Day of Week

This calculator finds the day of the week for any Gregorian calendar date using Sakamoto's algorithm, a compact closed-form formula rather than a lookup table or a full calendar library. It adjusts the year backward by one whenever the month is January or February (line 9), then combines that adjusted year with century and leap-year correction terms and a fixed per-month offset before taking the result modulo 7 (line 10) -- the same century rule real calendars use, so 1900 (not divisible by 400) and 2000 (divisible by 400) get different corrections even though both are divisible by 100. The result, 0 through 6, maps directly to Sunday through Saturday.

Month and Day are each floored and clamped before the formula runs -- Month to 1-12 and Day to 1-31 regardless of what month was chosen (lines 17-18); Year is floored with a fallback default but not clamped to any range (line 16) -- which means the calculator will still return a weekday for a date that does not exist on a real calendar, such as day 31 in a 30-day month or February 30th; it has no separate check for calendar validity, only for the input ranges on Month and Day. Because the underlying formula is genuinely modular arithmetic, no single input can be said to move the weekday result in one consistent direction the way a linear formula would: adding a week always returns to the same weekday, but adding a handful of days can land on an earlier weekday index than a smaller change did, and the algorithm's own year-adjustment step means a change in Year alone does not shift the result by a fixed, predictable amount either. Reading the weekday off the Index (0=Sun) field or the Weekday label always agrees with a real calendar's day of the week for any year the formula supports.