Dark matter is theorized to form massive haloes, which could be further condensed into so-called spikes when a black hole grows at the centre of such a halo. The existence of these spikes is instrumental for several dark matter detection schemes such as indirect detection and imprints on gravitational wave inspirals, but all previous work on their formation has been (semi-)analytical. We present fully numerically simulated cold dark matter spikes using the swift code. Based on these results, we propose a simple empirical density profile - dependent on only a single mass-ratio parameter between the black hole and total mass - for dark matter spikes grown in Hernquist profiles. We find that the radius of the spike scales differently compared to theoretical predictions, and show a depletion of the outer halo that is significant for high mass-ratio systems. We critically assess approximations of the spike as used in the field, show that our profile significantly deviates, and contextualize the potential influence for future DM detections by simulating binary black hole inspirals embedded in our profile.