When Will the Hijri Year Match the Gregorian Year? About 20,874 CE

Hijri year 1448 began on 16 June 2026, so from then until 31 December the Gregorian calendar says 2026 and the Hijri calendar says 1448: a gap of 578 years. From January until the next Hijri New Year the gap is 579, and then it is 578 again. Over the long run it is shrinking, because the Hijri year is shorter, so its number climbs faster. This article works out when the two numbers meet.

The short answer: around 20,874 CE, in a window of about 33 years. The exact year depends on how you define "match" and on a few decimals of the month length, and the whole estimate assumes that nothing about the Moon, the Earth or the calendars changes for the next 18,800 years. Every number below was reproduced with a script you can run yourself.

The Short Answer

Take the Hijri year to start on 1 Muharram, and ask in which Gregorian year that day falls. With a Hijri year of 354.3667 days (the tabular calendar's 10,631 days per 30 years):

So there is no single moment of catching up. The two numbers agree for a window of 34 consecutive years (20,841 to 20,874 inclusive, a span of about 33 years), and after that the Hijri number is the larger one.

What "Match" Means

"The year numbers are equal" can mean three different things, and they give slightly different answers.

1. At the new year. The Hijri year n begins in Gregorian year n. This is the definition used in the table above and in the chart below. It holds for 1 Muharram in 20,841 through 20,874.
2. On a given day. Some day on which both calendars show the same number. In the same model that first happens on 29 December 20,841 and last on 10 January 20,906, a stretch of about 64 years. Around 20,874 the match lasts for most of each year, because the Hijri year then begins in early January: 1 Muharram 20,874 falls on 3 January.
3. The same date. The two calendars do not lock together on day and month. The Hijri new year keeps moving about 11 days earlier through the Gregorian year, so it passes every date again and again.

Different sources that quote "20,874" or a year next to it are usually using the first definition with slightly different month lengths. We come back to that below.

Why It Happens: the Arithmetic

A Hijri year is twelve lunar months. A Gregorian year is the Sun's cycle through the seasons. They are different lengths:

Each Gregorian year, the Hijri count advances by 365.2425 / 354.3667 = 1.0307 years. So the Hijri number gains 0.0307 years on the Gregorian number every Gregorian year. Turn that round and it gains one whole year every 354.3667 / 10.8758 = 32.6 Gregorian years.

A quick check: Hijri year 1448 began in 2026, a gap of 578 years. Dividing by the gain rate: 578 / 0.0307 is about 18,830 years, and 2026 + 18,830 is about 20,856. That sits inside the 20,841 to 20,874 window. The staircase below is the same calculation done year by year, which is why the window has a width and not a single answer.

The year-by-year calculation uses the epoch of the calendar, 1 Muharram 1 AH on 16 July 622 in the Julian calendar (Julian Day 1948439.5). It places 1 Muharram of each later year exactly 354.3667 days after the one before, and converts that date to a Gregorian year. As a test, the model puts 1 Muharram 1448 in 2026: 16 June 2026. The Umm al-Qura table in the calendar gives the same day.

The Gap, Drawn

The chart plots the Gregorian year number of each 1 Muharram minus the Hijri year number, from 622 CE to about 21,000 CE. The line drops by one about every 32.6 years, which makes the staircase. It starts at 621 in the year of the epoch, is 578 in 2026, and reaches zero in the highlighted window.

The lower panel zooms in on the crossing. Zero holds from 1 Muharram 20,841 to 1 Muharram 20,874, and the next step takes the line below zero: the Hijri number is ahead.

Milestones on the Way

The same model, one row per milestone. The Hijri year shown is the one whose 1 Muharram falls in the Gregorian year on the left.

The gap shrinks by about 31 for every 1,000 years, so it looks almost frozen on a human timescale. Over a lifetime it changes by two or three.

Why It Is Only an Estimate

The result is a mean-motion model: it assumes the year lengths never change. Here is what is wrong with that, stated as far as we can check it.

Month length in the fourth decimal. Twelve mean synodic months (using 29.530589 days) make 354.3671 days, a hair longer than the tabular 354.3667. That small difference moves the window by one year, to 20,842 to 20,875. Our own check with the astronomy-engine library, which measured the mean new-moon-to-new-moon interval over 1,999 lunations from 2000, gave 29.53055 days and 12 months of 354.3666 days: that reproduces the tabular answer, 20,841 to 20,874. The differences are about 0.0004 day per year. Anything in that range is "right", and it is why nearby years appear in different places. For the background on the month, see the four kinds of lunar month.

Tides lengthen the day, and the Moon recedes. Tidal friction slows the Earth's rotation and moves the Moon outward. Lunar laser ranging gives the present recession as about 38.3 mm per year (3.8 cm). The day has lengthened on average by about 1.7 milliseconds per century over the last 2,700 years, from historical eclipse records. Both values come from the sources listed below. Neither is constant over geological time: the long-run average recession is about half the present rate. A calendar counts days, and a longer day means fewer days in a solar year, while a more distant Moon has a slower orbit. We have not modelled this. A rough scaling suggests the effect on the answer is a matter of years and not centuries, small next to the 33-year window, but treat that as our own back-of-envelope estimate, not a published result.

The Gregorian calendar drifts too. Its mean year, 365.2425 days, is about 0.0003 day longer than the tropical year (about 365.2422 days). Over the 18,800 years from now to 20,874, that adds up to roughly 6 days of drift against the seasons. In practice, nobody can say whether the Gregorian calendar will be in use then.

There is no sighting-based calendar that far ahead. The Hijri months used in real life begin with sighting or an agreed rule. The Umm al-Qura tables in the app end at 1500 AH, which is 2077 CE. Beyond them, "the Hijri year in 20,874" can only mean the tabular or mean-lunar count. The three rules are explained in the triple-engine Hijri calendar, and the basics of the calendar in how the Islamic lunar calendar works.

Reproduce It Yourself

The research script is docs/research/hijri-gregorian-catchup.mjs in the project repository. Run node docs/research/hijri-gregorian-catchup.mjs. It prints the first and last year of the match for both month lengths, and the 32.6-year gain rate. It uses a Julian Day to Gregorian year conversion from Meeus, Astronomical Algorithms. We cross-checked it with a second version that takes the month length from astronomy-engine and converts days to years with JavaScript's own proleptic Gregorian date arithmetic. Both agree.

Frequently Asked Questions

What is the Hijri year today?

In late 2026 it is 1448 AH. Hijri year 1448 began on 16 June 2026 in the Umm al-Qura calendar, and on 12 October 2026 the Umm al-Qura date is 1 Jumada al-Ula 1448. Open the calendar for today's date in each of the three systems.

Which number comes first?

The Gregorian number is ahead until 20,840. From 1 Muharram 20,841 to 1 Muharram 20,874 the two years carry the same number at the new year. After that the Hijri number is ahead, and it keeps gaining a year every 32.6 years. This is about the number and not the date: the Hijri calendar does not start earlier, it just counts faster.

Will the two calendars ever show the same date?

The year numbers match for a stretch, but the day and month will not line up in a lasting way. The Hijri year is about 10.9 days shorter, so its new year moves earlier through the Gregorian year each time. Across the 33 years of the window it makes one full lap of the Gregorian year.

Why do some sources say 20,874 and others a nearby year?

The result depends on the Hijri year length you assume. The tabular year of 354.3667 days gives 20,841 to 20,874. Twelve mean synodic months of 29.530589 days give 20,842 to 20,875. Different definitions of "match" (new year only, or any day) shift it again. All of them are the same estimate to within a year or two.

Does the Hijri year ever overtake the Gregorian one by lengths of months?

It does not overtake in a way you could notice. After the crossing, the Hijri number simply becomes the larger one: 21,004 AH begins in 21,000 CE. Since a Hijri year is shorter, you would find more Hijri years than Gregorian ones in any long period, one extra every 32.6 years.

Summary

The Hijri count gains a year on the Gregorian count every 32.6 years. Starting from a gap of 578 in 2026, the numbers meet from 20,841 to 20,874 CE in the tabular model, and that is the answer to quote: "about 20,874, in a window of 33 years, if nothing changes". The arithmetic is simple and the caveats are real, but none of them moves the answer by more than a few years.

See today's date in the Hijri systems on the calendar. If this kind of drift interests you, which years have two Eids is the same 11-day shift seen from the other side.

See Also

• How Old Are You in Hijri Years? A Calculator and the Arithmetic of the Hijri Birthday

References

• Hilal Vision. Hijri-Gregorian catch-up model, docs/research/hijri-gregorian-catchup.mjs.
• Meeus, J. (1998). Astronomical Algorithms (2nd ed.). Willmann-Bell. Chapter 7, Julian Day and calendar date.
• Williams, J. G., & Boggs, D. H. (2016). Secular tidal changes in lunar orbit and Earth rotation. Celestial Mechanics and Dynamical Astronomy, 126. Lunar laser ranging recession of 38.30 mm per year, as summarised in https://en.wikipedia.org/wiki/Tidal_acceleration
• Stephenson, F. R., Morrison, L. V., & Hohenkerk, C. Y. (2016). Measurement of the Earth's rotation: 720 BC to AD 2015. Proceedings of the Royal Society A. Average lengthening of the day of about 1.72 ms per century, as summarised in https://en.wikipedia.org/wiki/Tidal_acceleration
• Astronomy Engine documentation: SearchMoonPhase. https://github.com/cosinekitty/astronomy