ConstantID

Natural unit of energy

UnitsMeasured

mec2 = 8.187 105 7880(26) × 10−14 J

Value
8.187 105 7880 × 10−14 J
Standard uncertainty
2.6 × 10−23 J
Relative uncertainty
3.2 × 10−10 (318 parts per trillion)
Status
Measured
Symbol
mec2
Source
CODATA 2022 via NIST · NIST entry

Use in a calculation

# natural unit of energy, CODATA 2022 (NIST)
natural_unit_of_energy = 8.187105788e-14  # J, standard uncertainty 2.6e-23

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

What it is

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

In other units

UnitValue
CGS (cm2 g s−2)8.187 105 788 × 10−7
eV electronvolt510 998.950 69
keV kiloelectronvolt510.998 950 69
MeV megaelectronvolt0.510 998 950 69
Eₕ hartree18 778.865 07unit is itself measured
Ry rydberg37 557.730 14unit 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 energy: CODATA values 1998–2022 relative to the 2022 value, in parts per billion, with one-standard-uncertainty bars−300−200−1000+100+200+300parts per billion1998200220062010201420182022

Relative uncertainty

natural unit of energy: relative standard uncertainty in each CODATA adjustment, logarithmic scale10⁻¹⁰10⁻⁹10⁻⁸10⁻⁷10⁻⁶1998200220062010201420182022
CODATAValue (uncertainty)Relative uncertaintyChange from previous
20228.187 105 7880(26) × 10−143.2 × 10−10 +4.4 σ of 2018
20188.187 105 7769(25) × 10−143.1 × 10−10 +1.3 σ of 2014
20148.187 105 65(10) × 10−141.2 × 10−8 +1.6 σ of 2010
20108.187 105 06(36) × 10−144.4 × 10−8 +1.7 σ of 2006
20068.187 104 38(41) × 10−145.0 × 10−8 −0.2 σ of 2002
20028.187 1047(14) × 10−141.7 × 10−7 +0.9 σ of 1998
19988.187 104 14(64) × 10−147.8 × 10−8

“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).

Related constants

Units mec2 Natural unit of energy in MeV 0.510 998 950 69(16) MeV