We present pure rotational transitions of the rare iron monoxide isotopologues. 57Fe16O, 58Fe16O and 56Fe18O in their lowest spin states 5Δ4. For 57Fe16O, the rotational spectrum reveals hyperfine splitting due to the nuclear spin of I(57Fe)=1/2. We use Dunham-like parameters to analyse the new laboratory data together with data from the literature. In particular, we are able to derive the Born–Oppenheimer breakdown parameters ΔU01Fe=−9.886(24) and ΔU01O=−10.761(67) and the corresponding equilibrium bond length of reBO=1.6160302(20)10−10m. With these new accurate molecular parameters line positions on a sub-MHz accuracy level can be calculated, including those of the radioactive isotopologue 60Fe16O. The new data allow for an astronomical search for the rare FeO isotopologues using sensitive radio telescopes, like the Atacama Large Millimetre/submillimetre Array.