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permittivity of free space

What is the permittivity of free space?

The permittivity of free space is a physical constant that reflects the ability of electrical fields to pass through a classical vacuum. The constant is equal to approximately 8.854 x 10-12 F/m (farad per meter), with a relative standard uncertainty of 1.5 x 10-10. A farad is a standard unit of capacitance that indicates the ability of a substance to hold an electric charge. The substance in this case is the vacuum.

Vacuum permittivity equation image
Figure 1. The vacuum permittivity equation.

The permittivity of free space is also referred to as vacuum permittivity or the electric constant. Permittivity itself is a constant of proportionality between electric Displacement and electric field intensity in a given medium, such as a vacuum.

Vacuum permittivity is symbolized by the Greek letter epsilon followed by a subscript zero (ε0), and its value is represented by the equation shown in Figure 1.

The μ0 in the equation is a symbol for the permeability of free space, also known as vacuum permeability or the magnetic constant. Vacuum permeability is a constant of the proportionality between a vacuum's magnetic field strength and its magnetic flux density. It has an approximate value of 4π x 10-7 H/m (henry per meter).

Vacuum permittivity equation image with values plugged in
Figure 2. The equation with values plugged in.

The c in the ε0 equation represents the speed of light, or 299792458 m/s (meters per second) -- a value that must be squared when calculating the vacuum permittivity. Figure 2 shows what it looks like when the values are plugged into the ε0 equation.

When calculated, the equation comes to an ε0 value of about 8.854 x 10-12 F/m. The Committee on Data of the International Science Council provides more precise data about the ε0 value:

  • numerical value: 8.854 187 8128 x 10-12 F/m-1
  • standard uncertainty: 0.000 000 0013 x 10-12 F/m-1
  • relative standard uncertainty: 1.5 x 10-10
  • concise form: 8.854 187 8128(13) x 10-12 F/m-1

The value's uncertainty is a result of changes made in 2019 to the International System of Units. At the time, base unit definitions such as kilogram, ampere, kelvin and mole were updated. The ampere update affected the value of vacuum permeability (μ0), which now comes with a relative standard uncertainty. According to the National Institute of Standards and Technology, the μ0 value must now be "determined experimentally" because of this uncertainty. And as a result, this uncertainty passes to the ε0 equation because it incorporates the μ0 value.

Also see Table of physical units and Table of physical constants

This was last updated in September 2022

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