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

> Searchable CODATA 2022 physical constants: c, h, electron mass, fine-structure constant and 100+ more with uncertainties. Copy as LaTeX or code, convert units.

- URL: https://qilingtools.com/en/physics/constants
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- Last updated: 2026-10-29
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Over 100 constants from the CODATA 2022 recommended values, plus IAU nominal astronomical values and common conventional values, grouped as universal, electromagnetic, atomic and nuclear, physico-chemical, astronomical and Earth. Each constant is marked as exact or measured, with its standard and relative uncertainty. Search by name or symbol, copy the value as scientific notation, concise notation, LaTeX, JavaScript or Python, and convert it to units such as eV, MeV/c² or Å.

## How to use

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

## Features

- CODATA 2022 recommended values with exact/measured status and uncertainties
- IAU 2012/2015 nominal values: astronomical unit, solar and Earth mass parameters, planetary radii
- Seven copy formats: readable, scientific, concise, ±, LaTeX, JavaScript, Python
- Unit conversion for energies, masses, lengths and times (J↔eV, kg↔u↔MeV/c² …)
- 50+ derived relations checked live, e.g. ħ = h/2π and α = e²/(4πε₀ħc)
- Search in English or Chinese and keep favorites in your browser

## 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.

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