How to Calculate Years in the Metonic Cycle

The Metonic cycle, developed by the Greek astronomer Meton in the fifth century B.C., is the least common multiple between lunar months and tropical years. A tropical year is the time it takes for the sun to return to the same position in the cycle of earthly seasons, to pass from one vernal equinox to the next. In a full Metonic cycle, 235 lunar months and approximately 19 tropical years transpire. To calculate the exact amount of time in a Metonic cycle, though, you may want to use the number of hours in a year and the number of days in a Metonic cycle to lend your calculation extra precision.

Instructions

1. • 1

     Multiply the number of Metonic cycles by 6,939.6. This is the number of days in one Metonic cycle. Four Metonic cycles, for example, yield 27,758.41 days.

   • 2

     Divide the number of days by 365.24. This will give you the number of years in your cycle. The number of days from Step 1 divided by 365.24 gives 76 years, with a remainder of 0.00046.

   • 3

     Find the number of hours left over. Multiply the remainder by 8,765.76, the number of hours in a Gregorian-calendar year. In the given example, approximately four hours remain. The amount of time in four Metonic cycles is, thus, 76 years and four hours.