Prior to 963, Korean years were expressed as Korean era names. From 963 to 1895, Chinese era names were used.
Briefly, from 1894 to 1896, years were numbered using 1392 (the year of the founding of the Choson dynasty) as Year 1. To convert from Korean to Western years, add 1391. ('503' equates to '1894'.)
Between 1896 and 1910, Korean era names were used: Chonyang 1-2 (1896-1897), Kwangmu 1-11 (1897-1907), Unghui 1-4 (1907-1910).
During the period of the Japanese Occupation (1910-1945), Japanese era names were used in Korea itself. Korean nationalists outside of Korea, however, commonly numbered years using the Western year 2333 B.C. as year 1. This convention was maintained in South Korea until 1961. To convert from a 'Tangun' year, simply subtract 2333. ('4278' equates to '1945'.)
The Western calendar was adopted in 1961.
In North Korea, the Juche calendar dates years from 1912, the year of Kim Il-song's birth (Year 1). To convert from Juche to Western years, add 1911. ('89' equates to '2000'.)