  We construct a complete, hard X-ray flux-limited sample of intermediate
polars (IPs) from the Swift-BAT 70-month survey, by imposing selection cuts in
flux and Galactic latitude ($F_X > 2.5 \times
10^{-11}\,\mathrm{erg\,cm^{-2}s^{-1}}$ at 14--195~keV, and $|b|>5^\circ$). We
then use it to estimate the space density ($\rho$) of IPs. Assuming that this
sample of 15 long-period systems is representative of the intrinsic IP
population, the space density of long-period IPs is $1^{+1}_{-0.5} \times
10^{-7}\,\mathrm{pc^{-3}}$. The Swift-BAT data also allow us to place upper
limits on the size of a hypothetical population of faint IPs that is not
included in the flux-limited sample. While most IPs detected by BAT have
14--195~keV luminosities of $\sim 10^{33} {\rm erg s^{-1}}$, there is evidence
of a fainter population at $L_X \sim 10^{31} {\rm erg s^{-1}}$. We find that a
population of IPs with this luminosity may have a space density as large as
$5\times 10^{-6}\,\mathrm{pc^{-3}}$. Furthermore, these low-luminosity IPs,
despite appearing rare in observed samples, are probably at least as
intrinsically common as the brighter systems that are better represented in the
known IP sample.
