noun, used as a prefix, noun
Used as a prefix or noun to indicate half of something, or something incomplete/partial. Very common in compounds.
このケーキの半分を食べてもいい？
Can I eat half of this cake?
半年前に日本へ引っ越しました。
I moved to Japan half a year ago.
noun, used as a suffix
half-past
Used as a suffix after an hour number to indicate half-past that hour.
会議は三時半に始まります。
The meeting starts at half past three.
noun
Refers to an odd number, often used in contrast to 丁 (even number).
See also: 丁
サイコロで半が出たら勝ちです。
If an odd number comes up on the dice, you win.
noun
Archaic unit of land area, approximately 595.8 square meters. Not used in modern contexts.
江戸時代、この村の田んぼは五半あったと記録されている。
It is recorded that this village had five han of rice paddies in the Edo period.
半分 is the more common standalone noun for 'half' of a concrete amount, while 半 is often used as a prefix or in compounds.
丁 means 'even number', the opposite of 半 in the odd-number sense.
The kanji 半 depicts a cow being split in half, representing the concept of 'half'. The reading はん is the Sino-Japanese on'yomi.