Knowing when and how to use brackets and parentheses can be challenging. We will try and sort out the problem here.

Round brackets

Round brackets are used

• to add extra information in text

Leonardo da Vinci (1452–1519) is considered one of the greatest artists ever.
Cary Grant (born as Archibald Leach) starred in over seventy films.

• to add personal comment

Hum in Croatia is the smallest town in the world (and very beautifully situated on top of a hill).

• to define an abbreviation or acronym

UNITAR (The United Nations Institute for Training and Research) has its headquarters in Geneva, Switzerland.

• to refer to another part of the same text

Exports increased by 6 % (Table 3).
Production time can be reduced by using a new application (see Chapter 6). 

• in referencing

Such methods are based on direct observation (Jones et al., 2012).

Square brackets

Square brackets are used

• to show that text has been added to a quotation

Several new products were introduced [on the company’s website].

• to show that part of a quotation has been omitted (by using an ellipsis)

Relatives, friends and neighbours as well as his landlord, his employer, his former professor […] had all come to congratulate him.

(The Chicago Manual of Style recommends using the three dots without brackets. The Modern Language Association, on the other hand, recommends brackets to distinguish this kind of ellipsis from an ellipsis in the original text.)

• when you capitalize the first letter of a quotation that is not capitalized in the original (or use lowercase where the original is capitalized)

Original: 

The professor said, ”Perhaps the best example of Renaissance architecture is St. Peter’s Basilica in Vatican City”.

Paraphrased:

The professor told his students that ”[p]erhaps the best example of Renaissance architecture is St. Peter’s Basilica in Vatican City”.

• around the Latin abbreviation sic (read more here).

To sum up:

Use parentheses to add information to something you have written.

Use brackets to change or add comments to somebody else’s words that you are quoting.

Braces (Curly brackets)

Curly brackets are mainly used in computer programming, mathematics, and science. They often identify the elements of a set.

Angle brackets (Chevrons)

Angle brackets are seldom used in English. They may indicate a website or something said in a foreign language.  In some languages, double angle brackets are used instead of quotation marks.

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