Physics

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Gauss's Law Calculator.

Calculate enclosed charge from electric flux and permittivity.

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Results update as you type.

Enclosed charge: 0 C

Enclosed charge

0.000000C

Results update automatically as you type.

Use Cases

Physics homework and exam prep

Quickly verify your manual calculations for enclosed charge in electrostatics problems, saving time and reducing errors.

Example: Given electric flux of 500 N·m²/C and permittivity of 8.85e-12 F/m, find the enclosed charge.

Engineering design checks

Use in electrical engineering to estimate charge in capacitors or other components by measuring flux and knowing the medium's permittivity.

Example: Check the charge on a capacitor plate with known flux and dielectric permittivity.

Frequently Asked Questions

What does this Gauss's law calculator do?
It calculates the enclosed charge by multiplying the electric flux (in N·m²/C) by the permittivity (in F/m). This is based on Gauss's law, which relates the net electric flux through a closed surface to the charge enclosed within it.
What units should I use for electric flux and permittivity?
Electric flux should be entered in N·m²/C (newton square meters per coulomb), and permittivity in F/m (farads per meter). The calculator will output the enclosed charge in coulombs (C).
Can I use this calculator for any closed surface?
Yes, Gauss's law applies to any closed surface. The calculator uses the net electric flux through that surface, so as long as you have the correct flux value, it works for spheres, cylinders, or any arbitrary shape.

Tips & Common Mistakes

Tips

  • Ensure the electric flux is the net flux through the entire closed surface, not just a part of it.
  • Use the permittivity of the medium (e.g., free space is 8.85e-12 F/m) for accurate results.
  • Double-check unit consistency: flux in N·m²/C and permittivity in F/m will yield charge in coulombs.
  • For complex surfaces, break down the flux calculation carefully before entering the total.

Common Mistakes to Avoid

  • Using the electric field instead of the electric flux – flux is the field integrated over the surface area.
  • Forgetting to convert units, such as using cm² instead of m² for area when calculating flux.
  • Entering permittivity in different units (e.g., μF/m) without converting to F/m.

Last updated: August 13, 2026