CODATA Fundamental Physical Constants

The CODATA recommended values of the fundamental physical constants, expressed in SI units.

#include <mp-units/systems/codata.h>

using namespace mp_units;

quantity mu = measurement_of(codata::magnetic_constant).in(si::henry / si::metre);
std::cout << mu << "\n";  // 1.25664e-06 ± 2.01062e-16 H/m

Why a separate system

The SI fixes exactly seven constants, and those live in the SI system where they belong. Everything CODATA publishes beyond them is measured: each value carries a relative standard uncertainty and shifts with every adjustment.

Keeping them here rather than in si is a deliberate cost decision. <mp-units/systems/si.h> is the header most translation units reach for, and most of them never name a CODATA constant. Making everyone pay for the full table so that a minority need not write one extra #include is the wrong trade. Include this header when you want these constants.

Adjustments

Each CODATA adjustment gets its own namespace, because a measured constant has no single correct value:

quantity now = measurement_of(codata::magnetic_constant);                  // current
quantity pinned = measurement_of(codata::codata2018::magnetic_constant);   // a specific one

The most recent adjustment is inline, so the unqualified name always refers to it while older ones stay reachable by spelling them out. Moving that inline to a newer adjustment is a deliberate, documented change of the default rather than something that happens silently.

Constants that are exact under a given adjustment carry no uncertainty at all, which makes the exact-versus-measured distinction visible to the type system:

static_assert(MeasuredConstant<decltype(codata::codata2022::magnetic_constant)>);
static_assert(!MeasuredConstant<decltype(codata::codata2014::magnetic_constant)>);

The magnetic constant μ₀ (IEC 80000-6, item 6-26.1) shows why. Before 2019 the ampere was defined through μ₀, which made it exactly \(4\pi \times 10^{-7}\) H/m. The 2019 redefinition tied the ampere to the elementary charge instead, so μ₀ became measured, and its value departs from \(4\pi \times 10^{-7}\) in the tenth digit.

Not interchangeable with the hep constants

The HEP system provides codata2014/codata2018/codata2022 namespaces of its own, but those constants are not the same entities. HEP declares its own system of quantities, with energy as a base quantity and no mass dimension at all, so its constants are unrelated types that no conversion can reach.

Their published uncertainties can differ as well. Before 2019 the elementary charge was itself measured, so a mass expressed in kg and the same mass expressed in MeV/c² are separate CODATA table entries with different \(u_r\). Deriving one from the other would combine correlated uncertainties in quadrature and overstate them.

Working with the uncertainties

These constants are ordinary units, so they cost nothing until a conversion actually needs their value, and they cancel symbolically when they appear on both sides. To obtain a quantity that carries the uncertainty, use measurement_of, described in Working with Measurement Uncertainty.