How this calculator works
Gauss law connects total outward electric flux over a closed surface with the charge enclosed. Surface shape does not affect the net flux. In vacuum, use epsilon0 and total enclosed charge. In a uniform linear dielectric, using the same constant epsilon throughout the surface relates electric flux to enclosed free charge. For nonuniform materials use electric displacement flux instead; this scalar form cannot factor out a varying permittivity.
Formula
PhiE = integral_closed(E dot dA) = Qenclosed/epsilon. Qenclosed = epsilon PhiE and epsilon = Qenclosed/PhiE.
Worked example
A vacuum surface enclosing 8.8541878188e-12 C has outward electric flux 1 N m²/C. Flux -2 N m²/C corresponds to enclosed charge -1.77083756376e-11 C.
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Frequently asked questions
Does the enclosed charge have to be centred?
No. The net flux depends on total enclosed charge regardless of position.
Do charges outside the surface matter?
They change the local field, but their net flux through the closed surface is zero.
Does zero flux mean no electric field?
No. Inward and outward contributions can cancel while the local field remains nonzero.