During the reign of King Sejong (1418 – 1450) of the Joseon dynasty, several compact astronomical instruments such as So-ganui (小簡儀, small simplified armillary sphere), Ilseongjeongsiui (日星定時儀, sun-and-stars time-determining instrument), Hyeonju-Ilgu (懸珠日晷, plummet equatorial sundial), Jeongnam-ilgu(정남일구, south-fixing armillary sundial) and so forth were invented. It is considered that those instruments were made on the basis of the know-how to manufacture Honcheonui (渾天儀, armillary sphere), Honsang (渾象, celestial globe), Ganui (簡儀, Simplified armillary sphere), and Gyupyo (圭表, Gnomon) which were originated from the Song or Yuan dynasty of China. Meanwhile, astronomers of the latter and the Joseon dynasty divided the celestial equator (a celestial-circumference) and a day into 365.25 degrees and 100 intervals, respectively. The rings engraved the graduations for the celestial equator and the day were called Jucheodobun-hwan (周天度分還, celestial-circumference degrees ring) and Baekgak-hwan (百刻還, hundred-interval ring), respectively. In this paper, we investigate of ring graduations of compact astronomical instruments produced in the King Sejong’s era. As a result, we found that ring graduations were marked as the integer times of Bun (分, fraction), a length unit. For example, 1 degree corresponds to 1 fraction in the graduations of the celestial-circumference and hundred-interval rings with the diameters of 1.16 and 0.32 Cheok (尺, foot), respectively. We think that the same manner was applied to other compact astronomical instruments such as Jeongnam-ilgu, etc. In conclusion, we think that this study will be useful for reconstructing those sundials.