About

Subtracting time from a calendar date is not simple addition in reverse. Month lengths vary between 28 and 31 days. Leap years insert an extra day every 4 years, except centuries not divisible by 400. Decrementing March 31 by one month does not yield February 31 because that date does not exist. This tool handles end-of-month clamping, leap year boundaries, and BCE/CE transitions correctly. Errors in manual date arithmetic cause missed deadlines, incorrect contract terms, and compliance failures in legal or financial contexts.

The calculator operates on the proleptic Gregorian calendar. It applies native date rollover logic for day and week subtraction. For month and year subtraction, it clamps the day component to the last valid day of the resulting month. All results include the day of week, the ISO 8601 week number, and the exact span between the original and resulting date. Note: this tool assumes the Gregorian calendar throughout. Dates before October 15, 1582 are extrapolated, not historically accurate for Julian-calendar regions.

Formulas

For day and week subtraction, the tool computes a direct offset on the day component:

D_result = D_start − n × k

where D_start is the starting date, n is the decrement amount, and k = 1 for days or k = 7 for weeks. The native Date object handles month/year rollover automatically.

For month subtraction with end-of-month clamping:

m_new = m_start − n
d_result = min(d_start, daysInMonth(y_new, m_new))

where daysInMonth returns the number of days in the target month, accounting for leap years. This prevents invalid dates like February 30.

Leap year determination follows the Gregorian rule:

isLeap(y) = (y mod 4 = 0) ∧ (y mod 100 ≠ 0 ∨ y mod 400 = 0)

The ISO 8601 week number is computed by finding the Thursday of the result date's week, then counting weeks from January 1 of that Thursday's year.

Reference Data

Month	Days	Cumulative (non-leap)	Cumulative (leap)	Notes
January	31	31	31	Start of Gregorian year
February	28/29	59	60	Leap day added here
March	31	90	91	Equinox month
April	30	120	121	-
May	31	151	152	-
June	30	181	182	Solstice month
July	31	212	213	Named after Julius Caesar
August	31	243	244	Named after Augustus
September	30	273	274	Equinox month
October	31	304	305	Gregorian adoption (1582)
November	30	334	335	-
December	31	365	366	Solstice month
Leap Year Rules (Gregorian)
Divisible by 4		Leap year - unless century year
Divisible by 100		Not a leap year - unless also divisible by 400
Divisible by 400		Leap year (e.g., 2000)
ISO 8601 Day-of-Week Numbering
Monday	1	ISO week starts on Monday
Tuesday	2	-
Wednesday	3	-
Thursday	4	Determines ISO week-numbering year
Friday	5	-
Saturday	6	-
Sunday	7	-

Frequently Asked Questions

February has at most 29 days. The tool clamps the day to the last valid day of February. March 31 minus 1 month yields February 28 (or February 29 in a leap year). This end-of-month clamping follows the same convention used by ISO 8601 duration arithmetic and most financial software.

Subtracting 1 year from February 29, 2024 (a leap year) targets February 29, 2023. Since 2023 is not a leap year, the result is clamped to February 28, 2023. The leap year test uses the full Gregorian rule: divisible by 4, except centuries unless also divisible by 400.

In most cases, yes. Both target the same month and year. However, the clamping logic is identical: if the source day exceeds the target month's length, it is clamped. The results are equivalent for this tool because both operations reduce the month count by 12 and then apply the same day-clamping rule.

This tool uses the proleptic Gregorian calendar, extending Gregorian rules backward. Historical dates in regions that used the Julian calendar will not match contemporary records. For example, the Julian calendar had no century-year exception, so leap years differ before 1582. Use results for pre-reform dates as mathematical extrapolations, not historical facts.

Many business and legal calculations depend on the day of the week. Contract terms, payment schedules, and delivery deadlines often exclude weekends. Knowing that a result falls on a Saturday lets you adjust to the preceding Friday or following Monday. The ISO week number is also provided for logistics and manufacturing planning that uses week-based scheduling.

The tool accepts decrement values from 1 to 99,999. For days this covers over 273 years. For months it covers over 8,333 years. The JavaScript Date object can represent dates from approximately 271,821 BCE to 275,760 CE, so extremely large decrements are bounded by this range. The tool validates that the result falls within representable dates.