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Closed-Surface Electric Flux from Enclosed Charge

Relate positive enclosed charge, total electric flux and the permittivity parameter, retaining charge units, two flux units and an editable locked vacuum default.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

An enclosed charge of 8.8541878188 nC gives total electric flux 1000 V·m using the 2022 CODATA vacuum permittivity.

Φ_E = Q_enclosed / ε₀; V·m and N·m²/C are equivalent electric-flux units.

Worked example

Enter these known values and leave the other values blank.

Positive enclosed charge
8.8541878188 nC
Total closed-surface electric flux
1000 V·m

Assumptions and limitations

  • This is total outward electric flux through a closed surface, not electric field strength at a point. The charge must be enclosed by that surface.
  • The default is the NIST 2022 CODATA central value 8.8541878188 ×10⁻¹² F/m with standard uncertainty 0.0000000014 ×10⁻¹² F/m. Vacuum permittivity is measured, not an exact SI defining constant.
  • This calculation uses positive charge, positive flux and positive permittivity. It does not implement signed inward flux or the zero-charge boundary.
  • The permittivity control remains locked by default. Unlock it only to explore an explicit positive parameter or infer the parameter consistent with two known quantities; this does not establish a new measurement of the vacuum constant.
  • The starting parameter may display a rounded coefficient; calculations retain the complete stated CODATA central value. Changing charge or flux units preserves the physical quantity. The permittivity control displays a coefficient multiplied by 10⁻¹², so entering 8.8541878188 denotes 8.8541878188 ×10⁻¹² F/m.

Common questions

Is electric flux measured in volts or volts times meters?

Total electric flux has units V·m, equivalent to N·m²/C. It is not electric potential in volts.

Can I recover the enclosed charge?

Enter a positive total flux and retain the positive permittivity; enclosed charge equals flux times permittivity.

References

Use the NIST 2022 CODATA central vacuum-permittivity value for the locked scientific-notation default while preserving the positive captured flux model. Guard both dividing inverses with positive denominators; retain all charge and equivalent flux units.

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