CALCULATOR  +           %     x               =      /           <        
                         Home  ||  Bible-calculator  ||  About-Help-Contact  ||  Learning  ||  Reliability Testing  ||  Updates



Appendix IV.   Year Types

Time and calendars

Time flows to the rhythm of days, and years; these tempos are astronomically set.

While man does not control time's tempo, he has a certain latitude in how to group these units together.

Ultimately, the most undisputable format in which to name a day would resemble:

Day 2,638,753 of the earth's existence
Yet this naming format is rejected in favor of a scheme that reflects the cyclical nature of the year with its seasons, and so man applies names to year-long batches of days.  Besides, seven-digit numbers are difficult to remember or process mentally.

And, because it would be hard to swim through a sea of days with three-digit numbers, years are subdivided further into twelve smaller units, with each of these split into thirty or so days.  Thus man only need deal with two-digit numbers at once.  As for years, man can handle years of four digits, as his life covers only a handful of years which pass slowly; yet these he will often shorten to a simpler two-digit abbreviation.

For all their authority, calendars do not govern time.  They merely apply names to days and years, in an agreed-upon pattern, based on their distance from an agreed-upon starting day and year.

What is a year?

Actual years last slightly longer than 365 days. Scientific definitions:
Sidereal year:365.256363051 days
  One complete circle around the Sun, as using distant stars as reference points.

Mean tropical year:365.24218967 days
See Update BelowOne cycle of the seasons.  Completed when Sun resumes the same relative position with regard to tilt in Earth's axis.  (Observable by angle of setting Sun.)  A very gradual gyration of this tilted axis causes a minor variance from the sidereal year value.

Mean tropical rounded: 365.2422 days
See Update Below Used as as a convenient approximation of the above value.

Whole-day-based years:
The Gregorian calendar:
365.2425 days: (365 or 366)
(i.e. 3,652,425 days every 10,000 years)

BC Formula


Gregorian Leap Rules


AD Formula

n / a -4990, -4 ( in-between year ) 365 n / a 33, 1983
(YYYY-1) divisible by 4 (or Year 1 BC) -4989, -5 Every 4 years add a LEAP DAY 366 YYYY divisible by 4 36, 1984
(YYYY-1) divisible by 100 -4901, -101 ...but every century NO LEAP DAY 365 YYYY divisible by 100 100, 1900
(YYYY-1) divisible by 400 -12801, -401 ...but every 400 years add a LEAP DAY 366 YYYY divisible by 400 1600, 2000
Lack of Year Zero requires a BC-offset of 1, to preserve the spacing pattern between leap years:   ...-9, -5, -1, 4, 8, 12...
  The Gregorian calendar has successfully eased the inconvenience of scientific reality by removing the awkward decimal remainder (.24218967), allowing man to chart time with easily-understood whole days, while still allowing for great accuracy over the millennia.

Hypothetical 365-day year:

"Symbolic" years; exactly 365 x 24-hour days
  Not useable by man, as noticeable drift of seasons would occur.  Still, the number 365 is tied to symbolic, innate concepts:
- the concept of year
- the passage of time
- the completion of a journey or cycle
- continuing without break:  as in 24-7-365
  The Bible itself contains a reference to 365:
Genesis 5:23  And all the days of Enoch were three hundred sixty and five years:

  Update: Correction by Astronomers Bolsters Gregorian Accuracy

Astronomers have calculated what they term a "mean tropical year" of 365.24218967 days,  often rounded up to 365.2422 days.

Students of Biblical time intervals, desiring accuracy of computation, have dutifully used this precise value as one seasonal cycle in God's celestial clock.  Indeed, astronomers and textbooks suggested nothing else.

Yet in recent years, scientists and scholars have awakened to the grave flaw in using mean tropical year as a multiplicand in time-date-season calculations.

The "mean tropical year" is an artificially-derived timespan not occurring in nature.  It was calculated by astronomers using time values involved in seasonal points other than the vernal equinox.  These points constantly fluctuate among themselves due to: lesser-known rotational or "wobble" cycles of the earth; varying speeds the Earth takes along its elliptical orbit; and gravitational pull from the Moon and nearby planets.

If we are truly looking to the seasons to define year-length, then we should be using the vernal equinox year .

Throughout history, the astronomical event defining a new year has been the Vernal Equinox, for both agricultural and religious purposes.  Astronomers measure the "vernal equinox year" at 365.2424 days-- a figure that can fluctuaute slightly, yet has been holding steady for millenia.

But what does .2424 days actually mean?  No year as we know it contains "fractional days".  To remove this decimal value, multiply 365.2424 by 10,000 ... and see this as 3,652,424 complete days over 10,000 years.

Our modern ("Gregorian") calendar nearly matches this pace.  Over 10,000 years, this calendar sees the sun rise and set exactly 3,652,425 times. Each one of those periods of light and dark are counted and named.

One caveat:  At the rate quoted above, the v-e year and calendar year may accumulate about a day's difference after this stretch of 10,000 calendar years:

3562425 days vs 3652424 days

So, did an extra day get invented?  or get wiped out?  No.  It just means that the 10,000-year Gregorian 'odometer' will roll over to zero, some hours after the 10,000th seasonal turning point is reached.  This is of trivial importance if our window of history is only 13,000 years wide.  What is one day of seasonal slippage, when by comparison, there have been roughly 180 days of slippage against the "starfield"-year due to the well-known gyration of our axis?

Lesson:  The Mean Tropical Year should be replaced in our thinking by the Vernal Equinox Year:

365.2422   365.2424

Indeed, our modern calendar can be a trusted tool for the Bible student, once the facts are known:

  1. The Gregorian reforms were actually corrections.
  2. Pope Gregory shared our own desire, to connect accurately with the time of Christ.
  3. The changes were devised by learned mathematicians and astronomers.
  4. They had the capability at that time to measure a year within a few minutes.
  5. The Julian calendar they started with was an invention of Rome in the decades before Christ.
  6. The only change was to the leap-year rules.
  7. The date was then set ahead ten days to fix the error accrued since 325 AD, the earliest reliable record.
  8. The vernal equinox would resume its place at March 21, and stay there.
  9. God's celestial clock would be honored, as the flow of seasons defined time, and the calendar described it.


Error in Statement of Tropical Year
2.  Calendar Wiki:  Tropical Year / Subtleties
3.  Calendar Wiki:  Gregorian Calendar / Accuracy

John O'Leary / Bible-calculator