A calibration is made for the correlation between the X-ray Variability Amplitude ( XVA ) and black hole ( BH ) mass .
The correlation for 21 reverberation-mapped Active Galactic Nuclei ( AGNs ) appears very tight , with an intrinsic dispersion of 0.20 dex .
The intrinsic dispersion of 0.27 dex can be obtained if BH masses are estimated from the stellar velocity dispersions .
We further test the uncertainties of mass estimates from XVAs for objects which have been observed multiple times with good enough data quality .
The results show that the XVAs derived from multiple observations change by a factor of 3 .
This means that BH mass uncertainty from a single observation is slightly worse than either reverberation-mapping or stellar velocity dispersion measurements ; however BH mass estimates with X-ray data only can be more accurate if the mean XVA value from more observations is used .
With this calibrated relation , the BH mass and accretion rate may be determined for a large sample of AGNs with the planned International X-ray Observatory mission .

Proper interpretation of the first AGN X-ray quasi-periodic oscillation ( QPO ) , seen in the Seyfert galaxy RE J1034+396 , depends on its BH mass , which is not currently known very well .
Applying this relation , the BH mass of RE J1034+396 is found to be 4 ^ { +3 } _ { -2 } \times 10 ^ { 6 } M _ { \odot } .
The high end of the mass range follows the relationship between the 2 f _ { 0 } frequencies of high-frequency QPO and the BH masses derived from the Galactic X-ray binaries .

We also calculate the high-frequency constant C = 2.37 ~ { } M _ { \odot } Hz ^ { -1 } from 21 reverberation-mapped AGNs .
As suggested by Gierliński et al. , M _ { BH } = C / C _ { M } , where C _ { M } is the high-frequency variability derived from XVA .
Given the similar shape of power-law dominated X-ray spectra in ultra-luminous X-ray sources ( ULXs ) and AGNs , this can be applied to BH mass estimates of ULXs .
We discuss the observed QPO frequencies and BH mass estimates in the ULXs M82 X-1 and NGC 5408 X-1 and favor ULXs as intermediate mass BH systems .