ConstantID

Natural unit of time

UnitsMeasured

ℏ/mec2 = 1.288 088 666 44(40) × 10−21 s

Value
1.288 088 666 44 × 10−21 s
Standard uncertainty
4 × 10−31 s
Relative uncertainty
3.1 × 10−10 (311 parts per trillion)
Status
Measured
Symbol
ℏ/mec2
Source
CODATA 2022 via NIST · NIST entry

Use in a calculation

# natural unit of time, CODATA 2022 (NIST)
natural_unit_of_time = 1.28808866644e-21  # s, standard uncertainty 4e-31

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

What it is

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

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 time: 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 time: relative standard uncertainty in each CODATA adjustment, logarithmic scale10⁻¹⁰10⁻⁹10⁻⁸1998200220062010201420182022
CODATAValue (uncertainty)Relative uncertaintyChange from previous
20221.288 088 666 44(40) × 10−213.1 × 10−10 −4.5 σ of 2018
20181.288 088 668 19(39) × 10−213.0 × 10−10 +1.8 σ of 2014
20141.288 088 667 12(58) × 10−214.5 × 10−10 −1.5 σ of 2010
20101.288 088 668 33(83) × 10−216.4 × 10−10 +6.3 σ of 2006
20061.288 088 6570(18) × 10−211.4 × 10−9 −1.2 σ of 2002
20021.288 088 6677(86) × 10−216.7 × 10−9 +1.3 σ of 1998
19981.288 088 6555(95) × 10−217.4 × 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).