ABSTRACT We use data from the Sydney-AAO Multi-object Integral-field spectroscopy (SAMI) Galaxy Survey to study the dynamical scaling relation between galaxy stellar mass M∗ and the general kinematic parameter $S_K = \sqrt{K V_{\rm rot}^2 + σ ^2}$ that combines rotation velocity Vrot and velocity dispersion σ. We show that the log M∗ – log SK relation: (1) is linear above limits set by properties of the samples and observations; (2) has slightly different slope when derived from stellar or gas kinematic measurements; (3) applies to both early-type and late-type galaxies and has smaller scatter than either the Tully–Fisher relation (log M∗ − log Vrot) for late types or the Faber–Jackson relation (log M∗ − log σ) for early types; and (4) has scatter that is only weakly sensitive to the value of K, with minimum scatter for K in the range 0.4 and 0.7. We compare SK to the aperture second moment (the ‘aperture velocity dispersion’) measured from the integrated spectrum within a 3-arcsecond radius aperture ($σ _{3^{\prime \prime }}$). We find that while SK and $σ _{3^{\prime \prime }}$ are in general tightly correlated, the log M∗ − log SK relation has less scatter than the $\log M_* - \log σ _{3^{\prime \prime }}$ relation.