There is no single, trivial formula that works in all waters. 

For passive sensors, try methods such as those suggested in

1) Mobley et al. Applied Optics 07/2005; 44(17):3576-92. DOI:10.1364/AO.44.003576;

2) Lee et al. Journal of Applied Remote Sensing 12/2007; 1(1):17, DOI: 10.1117/1.2822610

3) Possibly Bachmann et al. IEEE Transactions on Geoscience and Remote Sensing 04/2009; DOI:10.1109/TGRS.2008.2005732, but this one is image driven. 

Option (1) and related requires modeling of many different types of water types, bottoms, and bathymetry and then an appropriate matching. This can be done. This is sensitive to the the number of spectral bands (Zhongping Lee has a really good paper about band selection, number of bands, etc.: Sensors 12/2007; 7(12). DOI:10.3390/s7123428  and Applied Optics 05/2002; 41(12):2191-201. DOI:10.1364/AO.41.002191 )

Option 2 is quasi-analytical. 

All three cases depend on there being some sort of atmospheric correction applied to the imagery. The better the atmospheric correction, the better the results. 

Don't know whether your study is global, regional or local (i.e., what is the spatial resolution you're looking for). There are bathymetry models derived from satellite altimetry in case you don't want to calculate one. (e.g., http://www.space.dtu.dk/english/Research/Scientific_data_and_models/Global_Bathymetry_Model)

In addition to the above

 Stumpf et al., 2003, L&O

http://onlinelibrary.wiley.com/doi/10.4319/lo.2003.48.1_part_2.0547/abstract

and citations.  

In deciding, assuming you are working at Landsat to WorldView resolution, you need to consider the application of the algorithms compared to the availability of reference data and also the variability in turbidity.

Which is the spatial resolution and depth accuracy you need. For coastal evolution monitoring accuracy is not good. Consider that for a depth of closure 1 km offshore an error of 10 cm in each survey can imply an error of 200 cubic meter for meter of coast; the same of a medium size beach nourishment. We decided to remain on traditional methods! Also marine Lidar has not the due accuracy.