Measurement - 12-hour and 24-hour Clock

The 12-hour clock system divides the 24 hours of a day into two periods: AM (ante meridiem, meaning before noon) and PM (post meridiem, meaning after noon). Visually, imagine a circular clock face where the hour hand goes around twice to complete a full day.

The 24-hour clock system counts the hours from $00:00$ (midnight) to $23:59$. It does not use AM or PM. Visually, this is like a long continuous timeline starting from zero at the start of the day and ending at 24 at the very end.

Midnight in the 12-hour system is written as $12:00$ AM. In the 24-hour system, it is written as $00:00$. This represents the very beginning of a new day.

Noon in the 12-hour system is written as $12:00$ PM. In the 24-hour system, it remains $12:00$. This marks the halfway point of the day.

To convert PM times (from $1:00$ PM to $11:59$ PM) to 24-hour format, you add $12$ to the hour value. For example, $3:00$ PM becomes $15:00$. Visually, you are adding the first $12$ hours of the morning to the current afternoon hour.

To convert 24-hour times (from $13:00$ to $23:59$) back to 12-hour format, you subtract $12$ from the hour and add the label PM. For example, $20:30$ becomes $8:30$ PM.

For the first hour of the day ($12:01$ AM to $12:59$ AM), the 24-hour clock replaces the $12$ with $00$. For example, $12:15$ AM becomes $00:15$.

Time intervals or duration is the amount of time that passes between a start time and an end time. Visually, you can use a 'time line' or 'jump' method, jumping by hours first and then by minutes to find the total difference.