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Our general rule is to avoid brackets as much as you can, but here's some advice when they have forced you into a corner.

Round brackets ( )

Use these when you need to expand on or clarify something:

It reached a length of 2.3m (7.5ft).

Or when you're using an acronym or an initialism for the first time:

The decision was made by the University Executive Board (UEB).

Otherwise, look for alternatives. For example, in sentences with parenthetical statements – like this one – dashes look much better:

The Hypsilophodon – a small dinosaur from the Early Cretaceous – was omnivorous.

When it comes to using punctuation in brackets, include it before the closing bracket if the complete sentence is in brackets.

I arrived at work at 9.30am. (That’s earlier than usual.)

Otherwise, punctuate after the closing bracket.

I arrived at work at 9.30am (which is earlier than usual).

But again, we'd prefer if you got rid of the brackets altogether. Funnily enough, a dash looks better here, too:

I arrived at work at 9.30am – which is earlier than usual.

Square brackets [ ]

Like their round cousins, try to steer clear of these. Only use them for comments, corrections, references or translations made by a subsequent author or editor:

The President remarked that the country had surrendered [sic].

Angle brackets < > and curly brackets { }

These are used only for technical purposes. So only use them in the correct context and if you're really sure they're appropriate.