  Star formation rate (SFR), metallicity and stellar mass are within the
important parameters of star--forming galaxies that characterize their
formation and evolution. They are known to be related to each other at low and
high redshift in the mass--metallicity, mass--SFR, and metallicity--SFR
relations. In this work we demonstrate the existence of a plane in the 3D space
defined by the axes SFR [log(SFR)(M_sun yr^-1)], gas metallicity [12+log(O/H)],
and stellar mass [log(M_star/M_sun)] of star-forming galaxies. We used
star--forming galaxies from the "main galaxy sample" of the Sloan Digital Sky
Survey--Data Release 7 (SDSS-DR7) in the redshift range 0.04 < z < 0.1 and
r-magnitudes between 14.5 and 17.77. Metallicities, SFRs, and stellar masses
were taken from the Max-Planck-Institute for Astrophysics-John Hopkins
University (MPA-JHU) emission line analysis database. From a final sample of
44214 galaxies, we find for the first time a fundamental plane for field
galaxies relating the SFR, gas metallicity, and stellar mass for star--forming
galaxies in the local universe. One of the applications of this plane would be
estimating stellar masses from SFR and metallicity. High redshift data from the
literature at redshift ~2.2 and 3.5, do not show evidence for evolution in this
fundamental plane.
