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Date Conversion Essentials: 
The Case of Persian to English Official Translation


Although facile access to the Internet makes everything easy, manual time reckoning in case of official translation, under circumstance of no-access to Dates Calculator Online, seems inevitable. Thus, this article intends to elaborate on conversion and interconversion among three kinds of calendars used in official translations in Iran: Solar, Lunar and Gregorian. To this end, first, it provides a thorough discussion of conceptual (calendarical) knowledge, focusing on inherent discrepancies existing between these calendars, then elaborates on the manual date calculations, and finally introduces some beneficial websites and software.

KEYWORDS: Conversion, interconversion, solar, lunar, Gregorian calendar, official translation

1. Date conversion in official translation

Official documents in Iran are dated based on the solar (Hejri-e Shamsi)1 calendar. Of course, certain documents of a religious nature may also contain lunar (Hejri-e Qamari) dates and captions. Yet, this piece of information is only secondary and will not be employed for recording or referring to the document unless it dates back to the time of Prophet Muhammad. This is because the Hijri calendar, which is based the lunar movement in the solar system, incurs changes that are difficult to keep track of. Therefore, the solar calendar, which is to some extend bereft of such fluctuations, is applied to date keeping purposes.

An indispensible component of any good translation attempt, therefore, is to have capability to convert dates from different calendars into each other. For our purpose, we need to know to convert solar dates into the Gregorian calendar and vice versa. To accomplish this, the first thing to know about date conversion is having ample conceptual knowledge concerning each Gregorian, solar, or lunar month, for instance, how many days there are in or what leap year is, and so forth.

2. Calendars

2.1. Solar calendar

The modern Persian calendar was adopted in 1925, supplanting (while retaining the month names of) a traditional calendar dating from the eleventh century. The calendar consists of 12 months, the first six of which are 31 days, the next five 30 days, and the final month 29 days in a normal year and 30 days in a leap year. The Solar months are as follows:

Months Days Months Days
1. Farvardin 31 7. Mehr 30
2. Ordibehesht 31 8. Aban 30
3. Khordad 31 9. Azar 30
4. Tir 31 10. Dey 30
5. Mordad 31 11. Bahman 30
6. Shahrivar 31 12. Esfand 30

Each year begins on the day in which the March equinox occurs at or after solar noon at the reference longitude for Iran Standard Time (52°30' E). Days begin at midnight in the standard time zone. There is no leap year rule; 366-day years do not recur in a regular pattern, but instead occurs whenever that number of days elapses between equinoxes at the reference meridian. The calendar, therefore, stays perfectly aligned with the seasons. No attempt is made to synchronize months with the phases of the Moon.

There is some controversy about the reference meridian at which the equinox is determined in this calendar. Various sources cite Tehran, Esfahan, and the central meridian of Iran Standard Time as that where the equinox is determined; in this implementation, the Iran Standard Time longitude is used, as it appears that this is the criterion used in Iran today. As this calendar is proleptic for all years prior to 1925 C.E., historical considerations regarding the capitals of Persia and Iran, do not seem to apply.  

Ahmad Birashk (1993) proposed an alternative means of determining leap years for the Persian calendar. His technique avoids the need to determine the moment of the astronomical equinox, replacing it with a very complex leap year structure. Years are grouped into cycles, which begin with four normal years after which every fourth subsequent year in the cycle is a leap year. Cycles are grouped into grand cycles of either 128 years (composed of cycles of 29, 33, 33, and 33 years) or 132 years, containing cycles of 29, 33, 33, and 37 years. A great grand cycle is composed of 21 consecutive 128-year grand cycles and a final 132 grand cycle, for a total of 2820 years. The pattern of normal and leap years, which began in 1925, will not repeat until the year 4745!

Each 2820-year great grand cycle contains 2137 normal years of 365 days and 683 leap years of 366 days; with the average year length over the great grand cycle of 365.24219852.So close is this to the actual solar tropical year of 365.24219878 days that this calendar accumulates an error of one day only every 3.8 million years.

2.2. Gregorian calendar

The Gregorian calendar was proclaimed by Pope Gregory XIII and took effect in most Catholic states in 1582, in which October 4, 1582 of the Julian calendar was followed by October 15 in the new calendar, correcting for the accumulated discrepancy between the Julian calendar and the equinox as of that date. When comparing historical dates, it is important to note that the Gregorian calendar used universally today in Western countries and in international commerce, was adopted at different times by different countries. Britain and her colonies (including what is now the United States), did not switch to the Gregorian calendar until 1752, when Wednesday 2nd September in the Julian calendar dawned as Thursday the 14th in the Gregorian. The Gregorian months are as follows:

Months Days Months Days
1. January 31 7. July 31
2. February 28 8. August 31
3. March 31 9. September 30
4. April 30 10. October 31
5. May 31 11. November 30
6. June 30 12. December 31

February, the shortest month in the Gregorian calendar, may fluctuate between 28 or 29 days depending on whether it occurs in a leap year or not. The Gregorian calendar is a minor correction to the Julian. In the Julian calendar, every fourth year is a leap year in which February has 29, not 28 days, but in the Gregorian, years divisible by 100 are not leap years unless they are also divisible by 400. As in the Julian calendar, days are considered to begin at midnight.

The average length of a year in the Gregorian calendar is 365.2425 days compared to the actual solar tropical year (time from equinox to equinox) of 365.24219878 days, so the calendar accumulates one day of error with respect to the solar year about every 3300 years. As a purely solar calendar, no attempt is made to synchronize the start of months to the phases of the Moon.

While one cannot properly speak of ‘Gregorian dates’ prior to the adoption of the calendar in 1582, the calendar can be extrapolated to prior dates. In doing so, this implementation uses the convention that the year prior to year 1 is year 0. This differs from the Julian calendar in which there is no year 0—the year before year 1 in the Julian calendar is year −1. The date December 30th, in the Gregorian calendar corresponds to January 1st, 1 in the Julian calendar.

A slight modification of the Gregorian calendar would make it even more precise. If you add the additional rule that years evenly divisible by 4000 are not leap years, you obtain an average solar year of 365.24225 days per year which, compared to the actual mean year of 365.24219878, is equivalent to an error of one day over a period of about 19,500 years; this is comparable to errors due to tidal braking of the rotation of the Earth.  

Lunar calendar  2.3.

The lunar (also called Islamic, Muslim and Hijri) calendar is purely lunar and consists of twelve alternating months of 30 and 29 days, with the final 29-day month extended to 30 days during leap years. Leap years follow a 30-year cycle and occur in years 1, 5, 7, 10, 13, 16, 18, 21, 24, 26, and 29. Days are considered to begin at sunset. The calendar begins on Friday, July 16th, 622 C.E. in the Julian calendar, Julian day 1948439.5, the day of Muhammad's migration from Mecca to Medina, with sunset on the preceding day reckoned as the first day of the first month of year 1 A.H., Anno Hegiræ, the Arabic word for ‘separate’ or ‘go away’. The names for the days are just their numbers: Sunday is the first day and Saturday the 7th; the week is considered to begin on Saturday. The lunar months are as follows:

Months Days Months Days
1. Muharram 30 7. Rajab 30
2. Safar 29 8. Shaban 29
3. Rabi al-Awwal 30 9. Ramadan 30
4. Rabi ath-Thani 29 10. Shawwal 29
5. Jumad al-Ula 30 11. Dhul-Qada 30
6. Jumad al-Thani 29 12. Dhul-Hijja 29

The calendar presented here is the most commonly used civil calendar in the Islamic world; for religious purposes, months are marked to start with the first observation of the crescent of the new Moon. Therefore, due to this, the same Gregorian date may have two to four Hijri equivalent dates according to the place and time of the crescent sighting.

As an attempt to rationalize the various systems in use at that time, it was agreed that the most appropriate reference point for the Islamic Calendar was the Hijra (Hijrah, Hegira). The Islamic (Hijri) Calendar – with dates that fall within the Muslim Era – is usually abbreviated AH in Western languages from the Latinized 'Anno Hejirae' in the year of the Hijra

3. Calculations 3.1. Solar to Gregorian conversion

As in the case of February, Esfand may fluctuate between 29 days in an ordinary year and 30 days in a leap year in the solar calendar. Nevertheless, the calendars do not seasonally match in that while February marks mid-winter in the Gregorian calendar, Esfand denotes the last month of winter and the last month of a year in the solar calendar. Thus, while a Gregorian New Year stars almost at the beginning of winter, the Persian New Year approximately begins at the beginning of spring.

A potential source of confusion is the turning moment of years, which is different across the two cultures. In the Gregorian calendar, the turning moment is always at 12:00 midnight, December 31; hence no concern about the extra 6-hour-or-so for the next leap year, and do not consider the turning moment to be at 12 midnight necessarily. To them the turning moment may be early morning in one year, late afternoon in another year, still 3:00 a.m. in another year and so on and so forth (Raee, 2007:187).

This discrepancy, of course, not only creates confusions in terms of date conversion between two calendars, but also leaves the Persians with some extra time between the last and the New Year that seemingly belongs to neither! Thus, when a New Year starts at, say, 6:00 p.m. people wonder to which year the time between 6:01 and midnight belongs! This why sometimes there is no complete match between converted dates. Only sophisticated software, which can actually keep a record of every single year in the history in both the Gregorian and the solar calendar, can come up with the exact date matches between the two calendars2.

Below a manual method of date, conversion between the foregoing calendars will be presented. Reservations, however, have to be made as the method could be flawed by a margin of one or two days. This, of course, is due to the discrepancies explained above. To convert a solar date to its Gregorian counterpart, add the sums 2/21/621 to the months/days/years figures respectively3. However, if a person was born on or after Dey (the Persian month), we must add up the years' figure by 622.For instance, if the Iranian date is on Farvardin 7th, the Gregorian equivalent will be something like:

Day: 7+21=28

Month: 1+2=3

Year: 1377+621=1998

Therefore, the converted date (with a reservation of one to two days) is March 28, 1998. However, things are not always so straightforward. What if the figures exceed their ceilings, i.e. what if 'days' figure exceeds a maximum of 31, or 'months' figure exceeds 12? Consider this Persian date: Bahman 17, 1354. Applying the above formula, we will have:

Day: 17+21=38

Month: 11+2=13

Year: 1354+622=1976

38 for 'days' and 13 for 'months' are not acceptable figures because there simply is no month with 38 days or any year with 13 months! To solve this dilemma, we subtract the months from 12 (a whole year), and add one unit to the 'years' figure. The remainder, whatsoever, stands for the 'months'. In our example above, the 'months' figure will then happen to be 1(13 minus 12).

However, we are not finished yet, as our 'days' figure still stands on 38, which is not acceptable. To solve this problem, we look back at the obtained 'months' figure 1, and check the Gregorian calendar to see how many days are in it. January is 31 days, so out of the 38 in our 'days' figure, 31 belongs to January. The remainder, whatever it is, will lead into February. This, the ultimate date will be something close to February 7, 1976.

As went earlier, the converted dates are unfortunately not precise. Different techniques have been utilized to deal with the issue, yet none has, to date, yielded impeccable results, at least to the author's knowledge. To this end, the best way, probably would be to design a piece of software that can record previous Iranian years and then match them up with the Gregorian counterpart year by year in both ways. Such software, of course, is now being developed here and there, yet, their precision is not ascertained as dates converted based on an existing Persian calendar, so and this is what we come up with:

Months Days Months Days
1. Farvardin +1 7. Mehr -1
2. Ordibehesht +1 8. Aban -1
3. Khordad P 9. Azar P
4. Tir P 10. Dey P
5. Mordad +1 11. Bahman +1
6. Shahrivar -1 12. Esfand +2

The (+) and (-) signs indicate the number of 'days' that the conversion is either ahead or behind the exact date. The letter (P) stands for precision.

Obviously, it is difficult to discern a pattern so that one can uniformly convert all dates. Remember this only holds true for the current year. No guarantee is made as to the states of the converted dates as they go farther and farther back into the past.

The reverse also holds true when converting dates from the Gregorian calendar into the solar calendar. If you reduce 21 from the 'days', 2 from the 'months', and 621 from the 'years' figure, you will obtain the approximate solar date equivalent. The situation, again, will be easy as long as the subtraction yields positive numbers. However, when negative figures result, things will be more complicated again. Yet the reader should, by now, be able to get through the problem simply by considering that minus figures denote that the date should go back into the previous day or month. It will be just the opposite of the procedure explained above, and as should not pose any problems.

 3.2. Lunar to Gregorian conversion

A formula to convert an Islamic date into a Gregorian counterpart is to divide the lunar date by 33.7, subtract the result from the lunar date and then add 622 or for an approximate equivalent, add 583 to the lunar date. Since the Islamic year is a lunar year, it is shorter than the western solar year. Therefore, 622 value just can be added or subtracted for a start date. For example, Year 2008 (Gregorian date) is equal to 2008 –622 = 1386. However, this is not real Muslim year; it is year in Persian calendar, because Muslim calendar is lunar calendar, not solar like Gregorian or Persian. One lunar year has about 354 days, so we need extra correction to find out real year. Easiest way to do this is to multiply or divide year on 354/365≈0.97. In our case, (2008-622)/0.97≈1429 year is Muslim calendar. Therefore, finally if we want to convert Muslim date to Gregorian date, we need to multiply original year by 0.97 and add 622:

Year Gregorian ≈ Year Muslim × 0.97 + 622.

If you want to convert Gregorian date to Muslim date, you need to subtract 622 from original year and after multiply by 1.03:

Year Muslim ≈ (Year Gregorian– 622) × 1.03.

As mentioned before, described formulas are very rough, so this way is admissible for precise calculations. Moreover, Muslim year does not start on 1st of January, so 2008 year corresponds to 1428-1429 years of Islamic calendar.

3.3. Lunar to solar conversion

No lunar dates are truly convertible because such undertaking is not too easy to do. Many problems exist between the two calendars. The Islamic calendar is purely lunar, as opposed to solar or some luni-solar, the lunar year is shorter than the solar year by about 11 days (10 days and 21 hours), and months in the lunar year are not related to any seasons at all, seasons are related to the solar cycle not the lunar ones. Due to this, it is a long cycle date system: a 33-year cycle of lunar months is required for a month to take a complete turn and fall during the same season again. Therefore, these two numbers, 33 and 34 can be employed for rough reckoning between the calendars. In accordance with this formula, solar year is divided by 33 and the result is added to the present solar year in lunar-to-solar conversion. For solar-to-lunar conversion, solar year roughly equals to lunar year divided by 34, and then subtracted by the present lunar year.

Year Muslim≈ Year Solar /33+1389 

Year Solar ≈ Year Muslim /34-1429 

For the sake of more precision in time reckoning, another formula can be exploited by converting Lunar calendar to Gregorian first, and then from January1 to March 20th, 622 value and in case of March 21th to the end of December, 621 value subtracted from the result. To avoid redundancy, check the related formulas in Lunar to Gregorian Conversion Section (3.2.).

4. Interconversion into other calendars

There are several reliable software for converting the Persian calendar dates into other calendar systems and vice-versa. For proper work of the Dates Calculator Online, JavaScript support in the browser should be activated. The 'Khayyam' Program:

set up for the conversion between the Persian and Gregorian calendars is proposed. Currently the leap years in the 33-year cycles are those years that after dividing by 33 leave a remainder of 1, 5, 9, 13, 17, 22, 26 and 30. For example, the year A.P. 1375 that begun on March 20, 1996 has the remainder of 22 and thus is the leap year. The rules are implemented in the ‘Khayyam program’. In a recent paper, Borkowski (1996) argues that the algorithm employed in that program is valid for the years A.D. 1799 to 2256 (A.P. 1178 to 1634). Moreover, he presents a concise code, which reconstructs the pattern of leap years over a time span of about 3000 years.

Another interesting tool is the Calendrica 2.0 software package, based on the algorithms in Calendrical Calculations: The millennium Edition, by Edward M. Reingold and Nachum Dershowitz (2008). The online version:

allows conversion not only between the Persian and Gregorian systems, but also among several other calendars, mainly: Armenian, Chinese, French revolutionary, Hebrew, Hindu, Islamic, and Mayan to name a few (Memari, 1997:94).

5. Conclusion

Prior to embarking on translating any official document, it is imperative for translators to cope with date conversion they encounter. Although the internet abounds in online date converters equipped with diverse facilities such as high-resolution graphics as well as multipurpose options, manual date reckonings, in case of lack of access to World Wide Web is an empowering solution. This article aims at shedding light on issues surrounding these calendars such as: conversion and interconversion, fluctuations, and discrepancies among them via focusing on conceptual knowledge of each calendar. Undoubtedly, the forenamed methods, viz, manual date reckoning and online date converter suffer from some flaws, but to alleviate this situation, it is advisable to integrate them into complementary procedure that definitely proves fruitful.


Bagher Zadeh, Hossein (2005). Date conversion. Online at calendar (consulted 01.08.2010)

Birashk, Ahmad (1993). A Comparative Calendar of the Iranian, Muslim Lunar and Christian Eras for 3000 Years.Tehran: Mazda Publications.

Borkowski, Kazimierz (1996)." The Persian calendar for 3000 years." Earth, Moon and Planets 74(3), 223-230.

Date Conversion (no date).Online at (consulted 11.08.2010)

Memari, Mohammad (1997).Documents and Correspondence Translation. Tehran: Ayat Publishers Company.

Raee Sharif, Masoud (2007).Translation of Legal Correspondence and Deeds. Vol 1. Tehran: SAMT Publications.

Reingold, Edward and Dershowitz, Nachum (2008).Calendrical Calculations. USA: CUP. Online at (consulted 05.08.2010)

Note 1:

It is transliteration for solar calendar. Contrary to the Hijri calendar, which has a lunar basis and is used as a religious reference in Persian, the Hejri e-Shamsi calendar is based on the 24-hour rotation of the Earth around its axis, thus more precise than the Hirji calendar.

Note 2:

In this respect then, Persian is still using similar to the Julian calendar of the old Roman Empire which introduced by Julius Caesar in 46 B.C. It consists of 365 days with an extra day every four years for the leap year.

Note 3:

Through this article, the American method of writing dates, wherein days appear in the middle will be applied.  


I am a simultaneous interpreter and lecturer at Esfahan Sheikhbahaee University. I got my M.A degree in Translation from State University of Esfahan in 2002. My research interest focuses on simultaneous, consecutive, legal, and scientific translation. Email: pahmadi05 at gmail .com

Published - November 2010

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