A long-standing question is whether active galactic nuclei (AGN) vary likeGalactic black hole systems when appropriately scaled up by mass 1-3 . If so, we can then determine how AGN should behave on cosmological timescales by studying the brighter and much faster varying Galactic systems. As X-ray emission is produced very close to the black holes, it provides one of the best diagnostics of their behaviour. A characteristic timescale, which potentially could tell us about the mass of the black hole, is found in the X-ray variations from both AGN and Galactic black holes 1-6 , but whether it is physically meaningful to compare the two has been questioned 7 . Here we report that, after correcting for variations in the accretion rate, the timescales can be physically linked, revealing that the accretion process is exactly the same for small and large black holes. Strong support for this linkage comes, perhaps surprisingly, from the permitted optical emission lines in AGN whose widths (in both broadline AGN and narrow-emission-line Seyfert 1 galaxies) correlate strongly with the characteristic X-ray timescale, exactly as expected from the AGN black hole masses and accretion rates. So AGN really are just scaled-up Galactic black holes.The first detailed observations of AGN X-ray variability showed scaleinvariant behaviour on all timescales from approximately days to minutes 8,9 , with no characteristic timescale from which black hole masses (M BH ) might be deduced.However, subsequent observations [1][2][3] showed that, on longer timescales, a characteristic timescale could be derived from the power spectral densities (PSDs; that is, variability power, P(ν), at frequency, ν, or timescale, 1/ν) of the X-ray light curves.All AGN PSDs are best fitted on long timescales by a powerlaw of slope −1 (P(ν) ∝ ν −α with α 1) which breaks to a steeper slope (α > 2) on timescales shorter than a 'break' timescale, T B . For some AGN, the α 1 slope can be followed to long timescales for >3 decades with no further break, similar to Galactic black hole X-ray binary systems (GBHs) in their 'soft' states 5,7,[10][11][12][13] . For other AGN, the slope can only be followed for <2 decades, which is insufficient to distinguish them from GBHs in their 'hard' states where, in the power-law description of the PSD, a second break, to slope α 0, is seen ~1.5-2 decades below the α 1-2 break. Here we use the timescale associated with the α 1-2 break as a characteristic timescale, irrespective of likely state. The reason for the sudden decrease in variability power on timescales shorter than T B is not clear, but the variability probably originates within the accretion disk 14 surrounding the black hole and T B may be associated with the inner edge of the disk.A major difficulty in establishing a quantitative timing link between AGN and GBHs has been the large scatter in the M BH -T B relationship 7 . In particular, for a given M BH , the high accretion rate narrow line Seyfert 1 galaxies (NLS1s) have smaller values of T B than other AGN 5,11 . ...