About

The ordinal date system assigns each day a sequential number from 1 (January 1) to 365 or 366 in leap years. This numbering follows ISO 8601 conventions used in aviation, military operations, and scientific data logging where unambiguous date references prevent costly errors. Misinterpreting dates in logistics or scheduling systems has caused supply chain failures exceeding $100M annually across industries. The day-of-year format eliminates month-boundary confusion entirely.

This tool calculates DOY using the formula DOY = d + floor(275m÷9) − K × floor((m+9)÷12) + L, where K depends on leap year status. Leap year detection uses the Gregorian rule: divisible by 4, except century years must also divide by 400. February 29 exists only when year mod 400 = 0 or (year mod 4 = 0 ∧ year mod 100 ≠ 0).

Formulas

The day of year (DOY) represents the ordinal position of a date within its year, ranging from 1 to 365 (or 366 in leap years).

DOY = floor(Date − Jan₀86400000 ms)

Where Jan₀ = December 31 of the previous year (day zero reference), and 86400000 ms represents one day in milliseconds.

Leap year determination follows the Gregorian calendar rule:

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

Reverse lookup from DOY to calendar date:

Date = new Date(year, 0, DOY)

ISO week number calculation uses the Thursday-based system where week 1 contains January 4:

W = floor(DOY − weekday + 107)

Where weekday = 1 (Monday) to 7 (Sunday).

Reference Data

Month	Days	Start DOY (Common)	End DOY (Common)	Start DOY (Leap)	End DOY (Leap)
January	31	1	31	1	31
February	28/29	32	59	32	60
March	31	60	90	61	91
April	30	91	120	92	121
May	31	121	151	122	152
June	30	152	181	153	182
July	31	182	212	183	213
August	31	213	243	214	244
September	30	244	273	245	274
October	31	274	304	275	305
November	30	305	334	306	335
December	31	335	365	336	366

Notable DOY	Date (Common Year)	Date (Leap Year)	Significance
1	January 1	January 1	New Year's Day
32	February 1	February 1	Start of February
60	March 1	February 29	Leap day / March start
91	April 1	March 31	Q2 start (common)
100	April 10	April 9	Day 100 milestone
152	June 1	May 31	Summer begins
182	July 1	June 30	Year midpoint (common)
183	July 2	July 1	Year midpoint (leap)
200	July 19	July 18	Day 200 milestone
256	September 13	September 12	Programmer's Day (2⁸)
273	September 30	September 29	Q3 end
300	October 27	October 26	Day 300 milestone
335	December 1	November 30	December start (common)
365	December 31	December 30	Year end (common)
366	-	December 31	Year end (leap only)

Frequently Asked Questions

In common years (365 days), March 1 is DOY 60. In leap years (366 days), February 29 is DOY 60, pushing March 1 to DOY 61. All dates from March onward have a DOY value one higher in leap years than common years. This offset persists through December 31, which is DOY 365 in common years but DOY 366 in leap years.

Ordinal dates eliminate ambiguity from varying month lengths and international date format differences (MM/DD vs DD/MM). Flight plans, satellite tracking, and logistics systems use DOY format (YYYY-DDD) because it provides a monotonically increasing sequence without month boundaries. GPS systems internally use week numbers and day-of-week, converting to DOY for human interfaces.

Programmer's Day falls on DOY 256, which equals 2^8 (the number of distinct values in an 8-bit byte). In common years this is September 13; in leap years it shifts to September 12. The choice of 256 honors the fundamental unit of computer memory and the binary nature of computing.

DOY resets to 1 each January 1 and ranges 1-366 within a year. Julian Day Number (JDN) is a continuous count of days since January 1, 4713 BC (Julian calendar). To convert: JDN = 367×year − floor(7×(year+floor((month+9)/12))/4) + floor(275×month/9) + day + 1721013.5. DOY is year-relative; JDN is absolute.

Remaining days = (365 or 366) − DOY. For a common year with DOY 200: 365 − 200 = 165 days remaining. For a leap year: 366 − 200 = 166 days. The tool displays this automatically when selecting any date, showing both elapsed and remaining day counts.

Yes. ISO weeks are Thursday-anchored, so if January 1 falls on Friday, Saturday, or Sunday, that day belongs to the last week of the previous ISO year. For example, January 1, 2022 (Saturday) was ISO week 52 of 2021. Conversely, late December days can belong to ISO week 1 of the following year.