About

Rounding a date to a coarser calendar unit is a deceptively complex operation. Minutes and hours follow uniform 60-second and 3600-second cycles, so modular arithmetic on a Unix timestamp suffices. Days, however, are sensitive to timezone offset. Weeks depend on your epoch weekday definition (ISO 8601 designates Monday as day 1). Months have variable lengths (28 - 31 days), making the midpoint ambiguous. Quarters and years compound that irregularity. Getting this wrong in financial reporting, log aggregation, or scheduling systems causes silent data misalignment - transactions attributed to the wrong period, dashboards showing shifted trends, cron jobs firing a day late. This tool implements calendar-aware rounding with three direction modes (nearest, ceiling, floor) across seven granularity levels from min to yr.

Limitation: all calculations assume the Gregorian calendar and do not account for leap seconds. Week rounding follows ISO 8601 (Monday start). The midpoint rule for "nearest" mode uses round-half-up convention. Pro tip: when rounding timestamps for database GROUP BY queries, always round in the same timezone your data was recorded in to avoid off-by-one period errors near DST transitions.

Formulas

For uniform sub-day units (minute, hour, and their multiples), rounding uses modular arithmetic on the Unix timestamp:

t_rounded = round(tU) × U

where t is the Unix timestamp in milliseconds and U is the unit size in milliseconds (e.g., 3600000 for one hour). The round function is replaced by floor for rounding down or ceil for rounding up.

For calendar-variable units (month, quarter, year), the algorithm computes two candidate boundaries - the floor boundary and the ceiling boundary - then selects based on direction mode:

{

t_floor if direction = FLOORt_ceil if direction = CEILcloser(t, t_floor, t_ceil) if direction = NEAREST

The closer function compares |t − t_floor| against |t_ceil − t|. On exact midpoint, the ceiling (round-half-up) is chosen.

Where t = input timestamp (ms), U = unit duration (ms), t_floor = start of current period, t_ceil = start of next period.

Reference Data

Unit	Cycle Length	Midpoint (Nearest)	Floor Snaps To	Ceil Snaps To	Notes
Minute	60 s	30 s	:00 of current min	:00 of next min	Uniform cycle
Hour	3600 s	30 min	:00:00 of current hr	:00:00 of next hr	Uniform cycle
Day	86400 s	12:00 noon	00:00:00 of current day	00:00:00 of next day	DST days may be 23 or 25 h
Week (ISO)	7 d	Thursday 00:00	Monday 00:00 of current wk	Monday 00:00 of next wk	ISO 8601: Mon = day 1
Month	28 - 31 d	~15th - 16th	1st of current month	1st of next month	Variable length
Quarter	3 months	~mid-month 2	1st of Q start (Jan/Apr/Jul/Oct)	1st of next Q	Q1=Jan, Q2=Apr, Q3=Jul, Q4=Oct
Year	365 - 366 d	~Jul 2	Jan 1 of current year	Jan 1 of next year	Leap year aware
5 Minutes	300 s	150 s	:X0/:X5 of current	:X0/:X5 of next	Common in billing
15 Minutes	900 s	7.5 min	:00/:15/:30/:45	Next quarter-hour	Standard time-tracking interval
30 Minutes	1800 s	15 min	:00/:30	Next half-hour	Meeting scheduling default
6 Hours	21600 s	3 h	00:00/06:00/12:00/18:00	Next 6-hour block	Synoptic meteorology intervals
12 Hours	43200 s	6 h	00:00/12:00	Next half-day	AM/PM boundary

Frequently Asked Questions

The algorithm computes the exact millisecond boundaries of the 1st of the current month and the 1st of the next month. The midpoint is calculated as the arithmetic mean of these two timestamps. A date on February 14 in a 28-day February falls past the midpoint (Feb 15 00:00 would be the midpoint), so it rounds down to Feb 1. The same day-of-month in a 31-day month like March would round down because the midpoint is later (~March 16). This means the effective midpoint day shifts depending on month length.

ISO 8601 defines Monday as day 1 of the week. Floor rounding snaps to Monday 00:00:00 of the current week. Ceiling rounding snaps to Monday 00:00:00 of the following week. The midpoint for nearest-mode falls on Thursday 00:00:00. If your business uses Sunday-start weeks, you would need to offset by one day before and after rounding, which this tool does not currently support.

Quarters follow the standard fiscal calendar: Q1 starts January 1, Q2 starts April 1, Q3 starts July 1, Q4 starts October 1. Floor rounding returns the first day of the current quarter. Ceiling rounding returns the first day of the next quarter. For nearest-mode, the midpoint is computed from the total milliseconds in the 3-month span. Because quarters contain months of varying length (Q1 has 90 or 91 days; Q2 has 91 days; Q3 has 92 days; Q4 has 92 days), the midpoint day differs per quarter.

Sub-day rounding (minute, hour) operates on UTC-equivalent millisecond timestamps, so a DST transition that makes a local day 23 or 25 hours long does not affect the arithmetic. Day-level rounding and above constructs boundaries using local-time Date constructors (midnight local time), which correctly handle the variable-length day. However, if you feed in a UTC timestamp representing 2023-03-12T02:30 in a US timezone where that time is skipped, the Date object will auto-adjust. Be aware of this edge case.

JavaScript Date objects have millisecond precision. The smallest rounding unit offered is 1 minute (60000 ms). Sub-millisecond precision is not supported. For dates, the valid range is approximately ±273,790 years from the Unix epoch (Jan 1 1970), constrained by the 8.64 × 10¹⁵ ms maximum of the Date object. Dates outside this range will produce an invalid result.

Excel's MROUND rounds to the nearest multiple of a fixed number, which works for uniform intervals but fails for calendar-variable units. Excel's EOMONTH and DATE-based rounding approaches vary by implementation. This tool uses true calendar boundary computation: it identifies the actual start of the current and next period using the Gregorian calendar, then compares distances. Spreadsheet functions often approximate months as 30 days, which introduces a 1 - 3 day error depending on the month.