ConstantID

Proton gyromagnetic ratio

Atomic & nuclearMeasured

γp = 2.675 221 8708(11) × 108 s−1 T−1

Value
2.675 221 8708 × 108 s−1 T−1
Standard uncertainty
0.11 s−1 T−1
Relative uncertainty
4.1 × 10−10 (411 parts per trillion)
Status
Measured
Symbol
γp
Source
CODATA 2022 via NIST · NIST entry

Use in a calculation

# proton gyromagnetic ratio, CODATA 2022 (NIST)
proton_gyromagnetic_ratio = 2.6752218708e8  # s^-1 T^-1, standard uncertainty 0.11

# SciPy: scipy.constants.physical_constants['proton gyromag. ratio']

What it is

The ratio of magnetic moment to angular momentum for the proton, the nucleus of the hydrogen atom. In a magnetic field B the spin precesses at angular frequency γB; this is the basis of magnetic resonance.

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).

proton gyromagnetic ratio: CODATA values 1998–2022 relative to the 2022 value, in parts per billion, with one-standard-uncertainty bars−150−100−500+50+100+150parts per billion1998200220062010201420182022

Relative uncertainty

proton gyromagnetic ratio: relative standard uncertainty in each CODATA adjustment, logarithmic scale10⁻¹⁰10⁻⁹10⁻⁸10⁻⁷1998200220062010201420182022
CODATAValue (uncertainty)Relative uncertaintyChange from previous
20222.675 221 8708(11) × 1084.1 × 10−10 −3.3 σ of 2018
20182.675 221 8744(11) × 1084.1 × 10−10 −1.4 σ of 2014
20142.675 221 900(18) × 1086.7 × 10−9 −1.7 σ of 2010
20102.675 222 005(63) × 1082.4 × 10−8 −1.3 σ of 2006
20062.675 222 099(70) × 1082.6 × 10−8 +0.2 σ of 2002
20022.675 222 05(23) × 1088.6 × 10−8 −0.6 σ of 1998
19982.675 222 12(11) × 1084.1 × 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

Atomic & nuclear e/mp Proton charge to mass quotient 9.578 833 1430(30) × 107 C kg−1 Atomic & nuclear λC,p Proton Compton wavelength 1.321 409 853 60(41) × 10−15 m Atomic & nuclear mp/me Proton–electron mass ratio 1836.152 673 426(32) Atomic & nuclear gp Proton g factor 5.585 694 6893(16) Atomic & nuclear γp/2π Proton gyromagnetic ratio in MHz/T 42.577 478 461(18) MHz T−1 Atomic & nuclear μp Proton magnetic moment 1.410 606 795 45(60) × 10−26 J T−1 Atomic & nuclear μp/μB Proton magnetic moment to Bohr magneton ratio 1.521 032 202 30(45) × 10−3 Atomic & nuclear μp/μN Proton magnetic moment to nuclear magneton ratio 2.792 847 344 63(82)