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Electric Flux calculator

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Table of Content


Our electric flux calculator is used to calculate the magnitude of the total charges enclosed by a surface. This gauss law calculator uses the field strength with their area and flux angle to compute total magnetic flux with inner and outer flux across a given area. 

What is Electric Flux?

Flux means how much something can go through a given area. So, the electric flux is defined as;

“The flow of electric field lines from a certain surface in a unit of time”

It is the dot product of the electric field and the surface area elements. The passing lines show the strength and direction of an electric field. 

  • The more field lines go through the larger area there is such stronger the electric field
  • When the electric field lines move away from the charges it causes a weaker field

SI Unit:

SI unit of electric flux is volt-metres (V m) which equals newton-metres squared per coulomb (N m2 C-1).

Gauss’s Law:

This law is stated as;

“Electric flux through any surface is equal to the total charges enclosed by a surface divided by the permittivity of free space”

How Electric Flux Calculator Work?

Utilize the electric flux calculator to determine the electric flux. It has a user-friendly interface that takes some values as inputs to streamline a process making electric flux determination efficient and accessible. 


  • Put the magnitude of the electric field
  • Put the surface area and angle of field lines
  • Select the unit of charge and put its value 
  • Also, enter the permittivity value


  • Electric Flux and its direction that cross from the surface area (Φ)
  • Electric flux for inward and outward flux
  • Total Charges Enclosed by a certain surface (Q)
  • Surface Charge Density (σ)
  • Complete calculations in steps 

Electric Flux Formula:

Our electric flux calculator allows you to find the electric flux magnitude which is generated by the electric field of charge. It uses the following electric flux equation:

Φ = ∫ E ⋅ dA


  • Φ _ Electric Flux 
  • E _ Electric Field 
  • dA _ Surface Area 

According to Gauss's law, the electric flux through a closed surface is equal to the total charge enclosed by the surface divided by the permittivity of free space. 

Φ = Q / ε₀


  • Q is the total charge enclosed by the surface
  • ε₀ is the permittivity of free space = 8.85 x 10^-12 F/m

Practical Example:

Assume that the 5 μC charge is enclosed within the 0.5 m² surface area. What is the flux due to the charge which has a 100 N/C magnitude of the electric field with an angle of 45 degrees? 

Given Data:

Magnitude of Electric Field = 100 N/C
Surface Area = 0.5 m²
Angle of Field Lines = 45 degrees
Charge Value = 5 μC
Permittivity = 8.85 x 10⁻¹² C²/(N·m²)


Plug the values in the electric flux equation:

$$ \dfrac{Q}{ϵ_0} $$

$$ \dfrac{5000}{8.854 × 10^{-12}} $$

Φ = 5.6471651231082E+14

Electric Flux for Inward Flux:

Φ = |E| ×|A| ×cos(180 - θ)

Φ = 100 | x 0.5 x cos(180 - 45)

Φ = 100 | x 0.5 x cos(135)

Φ = 100 | x 0.5 x -0.7071

Φ = -35.3553

Electric Flux for Outward Flux:

Φ = |E| ×|A| ×cos(θ)

Φ = 100 x 0.5 x cos(45)

Φ = 100 x 0.5 x 0.70711

Φ = 35.3553

Additional Queries:

What is the Relationship Between Electric Flux and Electric Charge?

The relation between the electric flux and the electric charge is determined by Gauss’s law in which we describe that the electric flux is equal to the charge that is closed by the surface is divided by the free space permitivity. 

What is an Electric Field?

The vector quantity describes the force acting on a charged particle at a certain space. The magnitude of an electric field is determined in volts per meter and in the direction of the electric field, the positive test charge would be accelerated.  


Wikipedia: Electric flux.

Britannica: Electric flux, Gauss’s law, and electric displacement.

Phys libre texts: Flux of the Electric Field, Example, Non-uniform fields, Closed surfaces.

Alan Walker

Studies mathematics sciences, and Technology. Tech geek and a content writer. Wikipedia addict who wants to know everything. Loves traveling, nature, reading. Math and Technology have done their part, and now it's the time for us to get benefits.

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