You could say "a half hour" or "half an hour".
The article choice depends on where in a phrase you place it.
Would you ever say "I'll be back in hour"?
No, because while possibly legal, the use of the article "an" would be needed to make it sound like a native English speaker.
english.stackexchange.com/users/366/warren
"half-hour" is commonly written with a dash (hyphen) and is a distinct word in the dictionary.
So, "a half-hour" = 30 minutes = "half an hour".
english.stackexchange.com/users/373/alexsome
In Australia we say 'half an hour'.
You might hear 'a half hour', but it would sound stilted.
This is probably changing with the influence of American television.
english.stackexchange.com/users/610/Richard A
The top one is correct.
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I'll be back in half hour would be OK if it said I'll be back in a half hour
Note that "a half hour" is an American usage, British people only use "half an hour".
english.stackexchange.com/users/None/
The very same question puzzles me these days.
The title should be "half an hour" versus "a half hour"
I used to apply the former.
I notice it is an issue when I read the entry in electronic dictionary of Longman contemporary English version 5.
It offers examples like, 1.
half a mile/pound/hour etc
half a pound of butter; It’s about half a mile down the road.
She drank half a bottle of wine.
half a million dollars; 2. a half hour/mile etc You can’t just waltz in a half hour late.
It’s about a half mile down the road.
a half day excursion to the island; He demanded a half share of the money.
Both items belong to entry of half with the meaning of "exactly or about 50% (½) of an amount, time, distance, number etc"
The dictionary does not explain the difference.
I infer it is the same and both are correct.
Maybe the only difference lies in habit or region.
For instance, many mention on this page, British people and Americans apply this in different ways.
english.stackexchange.com/users/36103/Jiancheng Zou
I'll be back in half an hour.  I'll be back in half hour.   Which is the correct sentence? Are there any differences between British English and American English?
"Half an hour" versus "half hour"
english.stackexchange.com
<word-choice><numbers><indefinite-articles>
english.stackexchange.com/questions/1174
english.stackexchange.com/users/252/kiamlaluno
You could potentially use either, however, in Britain and Australia, it is more common to hear "half an hour". However, in America, it is possible that you will hear "a half hour". In US English it is acceptable to say "a half hour" or "half an hour" but in British you should use only "half an hour".
You could potentially use either, however, in Britain and Australia, it is more common to hear "half an hour". However, in America, it is possible that you will hear "a half hour". You can say "a half hour" or "half an hour". "Half-hour" is commonly written with a dash (hyphen) and is a distinct word in the dictionary. Note that "a half hour" is an American usage, British people only use "half an hour".
"A half hour" is an American usage. British people only use "half an hour". The exact answer will depend on the region, but both are generally considered to be correct. For instance, Americans will say "a half hour" and British or Australian speakers will say "half an hour".
The article choice depends on where in a phrase you place it - for example you would not say "I'll be back in hour" because you need the article. In Australia we say 'half an hour'. Note that "a half hour" is an American usage, British people only use "half an hour".
You can say "a half hour" or "half an hour". "Half-hour" is commonly written with a dash (hyphen) and is a distinct word in the dictionary. Note that "a half hour" is an American usage, British people only use "half an hour".
Provided there is an article before "half hour", both are considered correct. Some people would accept "a half hour" as correct. Some people are comfortable using "half an hour". The exact answer may well depend on the region, with Americans preferring "a half hour" and British speakers preferring "half an hour".