  Lyman-alpha (Lya) is intrinsically the brightest line emitted from active
galaxies. While it originates from many physical processes, for star-forming
galaxies the intrinsic Lya luminosity is a direct tracer of the Lyman-continuum
(LyC) radiation produced by the most massive O- and early-type B-stars with
lifetimes of a few Myrs. As such, Lya luminosity should be an excellent
instantaneous star formation rate (SFR) indicator. However, its resonant nature
and susceptibility to dust as a rest-frame UV photon makes Lya very hard to
interpret due to the uncertain Lya escape fraction, f$_{esc,Ly\alpha}$. Here we
explore results from the CALYMHA survey at z=2.2, follow-up of Lya emitters
(LAEs) at z=2.2-2.6 and a z~0-0.3 compilation of LAEs to directly measure
f$_{esc,Ly\alpha}$ with H-alpha (Ha). We derive a simple empirical relation
that robustly retrieves f$_{esc,Ly\alpha}$ as a function of Lya rest-frame EW
(EW$_0$): f$_{esc,Ly\alpha}$= 0.0048 EW$_0$[A]$\pm0.05$ and we show that it
constrains a well-defined anti-correlation between ionisation efficiency and
dust extinction in LAEs. Observed Lya luminosities and EW$_0$ are easy
measurable quantities at high redshift, thus making our relation a practical
tool to estimate intrinsic Lya and LyC luminosities under well controlled and
simple assumptions. Our results allow observed Lya luminosities to be used to
compute SFRs for LAEs at z~0-2.6 within 0.2 dex of the Ha dust corrected SFRs.
We apply our empirical SFR(Lya,EW$_0$) calibration to several sources at z>2.6
to find that star-forming LAEs have SFRs typically ranging from 0.1 to 20
M$_{\odot}$/yr and that our calibration might be even applicable for the most
luminous LAEs within the epoch of re-ionisation. Our results imply high
ionisation efficiencies and low dust content in LAEs across cosmic time, and
will be easily tested with future observations with JWST.
