Gauss's Law

\oint \vec{E} \cdot d\vec{A} = \frac{Q_{enc}}{\varepsilon_0}

Electric flux through closed surface equals enclosed charge / ε₀.

Variables

∮E·dA

Electric flux

Through closed surface

In SI units: kg·m³/(A·s³)

V·m

Q_enc

Enclosed charge

Charge inside surface

In SI units: A·s

ε₀

Permittivity

8.85×10⁻¹²

In SI units: A²·s⁴/(kg·m³)

F/m

Derivation

One of Maxwell's equations.

Your notes

0/5000

Constants in this formula

ε₀

Vacuum Permittivity

8.854 × 10⁻¹². Measured (CODATA 2018).

F/m

Other electricity & magnetism formulas with the same quantities

Parallel Plate Capacitor (Capacitance) shares Permittivity
Capacitor with Dielectric (Capacitance) shares Permittivity
Energy Density (Electric Field) (Capacitance) shares Permittivity

Where this formula is listed

Electricity & Magnetism formulas, under Electrostatics, alongside Electric Potential, Electric Potential Energy, Uniform Electric Field, Electric Dipole Moment and Electric Dipole Field (Axial).
In the electricity & magnetism list it comes after Uniform Electric Field and before Electric Dipole Moment.
Electricity & Magnetism formula sheet, one of 48 formulas printed with symbol keys and SI units.
The full formula index, grouped by category and topic.

Common questions

What is the Gauss's Law formula?

Gauss's Law is written ∮E⃗ · dA⃗ = Q_enc/ε₀. Electric flux through closed surface equals enclosed charge / ε₀. It belongs to Electricity & Magnetism, under Electrostatics.

What are the units in ∮E⃗ · dA⃗ = Q_enc/ε₀?

In SI units, ∮E·dA is electric flux, measured in kg·m³/(A·s³); Q_e nc is enclosed charge, measured in A·s; ε₀ is permittivity, measured in A²·s⁴/(kg·m³).

How is the Gauss's Law formula derived?

One of Maxwell's equations. The result is ∮E⃗ · dA⃗ = Q_enc/ε₀.