Hijrah

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HIJRAH هجرة
Lit. "migration." (1) The departure of Muhammad from Makkah. (2) The Muslim era. (3) The act of a Muslim leaving a country under infidel rule. (4) Fleeing from sin. 
The date of Muhammad's flight from Makkah was the fourth day of the first month of Rabi', which by the calculation of M. Caussin de Perceval was June 20th, A.D. 622. The Hijrah, or the era of the "Hegira", was instituted seventeen years later by the Khalifah 'Umar, which dates from the first day of the first lunar month of the year when the era was established fell of Thursday the 15th of July A.D.622. But although 'Umar instituted the official era, according to at-Tabari, the custom of referring to events as happening before or after the Hijrah originated with Muhammad himself. 
Professor H.H. Wilson in his Glossary of Terms gives the following method of ascertaining the Muslim and Christian years:- 
Multiply the Hijrah year by 2,977, the difference between 100 solar and as many lunar Muslim years; divide the product by 100, and deduct the quotient from the Hijrah year; add to the result 621,569 (the decimal being the equivalent of the 15th July, plus 12 days for the change of the Kalendar); and the quotient will be the Christian year from the date at which the Muslim year begins; thus Hij. 1269 * 2.977 = 3777.8, which divided by 100 = 37.778 and 1269 - 37.778 = 1231.222; this + 621.569 = 1852.791, the decimals corresponding to 9 months, and 15 days, i.e. the 15th of October, which is the commencement of the Hij. Year 1269. The reverse formula for finding the corresponding Hijrah year to a given Christian year, is thus laid down: Subtract 622 from the current year; multiply the result by 1.0307; cut off two decimals and add .46; the sum will be the year, which, when it has a surplus decimal, requires the addition of 1; thus 1852-622=1230; 1260 * 1.0307=1267.761; 1267.76+.46=1268.22; add therefore 1, and we have the equivalent Hijrah year 1269. 
The Persian era of Yezdegird commenced on June 16, A.D. 632, or ten years later than the Hijrah.

Based on <a href="https://www.juancole.com/library/dictionary-of-islam-hughes">Hughes, Dictionary of Islam</a>

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