Calendars and Durations

How many days until your birthday? Sounds like an easy question — until you actually try to count. You have to hop across the days one by one, jump from one month into the next, and remember that not every month is the same length. Miss one of those and your answer is wrong.

Try another: your family goes away on holiday from the 28th of one month to the 3rd of the next — how many nights is that? You can't just subtract, because you're stepping over the end of the month. Working out durations across days, weeks and months — and reading a calendar — is a genuinely fiddly everyday skill, precisely because months have different lengths. Let's make it easy.

The units of time

We measure time with a handful of fixed facts. Each bigger unit is just a bundle of smaller ones:

Swapping between them is just multiplying or dividing. To go from a bigger unit to a smaller one, multiply: 3 weeks = 3 \times 7 = 21 days. To go the other way, divide: 42 days = 42 \div 7 = 6 weeks.

Months are all different lengths

Here is the tricky part. The months are not all the same size. Most have 30 or 31 days, while February is the odd one out with just 28 days — or 29 in a leap year.

An old rhyme helps you remember which months are short:

Thirty days hath September,
April, June, and November.
All the rest have thirty-one,
Except February alone…

Make a fist and look at the knuckles and the dips between them. Starting at your first knuckle, name the months as you go: January (knuckle), February (dip), March (knuckle), April (dip)… When you reach the end of one hand, jump to the start of the other hand's knuckles (don't count the gap between your two fists) and carry on.

Every month that lands on a knuckle (a bump) has 31 days. Every month that lands in a dip (a low bit) has 30 — except February, the shortest. July and August both have 31 days, which is why they land on the two knuckles that meet when you put your fists together!

Worked example 1 — days within one month

How many days is it from the 6th of March to the 20th of March?

Both dates are in the same month, so this is just a subtraction. Count how far the second date is past the first:

20 - 6 = 14 \text{ days later.}

The 20th is 14 days after the 6th. Easy — because we never leave March.

Worked example 2 — crossing a month boundary

How many nights is a holiday from the 28th of April to the 3rd of May?

Now we step over the end of the month, so we count in two pieces. First, count to the end of April. April has 30 days, so from the 28th to the end is:

30 - 28 = 2 \text{ days (to reach the 30th).}

Then carry on into May, from the 30th of April to the 3rd of May, which is another 3 days. Add the pieces:

2 + 3 = 5 \text{ days later.}

The big trap here is April's length. If you'd assumed April had 31 days, you'd have got the wrong answer. Always check the month's real length.

Days and weeks — sharing into 7s

Because 7 days make a week, turning a pile of days into weeks is just dividing by 7 — and the leftover is the extra days. For example, 23 days:

23 \div 7 = 3 \text{ remainder } 2,

so 23 days is 3 weeks and 2 days. This is handy for working out what day of the week something lands on: every jump of 7 days lands on the same weekday, so only the remainder matters. If today is a Monday, then 23 days from now is 2 days past a Monday — a Wednesday.

Worked example 3 — a date a number of weeks later

A club meets every 3 weeks. If it met on the 4th, what date is the next meeting?

Turn the weeks into days, then add: 3 weeks = 3 \times 7 = 21 days. So the next meeting is 21 days later:

4 + 21 = 25.

The next meeting is on the 25th of the same month. (If the total had gone past the end of the month, we'd have spilled into the next one, just like Example 2.)

Worked example 4 — how old, or how long until?

Someone was born in 2014. How old do they turn during 2026? Subtract the years:

2026 - 2014 = 12 \text{ years old.}

Counting days until an event works the same way — but here's a subtle point that trips almost everyone up. Watch the strip below: going "from the 3rd to the 10th" is 7 days later, yet it touches 8 different dates if you count both ends. That gap between "days later" and "dates touched" is the classic date-arithmetic mistake.

When you count the number of days between two dates, stop and ask: do I want the days that pass, or the dates I touch? They are different by one!

This is the fencepost problem: a fence 7 metres long with a post every metre needs 8 posts, not 7, because there's a post at both ends. Decide which one the question wants before you count. And don't forget the other trap: months have different lengths — never just assume 30.

Unlike days, months and years, the week isn't tied to the sky at all — there's nothing in space that takes exactly 7 days. The ancient Babylonians chose 7 thousands of years ago, probably because they could see seven moving lights in the sky (the Sun, the Moon and five planets), and because 7 is roughly a quarter of the Moon's month. It stuck so well that almost the whole world still runs on a 7-day week today — a very old habit that nobody has ever managed to change.

Leap years — the extra day

Roughly every 4 years, February gets a 29th day and the whole year has 366 days instead of 365. That year is called a leap year. 2024 was one; 2028 will be the next.

But "every 4 years" isn't quite exact. The real rule has a clever twist for century years (years ending in 00):

So 1900 was not a leap year (divisible by 100 but not 400), but the year 2000 was (divisible by 400). Neat, isn't it?

Because the Earth is uncooperative. One trip around the Sun doesn't take a whole number of days — it takes about 365.24 days. That leftover quarter-day is the source of all the fuss.

Our calendar is a 2000-year-old patch-up job. Julius Caesar added leap years to soak up the quarter-days. But 0.24 isn't quite 0.25, so over centuries the calendar still drifted, until Pope Gregory tidied it up in 1582 with the century rule (skip most leap years on 00 years, but keep the ones divisible by 400). We still occasionally add a "leap second" to the clocks to stay perfectly in step! Without any of this, the calendar would slowly slide out of line with the seasons, and in a few hundred years Christmas would drift into summer. Those fiddly rules are what keep the calendar marching along with the seasons.