Electric Flux (Gauss Law) Calculator

The will calculate the electric flux produced by electric field lines flowing through a closed surface:

When electric field is given
When the charge is given

Electric Flux (Gauss Law) Calculator
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Calculator Precision (Decimal Places)
Magnitude of electric field (\|E\|) V/m
Surface area^{Note 1} (\|A\|) m²
Angle between electric field lines and the area vector (θ) °
Electric charge (Q) C
Electric constant or vacuum permittivity (ϵ₀) C²/N∙m²	× 10 power of

Electric Flux (Gauss Law) Calculator Results (detailed calculations and formula below)
Electric flux calculations for inward flux
The electric flux (inward flux) through a closed surface when electric field is given is V ∙ m [Volt times metre]
The electric flux (outward flux) through a closed surface when electric field is given is V ∙ m [Volt times metre]
The electric flux through a closed surface when the charge is given using the Gauss Law is
Φ = \|E⃗ \| × \|A⃗ \| × cos(180 - θ) Φ = \| × × cos(180 - ) Φ = \| × × cos() Φ = \| × × cos() Φ =
Electric flux calculations for outward flux
Φ = \|E⃗ \| × \|A⃗ \| × cosθ Φ = × × cos() Φ = × × Φ =
Electric flux Gauss Law calculations
Φ = Q/ϵ₀ Φ = / Φ =
Electric Flux Calculator Input Values
Magnitude of electric field (\|E\|) V/m [Volt per metre]
Surface area^{Note 1} (\|A\|) m² [square metres]
Angle between electric field lines and the area vector (θ) ° [degrees]
Electric charge (Q) C [Coulombs]
Electric constant or vacuum permittivity (ϵ₀) C²/N∙m²

Please note that the formula for each calculation along with detailed calculations are available below. As you enter the specific factors of each electric flux calculation, the Electric Flux Calculator will automatically calculate the results and update the Physics formula elements with each element of the electric flux calculation. You can then email or print this electric flux calculation as required for later use.

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Discover Physics with free Physics Revision Notes and Physics Calculator: Electric Flux. This image shows the properties and electric flux formula for the Electric Flux. This calculator will calculate the electric flux produced by electric field lines flowing through a closed surface when electric field is given and/or when the charge is given with detailed formula and calculations

Electric flux calculations (inward flux) Formula and Calculation

Φ = |E⃗ | × |A⃗ | × cos(180 - θ)

Electric flux (outward flux) Formula and Calculation

Φ = |E⃗ | × |A⃗ | × cosθ

Electric flux Gauss Law Formula and Calculation

Φ = Q/ϵ₀

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