Islamic Hijri & Gregorian Lunar Calendar Converter
Bi-directional conversion between the Islamic Hijri lunar calendar and Gregorian solar calendar with Umm al-Qura algorithms, moon-sighting adjustment, and Arabic script rendering.
Compensate for physical crescent visibility in your geographical location or align with regional Hilal sighting declarations:
Understanding the Islamic Hijri Calendar: Lunar Astronomy, The Epoch, and Month Mechanics
The Islamic calendar (known in Arabic as al-Taqwīm al-Hijrī, التقويم الهجري) is a strictly observational and mathematical lunar calendar comprising 12 synodic lunar months in a year of 354 or 355 days. Established in 638 CE by the second Caliph, Umar ibn al-Khattab, the calendar designates its foundational epoch (1 AH, or Anno Hegirae) from the migration (Hijrah) of the Prophet Muhammad (PBUH) from Mecca to Yathrib (Medina) in 622 CE.
Unlike lunisolar calendars that insert intercalary leap months—such as the 19-year Metonic cycle calculated by our Hebrew lunisolar calendar date conversion engine—the Islamic calendar forbids intercalation (Nasi'). Consequently, the Islamic lunar year is approximately 10.875 days shorter than the standard Gregorian tropical solar year (365.24219 days). This causes sacred Islamic events—including the fasting month of Ramadan, Eid al-Fitr, and the annual Hajj pilgrimage—to drift backward through the Gregorian solar seasons by approximately one full cycle every 32.5 to 33 solar years.
Synodic Lunation Period
The average synodic lunar month spans 29.530588 days (29 days, 12 hours, 44 minutes, 2.8 seconds), alternating between 29 and 30 days in duration.
The Hijrah Epoch
Day 1 of Muharram 1 AH equates precisely to Julian Day 1,948,439.5, corresponding to Friday, July 16, 622 CE (Julian) or July 19, 622 CE (proleptic Gregorian).
Sunset Day Transitions
Unlike the civil midnight (00:00) day transition of the Gregorian calendar, an Islamic day commences immediately following astronomical sunset (Maghrib).
The Twelve Months of the Islamic Lunar Calendar
Four of the twelve months in the Islamic calendar are designated as sacred (al-Ashhur al-Hurum: Dhu al-Qi'dah, Dhu al-Hijjah, Muharram, and Rajab) during which armed conflict is historically prohibited:
| Order | English Name | Arabic Script | Tabular Length | Significance & Key Religious Observances |
|---|---|---|---|---|
| 1 | Muharram | مُحَرَّم | 30 Days | Sacred Month; Islamic New Year (1st); Day of Ashura (10th) |
| 2 | Safar | صَفَر | 29 Days | The month of departure; historic expeditions and travels |
| 3 | Rabi' al-Awwal | رَبِيع الأَوَّل | 30 Days | The First Spring; Mawlid al-Nabi (12th, birth of Prophet Muhammad PBUH) |
| 4 | Rabi' al-Thani | رَبِيع الآخِر | 29 Days | The Second Spring; continuation of the seasonal quarter |
| 5 | Jumada al-Awwal | جُمَادَى الأُولَى | 30 Days | First month of parched land / winter freeze in ancient Arabia |
| 6 | Jumada al-Thani | جُمَادَى الآخِرَة | 29 Days | Second month of frozen ground |
| 7 | Rajab | رَجَب | 30 Days | Sacred Month of respect; Isra and Mi'raj (27th) |
| 8 | Sha'ban | شَعْبَان | 29 Days | Month of scattering; Mid-Sha'ban (Laylat al-Bara'ah, 15th) |
| 9 | Ramadan | رَمَضَان | 30 Days | Month of intense heat; Holy Month of Fasting; Laylat al-Qadr (Odd nights of last 10) |
| 10 | Shawwal | شَوَّال | 29 Days | Month of lifting / carrying; Eid al-Fitr (1st Shawwal) |
| 11 | Dhu al-Qi'dah | ذُو القَعْدَة | 30 Days | Sacred Month of truce and cessation of warfare before Hajj |
| 12 | Dhu al-Hijjah | ذُو الحِجَّة | 29 or 30 Days | Sacred Month of Pilgrimage; Day of Arafah (9th); Eid al-Adha (10th) |
Mathematical Conversion Algorithms: The 30-Year Tabular Arithmetic Cycle
To calculate astronomical ephemerides and historical dates across centuries without relying on archived weather reports of moon sightings, medieval Muslim astronomers devised the Tabular Islamic Calendar (pioneered by al-Battani and Ulugh Beg). The system synchronizes the mean synodic month against a 30-year leap cycle:
30-Year Leap Cycle Distribution
A single 30-year tabular cycle contains 10,631 total days (19 common years of 354 days and 11 leap years of 355 days). A year is designated as leap (Kabisa) if:
Julian Day Number Bridge
Conversion between calendars uses the continuous scalar Julian Day Number (JD) as an invariant mathematical intermediary. To calculate precise time intervals, satellite epochs, or celestial positions from raw day counts, use our dedicated astronomical Julian Day and MJD converter:
Under the 30-year tabular algorithm, the mean Islamic year equals 354.36667 days, and the mean month equals 29.530556 days. This diverges from the astronomical synodic lunar period by only 2.8 seconds per month, accumulating an error of merely 1 day every 2,500 solar years.
Astronomical Criteria: Umm al-Qura, Ru'yat al-Hilal, and Yallop Visibility Curves
In contemporary civil and religious practice, Muslims navigate two distinct calendar paradigms: calculated astronomical standards and physical crescent sighting declarations.
The Saudi Umm al-Qura Criterion
Formulated by the Institute of Astronomical & Geophysical Research at King Abdulaziz City for Science and Technology (KACST), the official Umm al-Qura calendar dictates that a new lunar month begins if, on the 29th day of the current month:
- The geocentric conjunction (New Moon) occurs before astronomical sunset at the Holy Kaaba in Mecca.
- Moonset occurs after sunset at Mecca coordinates (21°25'N, 39°49'E).
Physical Crescent Sighting (Ru'yat al-Hilal)
Countries including Pakistan, India, Bangladesh, Oman, Morocco, and various North American and European Islamic juristic councils require empirical sighting of the new crescent moon by human witnesses using the naked eye or optical telescopes. Optical parameters modeled by British astronomer Bernard Yallop (HM Nautical Almanac Office) account for crescent width (W), lunar altitude, and solar depression to predict visibility zones.
Frequently Asked Questions (FAQ)
How is the Islamic Hijri calendar calculated compared to the Gregorian solar calendar?
The Islamic Hijri calendar is an unsolar, strictly lunar calendar consisting of 12 synodic lunar months in a year of 354 or 355 days. Because a lunar year is roughly 10 to 12 days shorter than the 365.2425-day Gregorian solar year, Islamic calendar dates cycle across all four solar seasons over an approximately 33-year cycle.
Why can Islamic calendar dates vary by one or two days across different countries?
Traditional Islamic months commence upon the physical naked-eye sighting (Ru'yat al-Hilal) of the waxing crescent moon shortly after sunset. Because moon visibility depends on local geographic coordinates, atmospheric transparency, elevation, and sunset timing, countries observing astronomical sighting criteria (like Saudi Arabia or Morocco) may declare months one day earlier or later than countries relying on regional physical sightings or alternate astronomical thresholds.
What is the Umm al-Qura calendar system?
The Umm al-Qura calendar is the official civil calendar of the Kingdom of Saudi Arabia. It calculates new lunar months based on celestial mechanics: if the moon's conjunction occurs before sunset at Mecca and moonset occurs after sunset, the subsequent day is declared the first day of the new Hijri month.
What is the Tabular Islamic calendar and how are leap years determined?
The Tabular Islamic calendar is an arithmetic, rule-based calendar designed by medieval Islamic astronomers to approximate lunar phases without requiring ongoing observational reports. It operates on a 30-year cycle containing 19 regular years of 354 days and 11 leap years of 355 days (specifically years 2, 5, 7, 10, 13, 16, 18, 21, 24, 26, and 29 of the cycle).
When did the Islamic Hijri calendar epoch begin?
The Hijri calendar epoch begins with the Hijrah—the migration of the Prophet Muhammad (PBUH) from Mecca to Medina in 622 CE. Day 1 of Year 1 AH corresponds to July 16, 622 CE in the proleptic Julian calendar (or July 19, 622 CE in the proleptic Gregorian calendar).
How does the moon-sighting adjustment slider in this converter work?
The moon-sighting slider allows users to add or subtract 1 or 2 days from the mathematical astronomical baseline. This aligns the output precisely with the official decrees issued by local Hilal sighting committees, national ministries of religious affairs, or community mosque councils.
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