About

A single date encodes more information than most users realize. The ISO week number alone causes accounting errors when confused with calendar weeks. Julian Day Numbers, used in astronomy since 1583, provide a continuous day count free of calendar reform discontinuities. This tool extracts over 20 distinct properties from any Gregorian date: day-of-year ordinal, ISO 8601 week number (W), Julian Day Number (JDN), Unix timestamp, lunar phase angle, Western and Chinese zodiac mappings, and meteorological season classification. It computes the exact age delta from today in years, months, and days. All lunar calculations use the synodic period T = 29.53059 days referenced to the J2000 new moon epoch. Results assume the proleptic Gregorian calendar for dates before October 15, 1582.

Formulas

The Julian Day Number for a Gregorian calendar date is computed as:

JDN = 367Y − floor(7(Y + floor(M + 912))4) + floor(275M9) + D + 1721013.5

Where Y = year, M = month (1 - 12), D = day of month.

The ISO 8601 week number is derived by finding the Thursday of the same ISO week:

W = floor(ordinal − weekday + 107)

Where ordinal = day of year and weekday = ISO day number (Monday = 1).

The moon phase age in days since last new moon:

age = (JD − 2451550.1) mod 29.53059

Where 2451550.1 is the Julian Date of the J2000 reference new moon (January 6, 2000, 18:14 UTC). Moon illumination percentage is approximated by:

illum = 1 − cos(2π ⋅ age29.53059)2 × 100%

The leap year test follows the Gregorian rule:

leap = (Y mod 4 = 0) ∧ (Y mod 100 ≠ 0 ∨ Y mod 400 = 0)

Reference Data

Property	Standard / Source	Range / Format	Notes
Day of Week	ISO 8601	Monday (1) - Sunday (7)	Monday-start convention
Day of Year	Ordinal Date	1 - 366	366 only in leap years
ISO Week Number	ISO 8601	W01 - W53	Thursday-based; year may differ from calendar year
Julian Day Number	IAU / Astronomy	Integer ≥ 0	Continuous count from 4713 BC Jan 1 (Julian)
Modified Julian Day	SAO (1957)	MJD = JDN − 2400000.5	Used in satellite tracking
Unix Timestamp	POSIX	Seconds since 1970-01-01T00:00Z	Negative for dates before epoch
Leap Year	Gregorian Rule	Boolean	Div by 4, not 100, unless 400
Moon Phase	Synodic Month	0 - 29.53 days	Approximate; ±1 day accuracy
Moon Illumination	Derived	0 - 100%	Cosine interpolation of phase angle
Western Zodiac	Tropical Astrology	12 signs	Based on Sun’s ecliptic longitude boundaries
Chinese Zodiac	Lunar Calendar	12 animals	Simplified: uses Gregorian year mod 12
Season (Northern)	Meteorological	Spring / Summer / Autumn / Winter	Mar - May / Jun - Aug / Sep - Nov / Dec - Feb
Season (Southern)	Meteorological	Inverted from Northern	Sep - Nov = Spring in S. Hemisphere
Quarter	Fiscal / Calendar	Q1 - Q4	Q1 = Jan - Mar
Days in Month	Gregorian	28 - 31	Feb varies by leap year
Days Remaining in Year	Derived	0 - 365	Total days minus day-of-year
Century	Convention	Integer	21st century = years 2001-2100
Millennium	Convention	Integer	3rd millennium = years 2001-3000
Synodic Period	Astronomical	29.53059 days	Mean lunation length
Rata Die	Proleptic Gregorian	Days since 0001-01-01	Used in calendar algorithms
ISO Date Format	ISO 8601	YYYY-MM-DD	Unambiguous international standard

Frequently Asked Questions

ISO 8601 defines week 1 as the week containing the first Thursday of the year. Consequently, December 29-31 may fall in ISO week 1 of the next year, and January 1-3 may belong to ISO week 52 or 53 of the previous year. This tool displays the correct ISO week-year alongside the week number to prevent accounting or scheduling errors.

The calculation uses a fixed synodic period of 29.53059 days from a known new moon epoch. This is a mean-value approximation. Actual lunations vary between 29.27 and 29.83 days due to orbital eccentricity. For dates within ±50 years of J2000, accuracy is typically within ±1 day. For precise astronomical work, use JPL ephemeris data.

This tool uses the proleptic Gregorian calendar for all dates, including those before the Gregorian reform of October 15, 1582. The JDN formula applied is the standard Gregorian algorithm. For historical dates in regions that adopted the Gregorian calendar later (e.g., Russia in 1918, UK in 1752), the computed JDN assumes the Gregorian system was always in effect. If you need Julian calendar JDN, subtract the appropriate correction days.

The simplified formula (year − 4) mod 12 maps Gregorian years to the 12-animal cycle. This is accurate for dates after the Lunar New Year (late January to mid-February) but may be off by one animal for January dates. For exact Chinese Zodiac determination, the lunar calendar new year date for each specific year must be consulted.

The Julian Day Number (JDN) counts days from January 1, 4713 BC (Julian calendar), noon UT. The Modified Julian Day (MJD) was introduced by the Smithsonian Astrophysical Observatory in 1957 as MJD = JDN − 2400000.5. MJD starts at midnight instead of noon, and uses smaller numbers, making it more practical for modern computing and satellite tracking.

Meteorological seasons align to calendar months for statistical convenience: Spring is March - May, Summer is June - August (Northern Hemisphere). Astronomical seasons are defined by solstices and equinoxes, which shift by 1-2 days each year. This tool uses meteorological seasons. Toggle the hemisphere switch to see Southern Hemisphere seasons, which are offset by 6 months.