Persian Calendar Converter
Convert between Gregorian, Hijri, and the Persian Solar Hijri (Jalali) calendar. Enter values for instant results with step-by-step formulas.
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The Julian Day Number (JDN) serves as an intermediary for calendar conversions. Each calendar system has algorithms to convert to and from JDN, enabling accurate date translation between Persian, Gregorian, and Hijri calendars.
Last reviewed: December 2025
Worked Examples
Example 1: Converting March 21, 2026 to Persian Calendar
Example 2: Converting Persian Date 1 Mehr 1404 to Gregorian
Background & Theory
The Persian Calendar Converter applies the following established principles and formulas. Date and time calculations underpin a vast range of applications from financial settlement to scheduling and age verification. The complexity arises because civil timekeeping uses irregular units: months have 28, 29, 30, or 31 days; years have 365 or 366 days; hours, minutes, and seconds use base-60 arithmetic; and time zones introduce offsets ranging from -12:00 to +14:00 relative to UTC. The Gregorian calendar's leap year rule is a compound condition: a year is a leap year if it is divisible by 4, except for century years, which must be divisible by 400. Thus 1900 was not a leap year but 2000 was. This rule keeps the calendar synchronized with the solar year to within about 26 seconds per year. For algorithmic date calculations, the Julian Day Number provides a continuous integer count of days since January 1, 4713 BCE, eliminating the irregularity of calendar months and making interval arithmetic straightforward. The Unix epoch, by contrast, counts seconds since 00:00:00 UTC on January 1, 1970, and is the basis of POSIX time used in most computing systems. ISO 8601 standardizes date and time representation as YYYY-MM-DD and combined datetime as YYYY-MM-DDTHH:MM:SS±HH:MM, ensuring unambiguous machine-readable interchange across locales that would otherwise differ in day/month/year ordering. Business day calculation requires excluding weekends and, optionally, a jurisdiction-specific list of public holidays. Duration calculations expressed in years, months, and days must account for the variable length of months, making them non-commutative: the interval from January 31 to February 28 is different from the interval from February 28 to March 31. Age calculation algorithms must handle the edge case of birthdays on February 29 and ensure that a person born on December 31 is not counted as one year older on January 1 of the following year until the clock passes midnight. Zeller's Congruence provides a closed-form formula to determine the day of the week for any Gregorian or Julian calendar date using only integer arithmetic.
History
The history behind the Persian Calendar Converter traces back through the following developments. The need to track time and predict astronomical events gave rise to calendrical systems independently across many civilizations. The Babylonians, around 2000 BCE, developed a lunisolar calendar with 12 months of alternating 29 and 30 days, inserting an intercalary month periodically to keep pace with the solar year. They also divided the day into 24 hours and the hour into 60 minutes, a sexagesimal convention that persists in every modern clock. The Egyptian civil calendar used 12 months of exactly 30 days plus five epagomenal days, totaling 365 days. Though simple for administrative purposes, it drifted against the solar year by one day every four years. Julius Caesar, advised by the Egyptian astronomer Sosigenes, reformed the Roman calendar in 45 BCE. The Julian calendar introduced a 365-day year with a leap day every four years, a system that served Europe for over sixteen centuries. By the 16th century, the accumulated error of the Julian calendar had shifted the spring equinox ten days from its ecclesiastically mandated date, disrupting the calculation of Easter. Pope Gregory XIII commissioned the calendar reform that bears his name, and the Gregorian calendar was introduced in Catholic countries in October 1582. The transition required skipping ten days: October 4 was followed by October 15. Protestant and Orthodox countries adopted the reform slowly; Britain and its colonies switched in 1752, Russia not until 1918, and Greece in 1923. The expansion of railways in the 1840s created an urgent practical problem: each city operated on its own local solar time, making train timetables impossible to coordinate. British railways adopted Greenwich Mean Time as a standard in 1847. The International Meridian Conference of 1884 in Washington formalized the prime meridian at Greenwich and established the global framework of 24 time zones. Daylight saving time was first adopted nationally during World War I to reduce coal consumption. The development of atomic clocks after World War II led to the definition of Coordinated Universal Time (UTC) in 1960, accurate to nanoseconds. The Y2K problem of 1999-2000 demonstrated that two-digit year storage in legacy systems could cause widespread failures, prompting a global remediation effort costing an estimated 300 to 600 billion dollars.
Frequently Asked Questions
Formula
JDN = day + floor((153m+2)/5) + 365y + floor(y/4) - floor(y/100) + floor(y/400) - 32045
The Julian Day Number (JDN) serves as an intermediary for calendar conversions. Each calendar system has algorithms to convert to and from JDN, enabling accurate date translation between Persian, Gregorian, and Hijri calendars.
Worked Examples
Example 1: Converting March 21, 2026 to Persian Calendar
Problem: Convert the Gregorian date March 21, 2026 to the Persian (Jalali) and Hijri calendars.
Solution: Using the Julian Day Number algorithm:\nJDN for March 21, 2026 = 2,461,826\nPersian epoch JDN = 1,948,321\nDays since epoch = 513,505\nUsing the 2820-year cycle algorithm:\nPersian date = 1 Farvardin 1405\nFor Hijri: JDN - 1,948,440 + 10632 = Hijri calculation\nHijri date = 22 Shaban 1447
Result: Gregorian: March 21, 2026 | Persian: 1 Farvardin 1405 | Hijri: 22 Shaban 1447
Example 2: Converting Persian Date 1 Mehr 1404 to Gregorian
Problem: Convert the Persian date 1 Mehr 1404 (first day of autumn in Persian calendar) to Gregorian.
Solution: 1 Mehr is the 187th day of the Persian year (6 months of 31 days + 1 day)\nPersian year 1404, month 7, day 1\nUsing the reverse algorithm through JDN:\nJDN = Persian epoch + yearly offset + day of year\nConverting JDN back to Gregorian gives September 23, 2025
Result: Persian: 1 Mehr 1404 | Gregorian: September 23, 2025 (Autumn Equinox)
Frequently Asked Questions
What is the Persian (Jalali) calendar and how does it differ from the Gregorian calendar?
The Persian calendar, also known as the Solar Hijri or Jalali calendar, is a solar calendar used officially in Iran and Afghanistan. It was reformed by Omar Khayyam and other astronomers in 1079 CE. Unlike the Gregorian calendar which starts from the estimated birth of Jesus, the Persian calendar counts years from the migration (Hijra) of Prophet Muhammad in 622 CE but uses solar year calculations rather than lunar. The first six months have 31 days each, the next five have 30 days, and the last month has 29 days (or 30 in leap years). The Persian New Year, Nowruz, falls on the vernal equinox around March 20-21, making it astronomically precise.
How accurate is the Persian calendar compared to the Gregorian and Hijri calendars?
The Persian calendar is considered one of the most accurate calendars ever devised. It has an error of only one day in approximately 3.8 million years, compared to the Gregorian calendar which accumulates an error of one day every 3,236 years. This remarkable accuracy comes from its leap year algorithm which uses a 2820-year grand cycle. The Hijri (Islamic) calendar, being purely lunar with 354 or 355 days per year, drifts approximately 11 days each year relative to the solar year, completing a full cycle through all seasons every 33 years. The Persian calendar stays perfectly aligned with the seasons because it is anchored to the vernal equinox.
What are the months and seasons of the Persian calendar?
The Persian calendar has twelve months organized into three groups reflecting the seasons. Spring months are Farvardin (31 days), Ordibehesht (31 days), and Khordad (31 days). Summer months are Tir (31 days), Mordad (31 days), and Shahrivar (31 days). Autumn months are Mehr (30 days), Aban (30 days), and Azar (30 days). Winter months are Dey (30 days), Bahman (30 days), and Esfand (29 or 30 days). The first day of Farvardin always coincides with the spring equinox, making the calendar naturally aligned with the astronomical seasons without any need for artificial adjustments.
How does the Hijri (Islamic) calendar conversion work?
The Hijri calendar is a purely lunar calendar consisting of 12 months that alternate between 29 and 30 days, resulting in a year of 354 or 355 days. Conversion between Gregorian and Hijri dates requires algorithms based on the Julian Day Number system, which provides a continuous count of days since January 1, 4713 BCE. The Hijri epoch corresponds to July 16, 622 CE in the Julian calendar. Because the Hijri year is about 11 days shorter than the solar year, Islamic dates cycle through all Gregorian seasons over a period of approximately 33 years. Important Islamic dates like Ramadan occur at different Gregorian dates each year.
What is the difference between business days and calendar days?
Calendar days include every day. Business days (or working days) exclude weekends (Saturday and Sunday) and public holidays. A 10-business-day deadline is typically 14 calendar days. Legal and financial deadlines often specify which type applies.
How do I verify Persian Calendar Converter's result independently?
The Formula section on this page shows the equation used. You can reproduce the calculation manually or in a spreadsheet using those steps. Compare your answer against the worked examples in the Examples section, which use known reference values so you can confirm the calculator is behaving as expected.
References
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