I recently applied for Social security and declared I was getting UK State Pension and immediately 475 dollars were deducted from my Social Security is this right?
I can't tell you whether or not the amount of the reduction is correct without additional information, but it's probably right. If a person who files for U.S. Social Security disability or retirement benefits based on their own earnings also receives a pension based on their earnings that were exempt from Social Security taxes, a less generous benefit computation formula is used to calculate their benefit rate unless they meet an exception to the Windfall Elimination Provision (WEP). For more information on WEP and it's exceptions, refer to the following Social Security publication: https://www.ssa.gov/pubs/EN-05-10045.pdf.
So, assuming that your UK pension is based on your earnings on which you paid no U.S. Social Security taxes, then your U.S. Social Security benefits would likely be subject to the WEP reduction. Our software is fully programmed to handle WEP calculations, so you may want to consider using the software to find out if your payment amount has been correctly calculated.