Let's start with the most popular calendar in the English speaking world, which has 12 months broken into days; the number of which range from 28 through 31. Those days are then organized into periods of 7 day weeks.
One would conclude that by dividing seven into the largest number of days in a month one would determine that the maximum number of horizontal lines of weeks would be four and a bit, or five weeks (rounding up).
31 / 7 = 4.43, rounded up to 5
The truth is that since the calendar makeup is comprised of some prime numbers, the months will often start on different days of the weeks and end on them on different days of the week most often too. Therefore, six lines of dates are needed to lay out a month without resorting to squishing more then one day in a single square.
Now, we live in a simple solar system and have a single moon revolving around a single planet with a single star at the center. Imagine how different a calendar might be if it took in the influence of a double moon (such as Mars has). Or if our Earth and some other planet revolved around each other on our annual orbit... or if we had a binary star at the center of our solar system. 921
One other thing that may affect a calendar's layout would be if our planet revolved around the sun with its axis at 90° to the its travel direction around the sun.
Our calendar is affected by our culture as well and needs to address the strict observance of religious holy days, and political observances. It's interesting to notice that in spite of the majority of this planet is covered in water, it is left to imposing a tide chart onto the calendar rather then allowing the time chart to drive the organization of the calendar. Additionally, any agricultural influence is made to superimpose itself on top of the religious/politico calendar too.
Many of Earth's cultures did fine and existed for centuries without a calendar at all; the American Indians for example. It bears reminding ourselves that some cultures in South America exist today with only a very vague sense of time and no counting system beyond the numbers two or three. So if I said to you, "I will be gone a long time." It is up to you to decide when the "long time" has passed; be it days, weeks of days, or even months or years. A very tricky thing when one barely imagine past tomorrow or the next day at best. 723