I am trying to construct a timeline of Prophet Muhammad (peace be upon him). Specifically, the last time he was in itikaf. I am sure there are English sources out there, but my (very) quick search, I did not come across one. I used an online calculator and I found that it should be between December 20 631, and December 30. Can somebody confirm that?
Your calculation would be closer to truth if you checked and considered 20 days i'tikaf in the prophet's () last Ramadan as the sahih hadith confirms that he usually used to do i'tikaf for ten days, but in the last Ramadan he doubled this duration:
The Prophet (ﷺ) used to perform I'tikaf every year in the month of Ramadan for ten days, and when it was the year of his death, he stayed in I'tikaf for twenty days.
Note that ibn Hajjar also pointed at ahadith saying that the prophet () used to do 'Itikaf 20 days if he intended to travel (see here in Sunan ibn Majah), or that he was not able to do or complete his 'Itikaf a year earlier as ibn al-'Araby said -in his commentary on Sunan abi Dawood- which is a reference to this hadith.
Further there's consensus among scholars that the prophet () fasted 9 Ramadan's as the fast of Ramadan was ordered in Sha'aban of the 2nd year after Hijrah and the prophet's () terminal illness started in the last days of Safar in the year 11 after Hijrah.
It says in al-Insaaf:
Fasting Ramadaan was enjoined in 2 AH according to scholarly consensus. The Messenger of Allaah (peace and blessings of Allaah be upon him) fasted nine Ramadaans according to scholarly consensus.
Al-Nawawi said in al-Majmoo’:
The Messenger of Allaah (peace and blessings of Allaah be upon him) fasted Ramadaan for nine years, because it was enjoined in Sha’baan 2 AH, and the Prophet (peace and blessings of Allaah be upon him) died in Rabee’ al-Awwal 11 AH.
See also Majmoo’ Fataawa by Shaykh al-Islam Ibn Taymiyah, 2/20.
(Source: Fatwa Islamqa #49679)
You should also be aware that the statement 20 days might be closer to an estimation than a fixed value.
And last but not least you should have in mind that the Julian calendar which was in use at that time has been revised by the gregorian calendar ten centuries later. I don't know which calculation is used and what is considered in the online calculator you've used. So the calculated approximate date might not match the at the time existing calendar at all.
If you are looking for corroboration then others have calculated that the prophet ﷺ died on 8 June 632 CE - That corresponds to 12 Rabiʽ al-Awwal 11 AH, so the last Ramadan before that should fall around December 631.
al-Mubarakpuri in Raheeq al-Makhtum states that the 28th or 29th of Shawwal in the year 10 A.H corresponded to 27th January 632 CE. This also puts the last Ramadan in December.
I would reemphasize what @Medi1Saif has said because of the nature of calendars there is a chance of some oversight in the calculation which could make it entirely wrong.