= 1.054 571 817… × 10−34 J s
- Value
- 1.054 571 817… × 10−34 J s
- Standard uncertainty
- exact
- Relative uncertainty
- exact
- Status
- Exact since the 2019 SI redefinition
- Symbol
- Source
- CODATA 2022 via NIST · NIST entry
NIST prints this exact value cut to 10 digits. ConstantID recomputes it from the defining constants: 1.054 571 817 646 156 391 262 428 0033 × 10−34…
Use in a calculation
# reduced Planck constant, CODATA 2022 (NIST)
hbar = 1.0545718176461563912624280033022807e-34 # J s, exact
# SciPy: scipy.constants.physical_constants['reduced Planck constant']What it is
The Planck constant divided by 2π, often called h-bar. It is the natural unit of angular momentum in quantum mechanics: the spin of an electron is ħ/2, and the uncertainty principle sets Δx·Δp ≥ ħ/2. Because h is exact, ħ is exact too, but it has infinitely many digits.
It is built only from constants that have exact values since 20 May 2019, so it is exact too; CODATA 2018 was the first adjustment to list it that way.
Equations
- definition
- uncertainty principle
- energy and angular frequency
In other units
| Unit | Value | |
|---|---|---|
| CGS (cm2 g s−1) | 1.054 571 818 × 10−27 | exact |
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.
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). Diamonds mark adjustments in which the value was exact.
Relative uncertainty
| CODATA | Value (uncertainty) | Relative uncertainty | Change from previous |
|---|---|---|---|
| 2022 | 1.054 571 817… × 10−34 | exact | exact |
| 2018 | 1.054 571 817… × 10−34 | exact | +1.3 σ of 2014 |
| 2014 | 1.054 571 800(13) × 10−34 | 1.2 × 10−8 | +1.6 σ of 2010 |
| 2010 | 1.054 571 726(47) × 10−34 | 4.5 × 10−8 | +1.8 σ of 2006 |
| 2006 | 1.054 571 628(53) × 10−34 | 5.0 × 10−8 | −0.3 σ of 2002 |
| 2002 | 1.054 571 68(18) × 10−34 | 1.7 × 10−7 | +1.0 σ of 1998 |
| 1998 | 1.054 571 596(82) × 10−34 | 7.8 × 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).