ConstantID

Atomic unit of length

UnitsMeasured

a0 = 5.291 772 105 44(82) × 10−11 m

Value
5.291 772 105 44 × 10−11 m
Standard uncertainty
8.2 × 10−21 m
Relative uncertainty
1.5 × 10−10 (155 parts per trillion)
Status
Measured
Symbol
a0
Source
CODATA 2022 via NIST · NIST entry

Use in a calculation

# atomic unit of length, CODATA 2022 (NIST)
atomic_unit_of_length = 5.29177210544e-11  # m, standard uncertainty 8.2e-21

# SciPy: scipy.constants.physical_constants['atomic unit of length']

What it is

The unit of length in the Hartree system of atomic units, where the electron mass, the elementary charge, ħ and 4πε₀ are all set to 1. Its value here is the SI equivalent of one atomic unit.

In other units

UnitValue
CGS (cm)5.291 772 105 44 × 10−9
nm nanometre0.052 917 721 0544
pm picometre52.917 721 0544
fm femtometre52 917.721 0544
Å ångström0.529 177 210 544
a₀ bohr (atomic unit)1unit is itself measured

Converted with ConstantID's unit table; digits are rounded to the precision of the value, and a long exact value is rounded only for display. The relative uncertainty is unchanged by conversion to an exactly defined unit.

How the value changed, 1998–2022

Each point is one CODATA adjustment, plotted as its difference from the 2022 value; the bars show one standard uncertainty (an arrowhead means the bar runs off the chart).

atomic unit of length: CODATA values 1998–2022 relative to the 2022 value, in parts per billion, with one-standard-uncertainty bars−6−4−20+2+4+6parts per billion1998200220062010201420182022

Relative uncertainty

atomic unit of length: relative standard uncertainty in each CODATA adjustment, logarithmic scale10⁻¹⁰10⁻⁹10⁻⁸1998200220062010201420182022
CODATAValue (uncertainty)Relative uncertaintyChange from previous
20225.291 772 105 44(82) × 10−111.5 × 10−10 −4.5 σ of 2018
20185.291 772 109 03(80) × 10−111.5 × 10−10 +1.9 σ of 2014
20140.529 177 210 67(12) × 10−102.3 × 10−10 −1.5 σ of 2010
20100.529 177 210 92(17) × 10−103.2 × 10−10 +6.5 σ of 2006
20060.529 177 208 59(36) × 10−106.8 × 10−10 −1.2 σ of 2002
20020.529 177 2108(18) × 10−103.4 × 10−9 +1.3 σ of 1998
19980.529 177 2083(19) × 10−103.6 × 10−9

“Change from previous” is the shift in the value divided by the standard uncertainty of the previous adjustment. Earlier values are converted into the current unit where NIST changed it (for example J s to J Hz⁻¹).