The release date showing on the Bureau of Prisons website is the real date, and it already has the math done for you.
Unlike state systems where you have to calculate good time credit yourself, the BOP's inmate locator at bop.gov displays the projected release date after the standard 15% good time reduction has already been applied. What you see is what you get, assuming he maintains a clean disciplinary record from now until release.
That last part matters. The 15% good time credit is granted on day one but it is not guaranteed to stay intact. Incident reports and disciplinary infractions can result in good time being taken away, which pushes the release date further out. Inmates who keep a clean record hold onto that credit and hit the date on the website. Those who accumulate violations serve longer.
The one thing that can move the date earlier is RDAP, the Residential Drug Abuse Program. If he qualifies based on documented substance abuse history and a qualifying conviction, completing RDAP can take up to a full year off the sentence and add up to six months of halfway house placement before the release date. That is worth looking into seriously if there is any eligibility at all.
You can track his projected release date at any time by searching his name or register number at bop.gov/inmateloc. That page updates when anything changes and is the most reliable source for current release information.