12-hour clock

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clock system
12-hour 24-hour
midnight
12:00 a.m.*		 00:00
  1:00 a.m. 01:00
  2:00 a.m. 02:00
  3:00 a.m. 03:00
  4:00 a.m. 04:00
  5:00 a.m. 05:00
  6:00 a.m. 06:00
  7:00 a.m. 07:00
  8:00 a.m. 08:00
  9:00 a.m. 09:00
10:00 a.m. 10:00
11:00 a.m. 11:00
noon
12:00 p.m.*		 12:00
  1:00 p.m. 13:00
  2:00 p.m. 14:00
  3:00 p.m. 15:00
  4:00 p.m. 16:00
  5:00 p.m. 17:00
  6:00 p.m. 18:00
  7:00 p.m. 19:00
  8:00 p.m. 20:00
  9:00 p.m. 21:00
10:00 p.m. 22:00
11:00 p.m. 23:00
undefined
(midnight)*		 24:00
* See section "Confusion
at noon and midnight"

The 12-hour clock is a timekeeping convention in which the 24 hours of the day are divided into two periods[1] called ante meridiem (a.m., Latin "before noon") and post meridiem (p.m., "after noon").[2] Each period consists of 12 hours numbered 12 (acting as zero), 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, and 11. The indication of noon and midnight in the 12-hour system is disputed.

The 12-hour clock was developed over time from the mid-second millennium BC, to the 16th century A.D. and was once popular throughout Northern Europe, but is now used as the dominant system in only a few former British and American Colonies. It is also used informally in most of the world. The notion has received much criticism, yet survives out of tradition.

Contents

[edit] History and use

Exeter Cathedral clock, showing the Double-XII numbering scheme.
Exeter Cathedral clock, showing the Double-XII numbering scheme.

The 12-hour clock can be traced back as far as Mesopotamia and Ancient Egypt,[3] but may also have roots in Ancient India.[citation needed] The lengths of the ancient hours varied seasonally, always with 12 hours from sunrise to sunset and 12 hours from sunset to sunrise.[citation needed] In Egypt the hour beginning and ending each half-day (four hours each day) were considered twilight hours.[citation needed] An Egyptian sundial for daylight use[4] and an Egyptian water clock for nighttime use found in the tomb of Pharaoh Amenhotep I,[5] both dating to c. 1500 BC, divided these periods into 12 hours each.

The Romans also used a 12-hour clock: the day was divided into 12 equal hours (of, thus, varying length throughout the year) and the night was divided into three watches. The Romans numbered the morning hours originally in reverse. For example, "3 a.m." or "3 hours ante meridiem" meant "three hours before noon", compared to the modern meaning of "three hours after midnight".[citation needed]

The first mechanical clocks in the 14th century, if they had dials at all, showed all 24 hours, using the 24 hour analog dial, influenced by astronomers' familiarity with the astrolabe and sundial, and their desire to model the apparent motion of the sun. In Northern Europe these dials generally used the 12 hour numbering scheme in Roman numerals, but showed both a.m. and p.m. periods in sequence. This is known as the Double-XII system, and can be seen on many surviving clock faces, such as those at Wells and Exeter. Elsewhere in Europe, particularly in Italy, numbering was more likely to be based on the 24 hour system (I to XXIV), reflecting the Italian style of counting the hours.

During the 15th and 16th centuries the 12 hour analog dial and time system, with its simpler and more economical construction, gradually became established as standard throughout Northern Europe for general public use. The 24 hour analog dial was reserved for the more specialist applications, such as for astronomical clocks and chronometers.

Most analog clocks and watches today use the 12-hour dial, on which the hour hand (shorter and sometimes thicker) rotates once every 12 hours and twice in a day. They are used even in cultures where the 24-hour notation is otherwise preferred. Some 12-hour dials show the numbers 13 to 23 written inside the primary 1 to 12 ring.

[edit] Use by country

Main article: Date and time notation by country

Although it has largely been replaced today by the 24-hour notation around the world, especially in written communication, the 12-hour notation with a.m. and p.m. suffixes is common in some parts of the world.

A typical analog 12-hour clock
A typical analog 12-hour clock
  • The 12-hour clock is the dominant system of time written and spoken in:

In many European countries, a 12-hour clock is commonly used in informal speech, but a.m. and p.m. are little known. If one wants to unambiguously refer to time in the 12-hour system, one uses descriptive phrases instead, such as in the morning, in the afternoon, in the evening, at night.

A typical digital 12-hour showing the p.m. as a dot on the left
A typical digital 12-hour showing the p.m. as a dot on the left

[edit] Abbreviations

The Latin abbreviations "a.m." and "p.m." (often written "am" and "pm"; "AM" and "PM"; and "A.M." and "P.M.") are used in English and Spanish.[citation needed] The equivalents in Greek are "πµ" and "µµ"[citation needed].

Most other languages lack formal abbreviations for "before noon" and "after noon" and their users use the 12-hour clock only orally and informally.[citation needed]

[edit] Criticism and practical problems

For more details on this topic, see Comparison of the 12-hour and 24-hour clocks.
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People who grew up with the 24-hour clock may see the 12-hour notation as a less practical and outdated convention, especially in the context of written communication, computers and digital clocks. The arguments for or against a change may be compared to the discussion on metrication. Even people who grew up with the 12-hour clock, however, often have problems indicating midnight and noon. Those who grew up with the 24-hour clock are also confused when they come across situations very common in, for example, Internet forums and email in which a message indicated as posted at "12:46 am" appears unintuitively and seemingly illogically before a message marked "11:05 am" for example.

The disadvantages most commonly voiced by critics in comparing the 12-hour notation to the 24-hour clock are:

  • confusion about the correct notation for noon and midnight
  • confusion about the difference between midnight at the start and end of a given date
  • The rollover from 12 to 1 happens an hour later than the change between a.m. and p.m.
  • The lexicographical order does not match the chronological order.
  • It's generally more complicated to understand and to implement in software and digital electronics.
  • Typographically, the a.m. and p.m. terms require more space.

[edit] Confusion at noon and midnight

Style Midnight
(start of day)		 Noon Midnight
(end of day)
24-hour clock, ISO 8601 00:00 12:00 24:00
Most digital 24-hour clocks 00:00 12:00 —
12-hour digital clocks with a.m. and p.m. * 12:00 a.m. 12:00 p.m. —
American Heritage Dictionary 12 a.m. 12 p.m. —
U.S. Government Printing Office — 12 a.m. 12 p.m.
Antiquated † 12:00 m.n. 12:00 m. 12:00 m.n.
Canadian Press
UK standard
NIST1 †		 midnight noon midnight
NIST2 † 12:00 Midnight 12:00 Noon 12:00 Midnight
Associated Press Style[6] midnight noon does not exist
U.S. de facto legal 12:01 a.m. — 11:59 p.m.
Britannica[1] Midnight
May 15-16		 12m Midnight
May 16-17
* Digital clocks and computers appear to show the times 12 a.m. and 12 p.m., as in this chart. While those phrases may be used practically, the "a.m." and "p.m." refer to the 12-hour periods following the instants of midnight and noon, respectively, not to the instants of midnight and noon themselves, strictly speaking.
† These standards are ambiguous with respect to the whether midnight is at the start and or end of each day. The style guide writers did not state their intention for the two midnights or for endpoint convention.

Since the word meridies means noon or midday, it is, strictly speaking, illogical to refer to noon as either "12 a.m." (12 ante meridiem, 12 hours before noon) or as "12 p.m." (12 post meridiem, 12 hours after noon). On the other hand, midnight could logically be called either "12 p.m." (12 post meridiem, 12 hours after the previous noon) or "12 a.m." (12 ante meridiem, 12 hours before the following noon); "x a.m." no longer literally means "x hours before noon", but "x hours into the day but before noon." or "x th hour before noon"

The National Maritime Museum, Greenwich, states:

To avoid confusion, the correct designation for twelve o'clock is 12 noon or 12 midnight. Alternatively, the twenty-four-hour-clock system may be used. The abbreviation a.m. stands for ante-meridiem (before the Sun has crossed the line) and p.m. for post-meridiem (after the Sun has crossed the line). At 12 noon the Sun is at its highest point in the sky and directly over the meridian. It is therefore neither "ante-" nor "post-".[7]

The Sun is only highest at noon measured in local Solar time, which is practically never equal to the civil time shown on clocks. [8].

In the United States, noon is often called "12:00 p.m." and midnight "12:00 a.m."

The American Heritage Dictionary of the English Language (Fourth Edition, 2000) has a similar usage note on this topic: "Strictly speaking, 12 a.m. denotes midnight, and 12 p.m. denotes noon, but there is sufficient confusion over these uses to make it advisable to use 12 noon and 12 midnight where clarity is required."[9]

The use of "12:00 a.m." for midnight and "12:00 p.m." for noon, however, is contrary to the U.S. Government Printing Office Style Manual[10] which recommends the opposite: "12 p.m." for midnight and "12 a.m." (formerly "12 m.") for noon.

Many U.S. style guides (including the NIST website) recommend that it is clearest if one refers to "noon" or "12:00 noon" and "midnight" or "12:00 midnight" (rather than to "12:00 p.m." and "12:00 a.m.", respectively). Some other style guides suggest "12:00 n" for noon and "12:00 m" for midnight,[11] but that conflicts with the older tradition of using "12:00 m" for noon[1](Latin meridies), and "12:00 mn" for midnight (Latin media nox).

The Canadian Press Stylebook (11th Edition, 1999, page 288) says, "write noon or midnight, not 12 noon or 12 midnight." Phrases such as "12 a.m." and "12 p.m." are not mentioned at all.

The use of "12:00 midnight" or "midnight" is still problematic because it does not distinguish between the midnight at the start of a particular day and the midnight at its end. To avoid confusion and error, some U.S. style guides recommend either clarifying "midnight" with other context clues, or not referring to midnight at all. For an example of the latter method, "midnight" is replaced with "11:59 p.m." for the end of a day or "12:01 a.m." for the start of the next day. That has become common in the United States in legal contracts and for airplane, bus, or train schedules, though some schedules use other conventions.

The 24-hour clock notation avoids all of those ambiguities by using 00:00 for midnight at the start of the day and 12:00 for noon. From 23:59:59 the time shifts (one second later) to 00:00:00, the beginning of the next day. Some variants of 24-hour notation (including the world standard ISO 8601) use 24:00 when referring to a midnight at the end of a day.

[edit] Endpoint convention

Endpoint is a term for the ends of an interval. Endpoint convention is whether the left endpoint (beginning), the right endpoint (end), both, or neither is included in the intervals; [12][13] In the case of the 12-hour clock endpoint convention refers to where midnight or noon are placed in the intervals a.m. and p.m. For example, if a.m. were to include midnight but not noon (left endpoint convention) then its interval in interval notation would be [midnight,noon). For most time intervals in everyday use the left endpoint convention is used; for example, something is considered to be "49 years old" up until the instant it becomes 50 years old, at which point it is considered "50 years old" for a year. The international standard of time notation ISO 8601:2004 besides using the 24-hour clock also states that unless otherwise stated time intervals include the start and end points.

Which endpoint convention to use depend on how one regards time. If time is regarded as discrete then a right or left end point convention should be used; left is preferable when the value has to be non-negative as it places zero with the positive numbers. If time is regarded as continuous and calculus is to be performed on functions of time then a closed interval should be used.[14]

[edit] Advantages of the 12-hour clock

Main article: Comparison of the 12-hour and 24-hour clocks

Some notable advantages to the 12-hour clock:

  • It corresponds to analog clocks, which almost all have just 12 hours. (However, that is caused by the existence of 12-hour notation.)
  • It makes distinct a.m. and p.m., while "11:00" with no suffix, as with the 24-hour clock, might be in the morning or evening if the clock being used is unknown. (However, that is caused ironically by the existence of 12-hour notation.)
  • The use of a leading zero, as is often used for 00:00 to 09:59, is awkward to pronounce out loud. That pronunciation is common mostly in the US military, not in countries primarily using the 24-hour clock. Sweden, however, is an exception from this rule - in Swedish, the leading zero is usually spoken out loud. Some other countries such as France usually pronounce time in 12-hour notation, even when reading a 24-hour display.
  • The presence of fewer numbers on a clock face makes it simpler, particularly on a watch.
  • The 1 to 12 chimes in a 12-hour clock tower are more practical than the 0 to 23 chimes or 1 to 24 chimes in a 24-hour clock tower.

[edit] Related conventions

[edit] Typography

The abbreviations "AM" and "PM" are variously written in small capitals ("am" and "pm"), uppercase letters ("AM" and "PM"), or lowercase letters ("am" and "pm"). Additionally, some styles use periods (full stops), especially in combination with lowercase letters (thus "a.m." and "p.m.").

The use of a.m. as written in the form of am, AM, or A.M. can be confusing because am is an English word, AM is an abbreviation for amplitude modulation and A.M. is an abbreviation for anno mundi, in the year of the world, and for Master of Arts.

There are symbols for "a.m." (U+33C2 = "㏂") and "p.m." (U+33D8 = "㏘") in Unicode. They are meant to be used only with CJK fonts, however, as they take up exactly the same space as one Chinese character.

Stylebooks use a space between the number and the abbreviation a.m. or p.m., although that convention is widely violated.

Style guides recommend not using a.m. and p.m. without a time preceding it,[15], although doing so can be advantageous when describing an event that always happens before or after noon. Generic words like "evening", however, do not apply for the whole year.

[edit] Informal speech and rounding off

It is common to round a time to the nearest five minutes and express the time as so many minutes past an hour (e.g., 5:05 is "five past five" or "five oh five") or minutes to an hour (e.g., 5:55 is "five to six"). The period 15 minutes is often expressed as "a quarter" (hence 5:15 is "a quarter past five") and 30 minutes is expressed as "half" (hence 5:30 is "half past five" or merely "half five", the latter expression not being common in the USA). The time 5:45 is spoken as "a quarter to six" in UK, Australia and other British-English countries, and "a quarter of six" in USA and other US-speaking locations.

Instead of meaning 5:30, the "half five" convention is sometimes used to mean 4:30, i.e., "half-way to five", especially in the more German-influenced parts of the U.S.A (the Midwest, essentially). "Half-way to five" follows the usage in German speaking countries. It is also found in Danish and Dutch.

[edit] Formal speech and times to the minute

Minutes may be expressed as an exact number of minutes past the hour specifying the time of day (e.g., 6:32 p.m. is "thirty-two minutes past six in the evening").

Times of day ending in ":00" minutes (full hours) are often said in English as the numbered hour followed by o'clock (10:00 as ten o'clock, 2:00 as two o'clock). This may be followed by the "a.m." or "p.m." designator, though phrases such as in the morning, in the afternoon, in the evening, or at night more commonly follow analog-style terms such as o'clock, half past three, and quarter to four. O'clock itself may be omitted, telling a time as four a.m. or four p.m. Minutes ":01" to ":09" are usually pronounced as oh one to oh nine (aught one to aught nine may still be in use in some Commonwealth countries). Minutes ":10" to ":59" are pronounced as their usual number-words. For instance, 6:02 a.m. can be pronounced six oh two a m; 6:32 a.m. could be told as six thirty-two a m.

When the speaker has recently mentioned the hour of the day or for some other reason believes it to be known to his or her hearers, he or she may omit all reference to it and simply declare the minutes, using expressions such as seventeen minutes past the (top of the) hour (to refer to 4:17 am, or 11:17 pm, etc.) or three minutes till the bottom of the hour (which similarly signals the bottom half of the clock, such as 7:27 pm, or 9:27 am, etc.). This is also true of television broadcasts whose signals are picked up in more than one time zone, since the hour varies with those zones.

[edit] U.S. military speech

Military circles use the 24-hour clock almost exclusively and typically pronounce times ending in :00 minutes as the hour followed by "hundred" with an optional "hours". For instance, 16:00 is "sixteen hundred" or "sixteen hundred hours". Leading zeros are voiced. For instance, 08:00 is "Oh eight hundred (hours)", or simply "zero eight".

[edit] See also

[edit] References

  1. ^ a b c "Time". The New Encyclopædia Britannica 28. (2005). 670 2a. 
  2. ^ National Institute of Standards and Technology's Physics Laboratory, Time and Frequency Division
  3. ^ The History of Clocks
  4. ^ Berlin instruments of the old Egyptian time of day destination
  5. ^ A Walk through Time - Water Clocks
  6. ^ Ed. Norm Goldstein, The Associated Press Stylebook and Briefing on Media Law: with Internet Guide and Glossary, P.161, 177, Perseus Publishing, 2002, Cambridge, Massachusetts, United States, LCCN 2002105974, ISBN, 0-7382-0740-3
  7. ^ National Maritime Museum: sea, ships, time and the stars : NMM
  8. ^ The equation of time : Time & timekeeping : Fact files & in-depth : Learning : NMM
  9. ^ A.M.
  10. ^ United States Government Printing Office Style Manual 2000, Section 9.54: References to Meridian in Statements of Time
  11. ^ Wisconsin Occupational Operator License Application
  12. ^ Endpoint conventions accessed 24 October 2007
  13. ^ Lecture notes accessed 24 October 2007
  14. ^ Most Calculus theorems require a continuous function on a closed interval. These theorems include: the intermediate value theorem, the mean value theorem, the extreme value theorem, the first and second fundamental theorems of calculus, and the mean value for intervals theorem.
  15. ^ Hacker, Diana, A Writer's Reference, six edition, Bedford, St Martin's, Boston, 2007, section M4-c, p.308.

[edit] External links