Re: Why are there 365 days in a year?

Question received from a 14yr old pupil: If it takes 28 days for the moon 
to orbit the earth, why do the length of calender months vary from 28 to 
31? Also if there are 12 months (or 12 orbits of the earth by the moon)in 
a year why is not a year 336 days (i.e 12 x 28. The earth orbits the sun 
once in 365.25 days - so why are there inconsistencies in the length of 
months?

All of the answers to your question appear in different responses that have already been posted, so I'll run down the numbers with each reference:

"Full moons happen about every 29.53059 days."

Jim Moskowitz

"The length of the tropical year is 365.24219 days."

Tom Cull

"Originally, the Roman calendar had 12 months of 29 or 30 days"

Dan Berger

"The number of days in the months has originated through a long and tortuous history of the calendar."

John Link

In other words: if the period of rotation of the Earth about its axis is defined as a day; and if the period of revolution of the Moon around the Earth (from full moon to full moon) is 29.53059 days; and the period of revolution of Earth around the Sun is 365.24219 days; then there are 12.37 lunar months in a year. Lunar calendars correct for the third of a month by adding a leap month every few years, while solar calendars simply divide the year into 12 divisions ("calendar months") and ignore lunar months altogether. Essentially, there is no physical reason why the ratios of the rotation of the Earth and the revolutions of the Earth and Moon should be rational numbers (the rotation of the Moon is a different story), even though humans have tried for years to impose order on the system.