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Dimensional Formula of Voltage

Dimensional formulas of physical quantitiesClass 10Class 12Updated 1 Nov 2026

[V]=[M1L2T−3I−1][V] = [M^{1} L^{2} T^{-3} I^{-1}]
SI unit
volt (V) = J/C = kg m² s⁻³ A⁻¹
Dimensions
[M¹ L² T⁻³ I⁻¹]
where
  • M dimension of mass kg
  • L dimension of length m
  • T dimension of time s
  • I dimension of electric current A

The dimensional formula of voltage is [M¹ L² T⁻³ I⁻¹]. Voltage, potential difference, electric potential and emf all have this one bracket, because each is work done per unit charge.

Work brings [ML²T⁻²] and charge brings [IT]. Dividing the two moves the time power from minus 2 to minus 3 and puts current below the line. In base units a volt is kg m² s⁻³ A⁻¹, a heavy expression that the simple name volt hides. Circuit problems that use the bracket's partner formulas are on the voltage formula guide.

Quick facts

  • Dimensional formula

    [M¹ L² T⁻³ I⁻¹]

  • Defining formula

    V=WqV = \frac{W}{q}

  • SI unit

    volt (V) = J/C = W/A

  • Base units

    kg m² s⁻³ A⁻¹

  • Type

    Scalar

  • Same bracket

    Potential difference, electric potential, emf

Derive the dimensional formula of voltage in four lines

  1. Definition: V=WqV = \frac{W}{q}, the work needed per coulomb to carry charge from one point to another.
  2. Work is force times distance: [W]=[MLT−2][L]=[ML2T−2][W] = [MLT^{-2}][L] = [ML^{2}T^{-2}].
  3. Charge equals current multiplied by time, so [q]=[IT][q] = [IT].
  4. Divide, adding the time powers: [V]=[ML2T−2]×[T−1I−1]=[ML2T−2−1I−1][V] = [ML^{2}T^{-2}] \times [T^{-1}I^{-1}] = [ML^{2}T^{-2-1}I^{-1}], that is [ML²T⁻³I⁻¹].

You can reach the same bracket from power. Electrical power is P=VIP = VI, so V=P/IV = P/I. Power is [ML2T−3][ML^{2}T^{-3}], and dividing by [I] gives the answer again. A board answer that shows one route clearly is enough, but knowing both helps you check yourself under time pressure.

Volt, joule per coulomb and watt per ampere

Three names, one unit. From V = W/q the volt is a joule per coulomb. From V = P/I it is a watt per ampere. From Ohm's law, V = IR, it is an ampere ohm. All of them collapse to kg m² s⁻³ A⁻¹.

Example: a phone charger supplies 5.0 V at 1.5 A for 40 minutes. How much energy does each coulomb receive, and how much energy is delivered in total?

Energy per coulomb: 5.0 V means 5.0 J per coulomb.

Charge moved: q=It=1.5×(40×60)=3600 Cq = It = 1.5 \times (40 \times 60) = 3600\ \text{C}.

Total energy: W=qV=3600×5.0=1.8×104 JW = qV = 3600 \times 5.0 = 1.8 \times 10^{4}\ \text{J}.

The electron volt is an energy, not a voltage: 1 eV = 1.602 × 10⁻¹⁹ J.

Checking circuit formulas with the voltage bracket

Example: confirm that P=V2RP = \frac{V^{2}}{R} gives a power.

Resistance: [R]=[V][I]=[ML2T−3I−2][R] = \frac{[V]}{[I]} = [ML^{2}T^{-3}I^{-2}].

[ML2T−3I−1]2[ML2T−3I−2]=[M2L4T−6I−2][ML2T−3I−2]=[ML2T−3]\frac{[ML^{2}T^{-3}I^{-1}]^{2}}{[ML^{2}T^{-3}I^{-2}]} = \frac{[M^{2}L^{4}T^{-6}I^{-2}]}{[ML^{2}T^{-3}I^{-2}]} = [ML^{2}T^{-3}]. That is power, so the formula passes.

Squaring the voltage doubles each of its powers, and the resistance bracket then strips out the current completely while removing one M, two L and three powers of time. The resistance bracket used in that check is derived in full on the resistance dimensions page, and Ohm's law itself is covered under Ohm's law.

One bracket, several electrical names

Quantities with [M L² T⁻³ I⁻¹]
QuantityFormulaComment
Potential differenceW/qW/qBetween two points
Electric potentialq4πε0r\frac{q}{4\pi\varepsilon_0 r}Relative to infinity
EmfEnergy supplied per coulombNot a force despite the name
Induced emf−N ΔΦ/Δt-N\,\Delta\Phi/\Delta tFlux per time

Two neighbors are easy to confuse with voltage. Electric field is voltage per metre and loses one L. Magnetic flux is voltage times time and gains one T. Keeping these three side by side is a quick way to revise electrostatics and induction together.

Where students go wrong with volts

  • Stopping at T⁻². That is the bracket of energy. Dividing by charge adds a power of time below the line.
  • Forgetting I. Every SI electrical bracket needs current somewhere.
  • Treating emf as a force. Its name is historical; its bracket is that of voltage.
  • Writing [ML²T⁻³A⁻¹] in one line and [ML²T⁻³I⁻¹] in the next. Both are fine, but pick one symbol for current and keep it.

Brackets for current, charge, resistance and capacitance are grouped together on the dimensional formulas hub, ideal for one final circuits revision.

Frequently asked questions

What is the dimensional formula of voltage?

Voltage has the bracket [M¹ L² T⁻³ I⁻¹]. It comes from work over charge: [ML²T⁻²] ÷ [IT] leaves that result.

Is the dimension formula of voltage the same as for potential difference?

Potential difference is another name for voltage between two points, so it shares [ML²T⁻³I⁻¹] and is also measured in volts.

Do emf and voltage have the same dimensional formula?

Yes. Emf is the energy a source gives each coulomb, which is work per charge, exactly like voltage. Both are [ML²T⁻³I⁻¹].

Does voltage have a direction?

No. Potential is a scalar: values at points simply add with their signs, and nothing about them points anywhere.

How many base units make up one volt?

Four: kilogram, metre, second and ampere. One volt equals kg m² s⁻³ A⁻¹, which is why the short name volt is so useful.