  Studies of flux anomalies statistics and perturbations in stellar streams
have the potential to constrain models of warm dark matter (WDM), including
sterile neutrinos. Producing these constraints requires a parametrization of
the WDM mass function relative to that of the cold dark matter (CDM)
equivalent. We use five WDM models with half-mode masses,
$M_\mathrm{hm}=[1.3,35]\times10^{8}$~$M_{\odot}$, spread across simulations of
the Local Group, lensing ellipticals and the $z=2$ universe, to generate such a
parametrization: we fit parameters to a functional form for the WDM-to-CDM halo
mass function ratio, $n_\mathrm{WDM}(M_{X})/n_\mathrm{CDM}(M_{X})$, of
($1+(\alpha M_\mathrm{hm}/M_{X})^{\beta})^{\gamma}$. For $M_{X}\equiv$ virial
mass of central halos we obtain $\alpha=2.3$, $\beta=0.8$, and $\gamma=-1.0$,
and this fit is steeper than the extended Press-Schechter formalism predicts.
For $M_{X}\equiv$ mass of subhalos we instead obtain $\alpha=4.2$, $\beta=2.5$
and $\gamma=-0.2$; in both mass definitions the scatter is $\sim20$~per~cent.
The second fit typically underestimates the relative abundance of $z=2$ WDM
subhaloes at the tens of per cent level. We caution that robust constraints
will require bespoke simulations and a careful definition of halo mass,
particularly for subhalos of mass $<10^{8}M_{\odot}$.
