In mails and documents I see the phrases「下記に表します」、「以下に表します」or
「下記の件。。。」、「以下の件。。。」.

I know they're both saying "the following (see below, etc)", but are there
cases when you should use one over the other or are they pretty much always
interchangeable?
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usage word-usage
「下記」vs 「以下」usage
Let me start by saying that 下記｛かき｝can only be used with the meaning of
"below", "hereafter", whereas 以下｛いか｝has many other meanings, most notably
"less than", "not more than", "not exceeding (some amount)".

When talking about text that will follow the current sentence, both can be
used. There is however a subtle difference, that shouldn't matter much outside
of formal contexts:

  * When using 以下, the following text should be on the same line / in the same paragraph, i.e. follow immediately without changes in appearance.
  * Using 下記 means that the follow-up text will occupy a whole text unit, i.e. a full paragraph, or maybe a bullet-point list. It can also refer to some bibliography item or attached document.
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In this context, 以下 just means "(something) below" whereas 下記 is "(something)
written below". You can say 以下に述べます, 以下に記します or 以下に記載, but 下記に述べます, 下記に記します or
下記に記載 would look like a weird
[重言](https://ja.wikipedia.org/wiki/%E9%87%8D%E8%A8%80) to me. In reality you
may occasionally see them, though.

以下 and 下記 are interchangeable in sentences such as 以下をご覧ください/下記をご覧ください,
以下の件/下記の件, 以下の通りです/下記の通りです and 以下参照/下記参照.

In vertical writings 下記 becomes 左記.
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answer