CMS reimburses differently depending on what part of the country you live and to my knowledge there isn't a free website that gives the answer for all areas of the country. CMS reimburses doctors higher in SF and NYC than Iowa City due to cost of living.
Private insurance reimburses a multiplier of CMS (usually a little less than 1.0 to 1.7-1.8 times as much, some lucky people might get more if they can negotiate well).
Of course you can charge whatever you want to the unisured, but who knows if they will pay it if it is excessively high.