# 360-day calendar

The 360-day calendar is a method of measuring durations used in financial markets, in computer models, in ancient literature, and in prophetic literary genres.

It is based on merging the three major calendar systems into one complex clock, with the 360-day year derived from the average year of the lunar and the solar: (365.2425 (solar) + 354.3829 (lunar))/2 = 719.6254/2 = 359.8127 days, rounding to 360.

A 360-day year consists of 12 months of 30 days each, so to derive such a calendar from the standard Gregorian calendar, certain days are skipped.

## Ancient Calendars

Ancient calendars around the world initially used a 360 day calendar.

### Rome

Romans initially used a calendar which had 360 days, with varying length of months.[1][2]

### India

The Rig Veda describes a calendar with twelve months and 360 days.[3]

### Mesoamerica

In the Mayan Long Count Calendar, the equivalent of the year, the tun, was 360 days.[4]

## Financial use

A duration is calculated as an integral number of days between start date A and end date B. The difference in years, months and days are usually calculated separately:

${\displaystyle duration(A,B)=(B_{y}-A_{y})\times 360+(B_{m}-A_{m})\times 30+(B_{d}-A_{d});A\leq B}$

There are several methods commonly available which differ in the way that they handle the cases where the months are not 30 days long, i.e. how they adjust dates:

European method (30E/360)[5][6][7][8][9]
If either date A or B falls on the 31st of the month, that date will be changed to the 30th.
Where date B falls on the last day of February, the actual date B will be used.
All months are considered to last 30 days and hence a full year has 360 days.
US/NASD method (30US/360)[10]
If both date A and B fall on the last day of February, then date B will be changed to the 30th.
If date A falls on the 31st of a month or last day of February, then date A will be changed to the 30th.
If date A falls on the 30th of a month after applying (2) above and date B falls on the 31st of a month, then date B will be changed to the 30th.
All months are considered to last 30 days and hence a full year has 360 days.
ISDA method[11][7][8][9]
If date A falls on the 31st of a month, then date A will be changed to the 30th.
If date A falls on the 30th of the month after applying the rule above, and date B falls on the 31st of the month, then date B will be changed to the 30th.
All months are considered to last 30 days except February which has its actual length. Any full year, however, always counts for 360 days.
BMA/PSA method[7][8][9]
If date A falls on the 31st of a month or last day of February, then date A will be changed to the 30th.
If date A falls on the 30th of the month after applying the rule above, and date B falls on the 31st of the month, then date B will be changed to the 30th.
All months are considered to last 30 days and hence a full year has 360 days.
Alternative European method (30E+/360)[7][9]
If date A falls on the 31st of a month, then date A will be changed to the 30th.
If date B falls on the 31st of a month, then date B will be changed to the 1st of the following month.
Where date B falls on the last day of February, the actual date B will be used.
All months are considered to last 30 days and hence a full year has 360 days.
360-day calendar implementation in spreadsheet functions
Package Function Variant
Microsoft Excel and StarOffice/OpenOffice.org DAYS360 NASD, but not SIA-compliant[12][13][14]
European
YEARFRAC NASD and European
SQL Server 2000 Analysis Services Days360
Mathworks Financial Toolbox days360 US/NASD
days360e European
days360isda ISDA
days360psa PSA
Gnumeric DAYS360
Apple Numbers DAYS360 NASD and European
YEARFRAC NASD and European

## References

1. ^ Stern, Sacha (2012). Calendars in Antiquity: Empires, States, and Societies. Oxford University Press. p. 208.
2. ^ Plutarch. "Life of Numa". The University of Chicago.
3. ^ B.G., Sidharth (1999). The Celestial Key to the Vedas. p. 86.
4. ^ "Maya Calendar Converter". Smithsonian National Museum of the American Indian. 2015. Retrieved September 10, 2015.
5. ^ ISMA book “Bond Markets: Structures and Yield Calculations”, ISBN 1-901912-02-7, and ISMA’s Circular 14 of 1997
6. ^ 2006 ISDA Definitions, Sec. 4.16 (g)
7. ^ a b c d http://docs.fincad.com/support/developerfunc/mathref/Daycount.htm
8. ^ a b c "Archived copy". Archived from the original on 2016-04-25. Retrieved 2016-03-25.
9. ^ a b c d Accrual & Discounting Conventions
10. ^ Standard Securities Calculation Methods, Fixed Income Securities Formulas for Price, Yield, and Accrued Interest: Volume 1, 1993, Jan Mayle, New York, NY: Securities Industry Association, ISBN 1882936019
11. ^ 2006 ISDA Definitions, Sec. 4.16 (f)
12. ^ See Microsoft Kb Article 916004. This bug is present in Excel versions 97 through 2007. This can be demonstrated by evaluating DAYS360(DATE(2006,2,28), DATE(2007,2,28)); here years starting and ending on the last day in February only have 358 days.
13. ^ Open Office is also not SIA-compliant, to maintain Excel compatibilitySee Issue 84934 — ODFF: DAYS360 compliance
14. ^ OpenOffice Documentation