Dimensional Formula of Current: [M⁰ L⁰ T⁰ I¹] Explained

The dimensional formula of current is [M⁰ L⁰ T⁰ I¹], normally shortened to [I], or [A] in books that use the ampere symbol. Electric current is one of SI's base quantities, so nothing else goes into its bracket; instead it feeds every other electrical bracket.

That surprises students who learn I = Q/t first and expect charge to be the basic quantity. SI made the opposite choice: the ampere is the base unit, and the coulomb is derived from it as one ampere second. The current formula guide covers the many ways of calculating I in circuits.

Quick facts

Dimensional formula
[M⁰ L⁰ T⁰ I¹], or [I]
Status
SI base quantity
SI unit
ampere (A), a base unit
Defining relation
$I = \frac{Q}{t}$
Type
Scalar, though it has a sense along a wire
Built from it
Charge [IT], voltage, resistance and more

Why the dimensional formula of current is simply [I]

Seven quantities are chosen as the base of SI. Electric current, with letter I, is one of them, next to luminous intensity, amount of substance, temperature, time, length and mass. A base quantity cannot be broken down, so its bracket is just its own letter.

So for current, $[I] = [M^{0}L^{0}T^{0}I^{1}]$ . Writing the zero powers is optional but some boards want them. The relation $I = \frac{Q}{t}$ is still true, but it is used the other way round in dimensional work: it defines charge as [IT]. The charge bracket follows directly from it.

The ampere is fixed today by giving the elementary charge an exact value, but in brackets current remains the base, not charge.

Checking that formulas give a current

Example: confirm that Ohm's law, $I = V/R$ , returns [I].

Voltage: [ML²T⁻³I⁻¹]. Resistance: [ML²T⁻³I⁻²].

$\frac{[ML^{2}T^{-3}I^{-1}]}{[ML^{2}T^{-3}I^{-2}]} = [I^{-1+2}] = [I]$ . Mass, length and time all cancel.

Example: check the drift velocity relation $I = nAev_d$ .

n is electrons per volume [L⁻³], A is area [L²], e is a charge [IT], and $v_d$ is a speed [LT⁻¹].

$[L^{-3}][L^{2}][IT][LT^{-1}] = [L^{-3+2+1}T^{1-1}I] = [I]$ . The relation is consistent.

More on that second formula is on the drift velocity formula guide.

From amperes to electrons: a worked problem

Example: a bulb draws 0.50 A for 1.0 minute. How much charge passes, and how many electrons is that?

Time in seconds: 1.0 min = 60 s.

Charge: $Q = It = 0.50 \times 60 = 30\ \text{C}$ .

Electrons: $n = \frac{Q}{e} = \frac{30}{1.602 \times 10^{-19}} = 1.87 \times 10^{20}$ .

The dimensions follow the units at each step: A times s gives C, the bracket [IT], and C divided by C leaves a pure count. Milliamperes are common in electronics, so remember that 1 mA = 10⁻³ A before multiplying.

Quantities sharing the bracket [I]

Things measured in amperes
Quantity	Example
Electric current	Current through a heater element
Displacement current	$\varepsilon_0 \frac{d\Phi_E}{dt}$ between capacitor plates
Magnetomotive force	Ampere turns NI of a coil, N being a count
Current in a loop of Ampère's law	$\oint \vec{B}\cdot d\vec{l} = \mu_0 I$

Compare with neighbors that are easy to mix up. Current density is current per area, [L⁻²I]. Charge is current times time, [IT]. Magnetic field intensity H is current per length, [L⁻¹I].

Common mistakes with the current bracket

Writing [QT⁻¹] in an SI answer. That uses charge as a base, which SI does not do.
Writing [IT⁻¹]. That bracket does not describe current; it has an extra time power.
Calling current a vector. Currents at a junction add as numbers, by Kirchhoff's rule, not as arrows. It is a scalar with a sense of flow.
Leaving out I in other electrical brackets. Every SI electrical quantity needs it.

Since current underlies every electrical bracket, the dimensional formulas table is a good place to see I appear in voltage, resistance and inductance.

Frequently asked questions

What is the dimensional formula of current?

It is [M⁰ L⁰ T⁰ I¹], written [I]. Current is an SI base quantity, so its bracket is just its own dimension letter.

Why is current a base quantity and not charge?

SI chose the ampere as its base electrical unit because current is what laboratories control and measure most directly. Charge is then derived as current times time.

What is the dimension of current in terms of charge?

In a system that took charge Q as its base, current would be [QT⁻¹]. In SI it is [I], and charge is [IT].

Is electric current a scalar?

Yes. Although we draw arrows to show its direction along a wire, currents combine by ordinary addition at junctions, not by vector rules.

Which SI unit is current measured in?

The ampere, symbol A. It sits among the base units of SI together with the metre, kilogram, second, kelvin, mole and candela.