He was born at Cyzicus, and studied under Eudoxus of Cnidus at the Academy of Plato. He also worked with Aristotle at the Lyceum, which means that he was active in Athens prior to Aristotle's death in 322. He observed the movements of the planets and attempted to use Eudoxus' scheme of connected spheres to account for their movements. However he found that 27 spheres was insufficient to account for the planetary movements, and so he added seven more for a total of 34. According to the description in Aristotle's Metaphysics (XII.8), he added two spheres for the Sun, two for the Moon, and one each for Mercury, Venus, and Mars.
He made careful measurements of the lengths of the seasons, finding them (starting with the spring equinox) to be 94 days, 92 days, 89 days, and 90 days. This variation in the seasons implies a variation in the speed of the Sun, called the solar anomaly. He also followed up on the work done by Meton of Athens to measure the length of the year and construct an accurate lunisolar calendar. The Metonic cycle has 19 tropical years and 235 synodic months in 6940 days. The Callippic cycle synchronized the lunar and solar years better than the Metonic cycle, by dropping 1 day after 4 Metonic cycles, a duration of 76 years, making the Callippic 19 year cycle equal to 6439 3/4 days, or exactly 365 1/4 days per year, nearly 3 centuries before Julius Caesar.
Dividing Meton's and Callippus's periods by 235 produces their calendars' lengths of the month, in error by 1.9 minutes and 22 seconds, respectively. There is no evidence for anyone's knowledge of the later-canonical Babylonian month of length 29 days 12 hours and 44+1/18 minutes, until well after 300 BC, by which time both Meton and Callippus were deceased. Calippus had his first cycle start at the summer solstice of 330 BC (28 June in the proleptic Julian calendar). These cycles were used by later astronomers for dating observations. Calippus crater on the Moon is named for him.