Anchor on today, count the elapsed days, fold in the leap years, and land on the weekday — before the answer reveals itself.
Pick an anchor you know — today's date and weekday. Count the days between today and the target date. The weekday only depends on that count mod 7, since the week repeats every 7 days.
When the target is exactly N years ahead on the same month and day, the day-count shortcut is: days ≈ N × 365 + leap days passed. A quick mental estimate for leap days is floor(N / 4) — then take that whole total mod 7 to get the weekday offset from today.
That quick estimate is occasionally off by one, because the Gregorian calendar skips leap years on century marks not divisible by 400 (1900 wasn't a leap year, 2000 was). For a date tens of years out this rarely bites — but this tool always counts the exact leap days for the real answer, while showing you the quick mental-math estimate alongside it.
When the target is an arbitrary number of days ahead, there's no leap-year step needed at all — just take the day count straight mod 7.