Paragraph length is an area where copywriting for the web is very different from other forms of writing. If you are proficient at other types of writing this can be a difficult adjustment. 

The concept of one idea per paragraph is especially important on the web. You should break more complex ideas into smaller chunks that stand alone as a paragraph. Always ask yourself what your user really needs to know and cut the rest. A good rule of thumb is that a paragraph should have between 1 and 3 sentences. 

This guidance applies to informational content but also to journalistic or persuasive content. This article from the Red Cross is a good example of a consistent use of short paragraphs in the context of a charity website.