  The absolute mass of $^{84}$Sr was determined using the phase-imaging
ion-cyclotron-resonance technique with the JYFLTRAP double Penning trap mass
spectrometer. A more precise value for the mass of $^{84}$Sr is essential for
providing potential indications of physics beyond the Standard Model through
high-precision isotope shift measurements of Sr atomic transition frequencies.
The mass excess of $^{84}$Sr was refined to be -80649.229(37) keV/c$^2$ from
high-precision cyclotron-frequency-ratio measurements with a relative precision
of 4.8$\times$10$^{-10}$. The obtained mass-excess value is in agreement with
the adopted value in the Atomic Mass Evaluation 2020, but is 30 times more
precise. With this new value, we confirm the previously observed nonlinearity
in the study of the isotope shift of strontium. Moreover, the double-beta
($2\beta^{+}$) decay $Q$ value of $^{84}$Sr was directly determined to be
1790.115(37) keV, and the precision was improved by a factor of 30.
