ConstantID

Atomic unit of force

UnitsMeasured

Eh/a0 = 8.238 723 5038(13) × 10−8 N

Value
8.238 723 5038 × 10−8 N
Standard uncertainty
1.3 × 10−17 N
Relative uncertainty
1.6 × 10−10 (158 parts per trillion)
Status
Measured
Symbol
Eh/a0
Source
CODATA 2022 via NIST · NIST entry

Use in a calculation

# atomic unit of force, CODATA 2022 (NIST)
atomic_unit_of_force = 8.2387235038e-8  # N, standard uncertainty 1.3e-17

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

What it is

The unit of force 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 g s−2)0.008 238 723 5038
dyn dyne0.008 238 723 5038

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 force: 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

atomic unit of force: relative standard uncertainty in each CODATA adjustment, logarithmic scale10⁻¹⁰10⁻⁹10⁻⁸10⁻⁷10⁻⁶1998200220062010201420182022
CODATAValue (uncertainty)Relative uncertaintyChange from previous
20228.238 723 5038(13) × 10−81.6 × 10−10 +4.6 σ of 2018
20188.238 723 4983(12) × 10−81.5 × 10−10 +1.4 σ of 2014
20148.238 723 36(10) × 10−81.2 × 10−8 +1.6 σ of 2010
20108.238 722 78(36) × 10−84.4 × 10−8 +1.8 σ of 2006
20068.238 722 06(41) × 10−85.0 × 10−8 −0.3 σ of 2002
20028.238 7225(14) × 10−81.7 × 10−7 +1.1 σ of 1998
19988.238 721 81(64) × 10−87.8 × 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).