AbstractHelium-3 has nowadays become one of the most important candidates for studies in fundamental physics^1–3, nuclear and atomic structure^4,5, magnetometry and metrology⁶, as well as chemistry and medicine^7,8. In particular, ³He nuclear magnetic resonance (NMR) probes have been proposed as a new standard for absolute magnetometry^6,9. This requires a high-accuracy value for the ³He nuclear magnetic moment, which, however, has so far been determined only indirectly and with a relative precision of 12 parts per billon^10,11. Here we investigate the ³He⁺ ground-state hyperfine structure in a Penning trap to directly measure the nuclear g-factor of ³He⁺${g}_{I}^{{\prime} }=-\,4.2550996069(30{)}_{{\rm{stat}}}(17{)}_{{\rm{sys}}}$ g I ′ = − 4.2550996069 ( 30 ) stat ( 17 ) sys , the zero-field hyperfine splitting ${E}_{{\rm{HFS}}}^{\exp }=-\,8,\,665,\,649,\,865.77{(26)}_{{\rm{stat}}}{(1)}_{{\rm{sys}}}$ E HFS exp = − 8 , 665 , 649 , 865.77 ( 26 ) stat ( 1 ) sys Hz and the bound electron g-factor ${g}_{e}^{{\rm{\exp }}}=-\,2.00217741579(34{)}_{{\rm{stat}}}(30{)}_{{\rm{sys}}}$ g e exp = − 2.00217741579 ( 34 ) stat ( 30 ) sys . The latter is consistent with our theoretical value ${g}_{e}^{{\rm{theo}}}=-\,2.00217741625223(39)$ g e theo = − 2.00217741625223 ( 39 ) based on parameters and fundamental constants from ref. ¹². Our measured value for the ³He⁺ nuclear g-factor enables determination of the g-factor of the bare nucleus ${g}_{I}=-\,4.2552506997(30{)}_{{\rm{stat}}}(17{)}_{{\rm{sys}}}(1{)}_{{\rm{theo}}}$ g I = − 4.2552506997 ( 30 ) stat ( 17 ) sys ( 1 ) theo via our accurate calculation of the diamagnetic shielding constant¹³${σ }_{{}^{3}{\mathrm{He}}^{+}}=0.00003550738(3)$ σ 3 He + = 0.00003550738 ( 3 ) . This constitutes a direct calibration for ³He NMR probes and an improvement of the precision by one order of magnitude compared to previous indirect results. The measured zero-field hyperfine splitting improves the precision by two orders of magnitude compared to the previous most precise value¹⁴ and enables us to determine the Zemach radius¹⁵ to ${r}_{Z}=2.608(24)$ r Z = 2.608 ( 24 ) fm.