What is a Julian day?

What is a Julian day?

A Julian day number (JDN) is the integer count of days that have elapsed since the start of a long counting period, with day zero set at noon on 1 January 4713 BC.¹ Carry the count down to the moment within the day — the fraction of a day since the most recent noon — and the result is the Julian date (JD), a single decimal number that identifies any instant in history to whatever precision the decimal is carried. About 2.5 million days have elapsed since the starting point, so a Julian date in the present era is a number a little above 2,460,000, climbing by exactly one every twenty-four hours.¹

The point of the scheme is that it strips a date down to a plain number on a uniform scale. An ordinary calendar date is awkward to compute with: months have 28, 29, 30, or 31 days, years have 365 or 366, and the rules for which is which carry centuries of accumulated convention. A Julian date has none of that structure. To find how much time separates two events, you subtract one Julian date from the other and read the answer in days; there is no borrowing across month boundaries and no leap year to special-case.¹ That single property — a calendar-agnostic, uniformly incrementing day count — is why the Julian date became the standard time variable of astronomy and survives in software wherever date arithmetic has to be exact.

The instant a Julian date refers to is reckoned in Universal Time, the worldwide civil time scale tied to the Greenwich meridian, so the same Julian date denotes the same physical moment everywhere on Earth.² A Julian date carries no time zone and no notion of local clock time; converting it to a wall-clock reading in a particular place is a separate step.

Why does the Julian day begin at noon?

The Julian day rolls over at noon Universal Time rather than at midnight, so a whole Julian day number runs from one noon to the next.¹ The consequence shows up in the fractional part of every civil-midnight Julian date: because midnight is half a day after the previous noon, 2000 January 1 at 00:00 UT is JD 2451544.5, and any Julian date for a civil midnight ends in .5.¹²

The convention is older than electronic computing and comes from observational astronomy. An astronomer working through the night wants every observation in a single session to carry the same date, and a midnight rollover would split each night's work across two calendar days. Reckoning the day from noon — the middle of the working day for an observatory, since the Sun is up and nothing is being observed — keeps a full night of observations under one date number. National almanacs kept this noon-based astronomical day into the early twentieth century, and the Julian day system preserves the convention to this day.¹

Because the fractional day is measured against a time scale, precise work has to say which one. For civil purposes the Julian date is reckoned in Universal Time; for the highest-precision astronomy it is reckoned in a uniform atomic-based scale called Terrestrial Time, which is why the modern reference epoch is written J2000.0 = JD 2451545.0 TT, corresponding to 2000 January 1 at 12:00 — a noon, so the Julian date is the clean whole number 2451545.0.⁴

Where does the starting point of 4713 BC come from?

The 4713 BC origin predates astronomy's use of it by nearly three centuries. It was devised in 1583 by the French scholar Joseph Justus Scaliger, who was trying to put the tangle of ancient and medieval dating systems — regnal years, indictions, Olympiads — onto one uninterrupted count.³ Rather than allow negative years, he looked for a starting epoch earlier than any recorded historical event.

Scaliger combined three calendrical cycles that ran independently in his era: the 28-year solar cycle that governs the days of the week, the 19-year cycle used to place the Moon's phases, and the 15-year administrative cycle of the Roman indiction. A particular combination of positions in all three cycles recurs only once every 28 × 19 × 15 = 7,980 years, a span he called the Julian Period.³ Working backwards, he found that all three cycles last stood at 1 together in the year 4713 BC — astronomers now write it −4712 — and counted the years of his period forward from there. The noon-of-1-January-4713-BC instant was later adopted as the zero point of the Julian day numbers, and the long count of days has run from it ever since.³

How is the Julian day different from the Julian calendar?

The Julian day and the Julian calendar are different things that share a word. The Julian calendar is a scheme of months and years — the calendar Julius Caesar introduced in 46 BC, with a leap day every fourth year, that the Gregorian calendar later refined. The Julian day is a running count of days with no months, no years, and no leap-day rule at all. One is a way of naming a date; the other is a way of numbering days.¹³

The shared name is a historical accident of Scaliger's choice: he reckoned the years of his Julian Period in Julian-calendar years, and named the period after the calendar on which it was built — not, despite a common belief, after his father Julius, and not after Julius Caesar directly.³ The day count inherited the adjective when astronomers adopted Scaliger's epoch, but it is independent of which calendar anyone happens to be using. The starting instant is conventionally stated as a Julian-calendar date (1 January 4713 BC) because that calendar was the one in use when Scaliger worked, but the Julian day number itself is the same whichever calendar is used to name the epoch.²

The clearest demonstration that the day count ignores the calendar is the Gregorian reform itself. When ten days were struck from the civil calendar in October 1582, the Julian day count did not skip: the last day of the Julian calendar, 4 October 1582, is JD 2299160 at its noon, and the first day of the Gregorian calendar, 15 October 1582, is JD 2299161 — consecutive day numbers, because the two dates were consecutive physical days.¹ The calendar relabelled the days; the day count never noticed. The knowledge graph keeps the two entities apart as well: the day count is catalogued as a distinct concept — "days since the beginning of the Julian Period" — separate from the entry for the Julian calendar itself.⁵

What is the Modified Julian Date?

The Modified Julian Date (MJD) is the Julian date with a fixed offset removed: MJD = JD − 2400000.5.¹ The subtraction does two useful things at once. It strips off the leading digits that scarcely change within a human lifetime, turning an unwieldy seven-digit number into a five-digit one, and the extra half-day in the offset shifts the start of the count back from noon to midnight, so an MJD ticks over at civil midnight like an ordinary date. An MJD is therefore a whole number at 00:00 UT and grows by one each civil day.

Subtracting 2400000.5 places MJD zero at midnight beginning 17 November 1858.¹ The form was adopted for fields that handle dense streams of modern-era observations — satellite tracking, geodesy, radio astronomy, spacecraft telemetry — where the leading 24 of every Julian date is dead weight and a midnight rollover matches the way clocks and logs are kept.¹ Both numbers describe the same instant; MJD is simply the Julian date rebased for everyday convenience.

How do you convert a calendar date to a Julian date?

Conversion is a matter of counting days from the epoch and adding the fraction of the day. Take a worked example, 2000 January 1 at 12:00 UT. That instant sits exactly on a noon boundary, so its Julian date is a clean whole number — 2451545.0, the epoch astronomers call J2000.0.⁴ From there the rest follows by arithmetic:

• 2000 January 1, 12:00 UT (noon) → JD 2451545.0
• 2000 January 1, 00:00 UT (midnight, half a day earlier) → JD 2451544.5
• Modified Julian Date of that midnight → 2451544.5 − 2400000.5 = 51544

The midnight value ends in .5 because of the noon convention, and the Modified Julian Date comes out a whole number because the half-day offset in its definition is exactly what cancels that .5.¹ Production software does not count days by hand: a standard integer algorithm, published by Fliegel and Van Flandern in 1968 and reproduced by the U.S. Naval Observatory, converts any Gregorian calendar date to a Julian day number with a short run of integer divisions, and a companion routine runs the conversion in reverse.² The arithmetic uses the proleptic Gregorian calendar by convention, so it returns a single consistent answer for dates before 1582 rather than depending on when a given country adopted the reform.

Where are Julian dates used?

Astronomy is the native home of the Julian date. The brightness measurements that define a variable star's period, the tabulated positions in an ephemeris, and the reference epoch J2000.0 against which star catalogue coordinates are given are all expressed in Julian dates, precisely because the period between two observations is then a plain subtraction rather than a calendar calculation.⁴ An observing log that records each measurement's Julian date can be folded, differenced, and phased with ordinary decimal arithmetic.

Beyond astronomy, the same reasoning makes the Julian day number a common internal representation for dates in software, much as Unix time is a continuous count of seconds for the same reason. Spreadsheet and database date systems store dates as day counts from a fixed epoch and convert to a human-readable calendar only for display, and the Julian day number is the canonical such count in scientific computing. The one caveat is the time scale: because a Julian date's fraction is measured against a clock, exact work specifies whether it is reckoned in Universal Time or in a uniform scale such as Terrestrial Time, the two differing by the slowly growing gap between atomic time and the Earth's rotation. The day-numbering backbone, meanwhile, is the same regardless of whether the underlying calendar drifts against the seasons or the tropical year shortens by fractions of a second a century.⁴

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