ConstantID

Natural unit of length

UnitsMeasured

λ¯C = 3.861 592 6744(12) × 10−13 m

Value
3.861 592 6744 × 10−13 m
Standard uncertainty
1.2 × 10−22 m
Relative uncertainty
3.1 × 10−10 (311 parts per trillion)
Status
Measured
Symbol
λ¯C
Source
CODATA 2022 via NIST · NIST entry

Use in a calculation

# natural unit of length, CODATA 2022 (NIST)
natural_unit_of_length = 3.8615926744e-13  # m, standard uncertainty 1.2e-22

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

What it is

The unit of length in the natural units of relativistic quantum mechanics, where ħ, c and the electron mass are set to 1.

In other units

UnitValue
CGS (cm)3.861 592 6744 × 10−11
pm picometre0.386 159 267 44
fm femtometre386.159 267 44
Å ångström0.003 861 592 6744
a₀ bohr (atomic unit)0.007 297 352 564unit 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).

natural unit of length: CODATA values 1998–2022 relative to the 2022 value, in parts per billion, with one-standard-uncertainty bars−15−10−50+5+10+15parts per billion1998200220062010201420182022

Relative uncertainty

natural unit of length: relative standard uncertainty in each CODATA adjustment, logarithmic scale10⁻¹⁰10⁻⁹10⁻⁸1998200220062010201420182022
CODATAValue (uncertainty)Relative uncertaintyChange from previous
20223.861 592 6744(12) × 10−133.1 × 10−10 −4.3 σ of 2018
20183.861 592 6796(12) × 10−133.1 × 10−10 +1.8 σ of 2014
2014386.159 267 64(18) × 10−154.7 × 10−10 −1.4 σ of 2010
2010386.159 268 00(25) × 10−156.5 × 10−10 +6.4 σ of 2006
2006386.159 264 59(53) × 10−151.4 × 10−9 −1.2 σ of 2002
2002386.159 2678(26) × 10−156.7 × 10−9 +1.3 σ of 1998
1998386.159 2642(28) × 10−157.3 × 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).