Collection of fundamental physical constants with uncertainties. It supports arbitrary-precision constants
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September 2018


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PhysicalConstants.jl provides common physical constants. They are defined as instances of the new Constant type, which is subtype of AbstractQuantity (from Unitful.jl package) and can also be turned into Measurement objects (from Measurements.jl package) at request.

Constants are grouped into different submodules, so that the user can choose different datasets as needed. Currently, 2014 and 2018 editions of CODATA recommended values of the fundamental physical constants are provided.


The latest version of PhysicalConstants.jl is available for Julia 1.0 and later versions, and can be installed with Julia built-in package manager. After entering the package manager mode by pressing ], run the command

pkg> add PhysicalConstants


You can load the package as usual with using PhysicalConstants but this module does not provide anything useful for the end-users. You most probably want to directly load the submodule with the dataset you are interested in. For example, for CODATA 2018 load PhysicalConstants.CODATA2018:

julia> using PhysicalConstants.CODATA2018

julia> SpeedOfLightInVacuum
Speed of light in vacuum (c_0)
Value                         = 2.99792458e8 m s^-1
Standard uncertainty          = (exact)
Relative standard uncertainty = (exact)
Reference                     = CODATA 2018

julia> NewtonianConstantOfGravitation
Newtonian constant of gravitation (G)
Value                         = 6.6743e-11 m^3 kg^-1 s^-2
Standard uncertainty          = 1.5e-15 m^3 kg^-1 s^-2
Relative standard uncertainty = 2.2e-5
Reference                     = CODATA 2018

SpeedOfLightInVacuum and NewtonianConstantOfGravitation are two of the PhysicalConstants defined in the PhysicalConstants.CODATA2018 module, the full list of available constants is given below.

PhysicalConstants can be readily used in mathematical operations, using by default their Float64 value:

julia> import PhysicalConstants.CODATA2018: c_0, ε_0, μ_0

julia> 2 * ε_0
1.77083756256e-11 F m^-1

julia> ε_0 - 1 / (μ_0 * c_0 ^ 2)
-3.8450973786644646e-25 A^2 s^4 kg^-1 m^-3

If you want to use a different precision for the value of the constant, use the function float(float_type, constant), for example:

julia> float(Float32, ε_0)
8.854188f-12 F m^-1

julia> float(BigFloat, ε_0)
8.854187812799999999999999999999999999999999999999999999999999999999999999999973e-12 F m^-1

julia> big(ε_0)
8.854187812799999999999999999999999999999999999999999999999999999999999999999973e-12 F m^-1

julia> big(ε_0) - inv(big(μ_0) * big(c_0)^2)
-3.849883307464075736533920296598236938395867709081184624499315166190408485179288e-25 A^2 s^4 kg^-1 m^-3

Note that big(constant) is an alias for float(BigFloat, constant).

If in addition to units you also want the standard uncertainty associated with the constant, use measurement(x):

julia> using Measurements

julia> import PhysicalConstants.CODATA2018: h, ħ

julia> measurement(ħ)
1.0545718176461565e-34 ± 0.0 J s

julia> measurement(Float32, ħ)
1.0545718e-34 ± 0.0 J s

julia> measurement(BigFloat, ħ)
1.054571817646156391262428003302280744722826330020413122421923470598435912734741e-34 ± 0.0 J s

julia> measurement(BigFloat, ħ) / (measurement(BigFloat, h) / (2 * big(pi)))
1.0 ± 0.0

For more information read the documentation, which includes the full list of constants defined by the package.


The PhysicalConstants.jl package is licensed under the MIT "Expat" License. The original author is Mosè Giordano.