There are many online resources for finding the quietest dishwashers by decibel rating. TopTenReviews.com and DishwasherCritic.com are two resources that lay out the information in an easy-to-compare format, as of 2015.
While seeing a list of dishwashers by decibel rating is helpful, it's important to understand what the measurement means. Decibels measure sound power, the energy produced by the sound, which is different from what the ear perceives. A difference of 3 A-weighted decibels is considered to be imperceptible to the human ear. So the difference between a 41 A-weighted decibel dishwasher and a 44 A-weighted decibel dishwasher is not significant. However, a difference of 10 A-weighted decibels is perceived to be twice as loud. So a dishwasher at 54 A-weighted decibels is perceived to be twice as loud as one that is rated at 44 A-weighted decibels.