The formula, in words

The calculation adds the deferral to the start as whole Gregorian calendar days. It converts that deferred date to the tabular civil Hijri calendar, adds the whole term as Hijri months, and converts the result back to a Gregorian date. In parallel it adds the same whole month count to the deferred Gregorian date. It then subtracts one integer day number from the other. All of it is integer arithmetic, with no time zone and no clock.

If the day of the month does not exist in the target Hijri or Gregorian month, it is clamped to that month's last day.

The calendar identity, in full

The model is the tabular civil Islamic calendar with the Friday civil epoch, one of several identities distinguished by the same standard.

Odd numbered months run 30 days, even numbered months run 29, and the twelfth month runs 30 in years 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 and 29 of each thirty year cycle. The same standard separately distinguishes a Thursday epoch tabular calendar, an Umm al Qura calendar and sighting based calendars, and this page is none of those three.

This arithmetic anchors day 1 of Hijri month 1, المحرم, in year 1 to 19 July 622 in the proleptic Gregorian calendar.

A worked example

1. The start is 2026-01-31 and the deferral is 0 days, so the deferred start stays 2026-01-31.
2. The integer conversion gives tabular civil Hijri 1447-08-12.
3. Starting Hijri month index: $(1447-1)\times12+(8-1)=17{,}359$.
4. Target Hijri month index: $17{,}359+36=17{,}395$.
5. Target Hijri year: $\left\lfloor\frac{17{,}395}{12}\right\rfloor+1=1450$, and the target month is 8.
6. Day 12 exists in month 8, so no Hijri clamp is needed and the target is 1450-08-12.
7. Converting the target to Gregorian gives 2028-12-29.
8. Gregorian month index: $2026\times12+(1-1)=24{,}312$.
9. Adding 36 gives 24,348, which resolves to January 2029, where day 31 exists.
10. The Gregorian counted date is 2029-01-31.
11. From 2028-12-29 to 2029-01-31, two days of December and 31 days of January: $2 + 31 = 33$ whole days.
12. Hijri year 1450 is year 10 of its cycle, so its twelfth month has 30 days and its total is 355 days.

The example that reverses the title's order

At the same start with a term of one Hijri month, the Hijri count reaches 2026-03-01.

The Gregorian count reaches February 2026, where day 31 does not exist, so it clamps to 2026-02-28.

The difference is negative 1 day, so the Hijri ending is the later one.

What this does not model

It counts on one named arithmetic and compares it with a Gregorian count. It does not decide which calendar a document adopts, when a term legally begins or ends, whether the first or the last day is inside the term, or whether a renewal or a notice was in time. It carries no almanac, no month length envelope and no announcement.

A month that begins on a sighting cannot be tabulated in advance. This page tabulates, so it is not that calendar.

Check it yourself

Set the sweep to run from 0 to 12 in steps of 1. Thirteen values are checked. The month holds at December through two days of deferral and changes to January at three. The distance between the two endings is 33 days at every one of the thirteen. A deferral moves both endings together, and it moves neither the term nor the distance.

The calculation domain

The calculation accepts dates from 1600-01-01 to 2400-12-31, terms of 1 to 1200 whole Hijri months, and deferrals of 0 to 120 whole days. This page offers dates from 1900-01-01 to 2100-12-31 and terms to 120 so the date choice and chart stay readable.

Boundary

It describes what counting a term on one named arithmetic calendar reaches, with the Gregorian count of the same term beside it. It does not determine which calendar your document adopts, when a term begins or ends in law, whether the first or the last day is inside it, or whether a renewal or a notice was effective.

Source anchor

Unicode LDML calendar type identities, and Unicode CLDR Islamic calendar types. Those published pages identify the calendar this page computes on and distinguish it from the Thursday epoch tabular calendar, from Umm al Qura and from sighting based calendars. No month table, no almanac and no announcement from them or from anywhere else appears on this page.