Vacuum permittivity, ε₀

The constant that sets the strength of electric forces in a vacuum, also called the permittivity of free space or the electric constant. Since 2019 it has been measured rather than defined.

ε₀ = 8.8541878188(14) × 10⁻¹² F/m

CODATA 2022, measured. Standard uncertainty 0.0000000014 × 10⁻¹² F/m, which is 1.6 × 10⁻¹⁰ of the value.

Not a row of the physical constants table, which leaves the electromagnetic constants out because their digits moved between the 2018 and 2022 CODATA adjustments.

In other units

Measured values are in CODATA’s concise form: the digits in brackets are the standard uncertainty in the last two places, so 6.67430(15) means 6.67430 ± 0.00015.

Vacuum permittivity in SI units and in other units
Quantity	Value
ε₀	8.8541878188(14) × 10⁻¹² F/m
ε₀	8.8541878188(14) × 10⁻¹² C²/(N·m²)
ε₀	8.8541878188(14) pF/m

ε₀ in C²/(N·m²)

1 F = 1 C/V and 1 V = 1 N·m/C, so F/m = C²/(N·m²)
= 8.8541878188(14) × 10⁻¹² C²/(N·m²)

The same number in the units Coulomb’s law is usually written in.

ε₀ in pF/m

8.8541878188(14) × 10⁻¹² F/m × 10¹² pF/F
= 8.8541878188(14) pF/m

The engineer’s form, which gives a capacitance in picofarads directly.

Where the value comes from

Before 2019 the ampere was defined by the force between two parallel wires, which fixed μ₀ at exactly 4π × 10⁻⁷ N/A², and because ε₀μ₀c² = 1, ε₀ was exact as well.

The 2019 revision defined the ampere through the elementary charge instead. With e, h and c fixed, ε₀ is tied to the fine-structure constant α by ε₀ = e²/(2αhc), and α has to be measured, so ε₀ inherits α’s relative uncertainty: 1.6 × 10⁻¹⁰ in CODATA 2022.

Its digits have moved between adjustments. CODATA 2018 gave 8.8541878128(13) × 10⁻¹² F/m, and the 2022 value is higher by more than 4 times the uncertainty quoted in 2018. That is why the physical constants table leaves the electromagnetic constants out, and why this page names its adjustment.

ε₀ from the fine-structure constant

ε₀ = e² ÷ (2αhc)
= (1.602176634 × 10⁻¹⁹)² ÷ (2 × 7.2973525643(11) × 10⁻³ × 6.62607015 × 10⁻³⁴ × 299,792,458)
= 8.8541878188(14) × 10⁻¹² F/m

Which form to use

ε₀ enters Coulomb’s law written as F = q₁q₂/(4πε₀r²), Gauss’s law, and the capacitance of a parallel-plate capacitor, C = ε₀εᵣA/d. Engineers often quote it as 8.854 pF/m, which gives a capacitance in picofarads when the area and the gap are in metres.

For almost any calculation 8.854 × 10⁻¹² F/m is plenty. Rounding to four figures introduces a relative error of 2.1 × 10⁻⁵, far larger than the measurement’s own uncertainty of 1.6 × 10⁻¹⁰.

Common mistakes

Treating ε₀ as exact. Tables from before 2019 did, with 8.854187817… × 10⁻¹² F/m, a figure that differs from today’s in the tenth significant figure.
Leaving out the relative permittivity. ε₀ is the value for a vacuum, and air is very close to it, but a capacitor filled with a dielectric has C = ε₀εᵣA/d, with εᵣ from about 2 for a plastic film to thousands for some ceramics.
Swapping ε₀ and Coulomb’s constant. kₑ = 1/(4πε₀), so a formula written with one cannot simply take the other.

Tools that use it

Coulomb’s Law Calculator computes with Coulomb’s constant, kₑ = 1/(4πε₀), derived from it.
Electric Field Simulator computes the field and potential of each charge with kₑ = 1/(4πε₀), derived from it.

Related constants

Coulomb’s constant, kₑ = 8.9875517862(14) × 10⁹ N·m²/C²
Vacuum permeability, μ₀ = 1.25663706127(20) × 10⁻⁶ N/A²
Speed of light in vacuum, c = 299,792,458 m/s
Elementary charge, e = 1.602176634 × 10⁻¹⁹ C