Battery mA h ratings are charge, not energy. To get energy you also need the battery voltage.

Checking formulas that contain charge

Example: is $Q = CV$ dimensionally consistent?

Take capacitance as [M⁻¹L⁻²T⁴I²] and voltage as [ML²T⁻³I⁻¹].

Product: $[M^{-1+1} L^{-2+2} T^{4-3} I^{2-1}] = [TI]$ . It matches the charge bracket.

A second quick test: in Q = ne, n counts electrons and has no dimensions, so ne has the dimensions of e, which is a charge. The number of electrons in 1 C is $1 / (1.602 \times 10^{-19}) = 6.24 \times 10^{18}$ , a pure number.

Quantities linked to the charge bracket

Charge and its close relatives
Quantity	Dimensions	How it relates
Charge Q	[TI]	Current times time
Current	[I]	Charge per time
Linear charge density λ	[L⁻¹ T I]	Charge per length
Surface charge density σ	[L⁻² T I]	Charge per area
Electric dipole moment p	[LTI]	Charge times separation

Only the first row is charge itself. The others are useful because their brackets show at once how charge was divided or multiplied. Any quantity measured in coulombs, such as induced charge or elementary charge, shares [TI].

Slips that cost marks

Writing [I T⁻¹]. That is current divided by time. Charge is current multiplied by time.
Treating charge as a base quantity in an SI answer. The base is current. Use [IT], not [Q], unless the question says otherwise.
Adding mass because charges are particles. An electron has mass, but charge as a quantity has M⁰.
Confusing C for coulomb with C for capacitance. Read the question carefully.

Need the bracket for capacitance or resistance next? The dimensional formulas collection groups every electrical quantity beside the coulomb.

Frequently asked questions

What is the dimensional formula of charge?

It is [M⁰ L⁰ T¹ I¹], often written [IT] or [AT]. It comes from Q = It, current multiplied by time.

What is the dimension formula of charge in terms of Q?

In systems that take charge as a base quantity it is simply [Q]. Under SI rules, current is chosen as the base and so charge turns into [IT].

Which SI unit goes with the bracket [IT]?

Put ampere for I and second for T and you get the ampere second, named the coulomb. So a torch bulb drawing half an ampere for ten seconds passes five coulombs through its filament.

Does charge have a direction like a vector?

No. Charge only adds up algebraically, with plus and minus values cancelling. It points nowhere, so it is a scalar, and its bracket [IT] says nothing about direction either.

Do charge and current have the same dimensions?

No. Current is [I], a base quantity. Charge is [IT], which carries one extra power of time.