Below & under

1) 'lower than': below or under

The prepositions below and under can both mean 'lower than':

Look in the cupboard below/under the sink.

2) not directly under: below

We prefer below when one thing is not directly under another:

The climbers stopped 300m below the top of the mountain.

A moment later the sun had disappeared below the horizon.

3) covered: under

We prefer under when something is covered or hidden by what is over it, and when things are touching.

I think the cat's under the bed.

What are you wearing under your sweater?

The whole village is under water.

4) measurements: below

Below is used in measurements of temperature and height, and in other cases where we think of a vertical scale:

The temperature is three degrees below zero.

Parts of Holland are below sea level.

The plane came down below the clouds.

She's well below average in intelligence.

5) 'less than': under

We usually use under, not below, to mean 'less than' or 'younger than':

There were under twenty people at the lecture.

You can't see this film if you're under 18.

6) underneath

Underneath is sometimes used as a preposition instead of under, but only for physical position. Compare:

There's a mouse under(neath) the piano.

He's still under 18. (*not .. .underneath 18.)

7) adverbs

Below can be used as an adverb. Under can be used as an adverb particle with some verbs, but in other cases we prefer underneath for adverbial use:

We looked over the cliff at the waves crashing on the rocks below.

A lot of businesses are going under because of the economic crisis.

I can't take my sweater off-I don't have anything on underneath.

In a book or a paper, see below means 'look at something written later'.

The difference between above and over is similar to the difference between below and under.