📖Physical Constants Table - CODATA 2022 Values, Uncertainties, Copy

How to use Physical Constants Table (CODATA 2022)

1. 1Type a name or symbol (e.g. “electron mass”, “hbar”, “G”) or pick a group
2. 2Choose the copy format at the top right and use each row's Copy button
3. 3Open a row to see every format, unit conversions and the relations it appears in
4. 4Star the constants you use often and find them under Favorites

FAQ

Why do c, h and e have no uncertainty?

Since the 2019 SI redefinition the second, metre, kilogram, ampere, kelvin, mole and candela are defined by fixing the values of c = 299 792 458 m/s, h = 6.626 070 15 × 10⁻³⁴ J s, e = 1.602 176 634 × 10⁻¹⁹ C, k = 1.380 649 × 10⁻²³ J/K, N_A = 6.022 140 76 × 10²³ mol⁻¹, the caesium hyperfine frequency and Kcd. They are exact. Combinations such as ħ, R, F and σ are exact too but have endless digits, so they are truncated as CODATA does and marked “…”.

What does the number in parentheses in 6.674 30(15) × 10⁻¹¹ mean?

That is concise notation: the digits in parentheses are the standard uncertainty in the last digits of the value. 6.674 30(15) means a standard uncertainty of 0.000 15, i.e. (6.674 30 ± 0.000 15) × 10⁻¹¹. The relative uncertainty is the standard uncertainty divided by the value; for G it is about 2.2 × 10⁻⁵, which makes G one of the least precisely known fundamental constants.

Isn't the vacuum permeability μ₀ exactly 4π × 10⁻⁷?

It was until 2019, when the definition of the ampere fixed μ₀. Now the elementary charge is fixed instead, and μ₀ follows from the measured fine-structure constant: μ₀ = 2αh/(e²c). CODATA 2022 gives 1.256 637 061 27(20) × 10⁻⁶ N/A², which differs from 4π × 10⁻⁷ only at the 10⁻¹⁰ level. The old value is fine for everyday work, but strictly μ₀, ε₀ and Z₀ now carry an uncertainty.

Why is the solar mass known to only about five digits?

Planetary dynamics measures the solar mass parameter GM⊙ extremely well (IAU nominal value 1.327 124 4 × 10²⁰ m³/s²), but turning it into a mass means dividing by G, whose relative uncertainty is about 2.2 × 10⁻⁵. So M⊙ = GM⊙/G is good to roughly five digits. Celestial mechanics therefore works with GM directly rather than with M and G separately.

How are the unit conversions and relation checks computed?

Conversions use exact constants or table values as factors, for example 1 eV = 1.602 176 634 × 10⁻¹⁹ J and 1 u = m_u; the converted relative uncertainty adds relative uncertainties in quadrature and ignores correlations between constants. The relation checks recompute values such as ħ = h/2π, R∞ = α²m_ec/2h and μ_B = eħ/2m_e from the table and compare the deviation with the combined uncertainty, confirming that the table is self-consistent.