To find out the size of your Outlook mailbox from:

The Outlook Web App (OWA):

• From your email view, click on the cog icon just to the right of your name (top right of screen) to get a drop-down menu.
• Click on Options.
• Account, My Account section should appear by default (otherwise select accordingly from left navigation) - this shows a graphic indicating the size of the complete mailbox.
• Previous OWA version - which has a default livery of orange/yellow and white
  
  • Select Options (top right of screen) and then click on See All Options.
  • My Account, Account Information section should appear which shows a graphic and indicates the size of the complete mailbox.

The Outlook client:

• Select File tab and view the Mailbox settings section which shows a graphic and indicates the size of the complete mailbox.

It is also possible to find out the size of an individual folder with the client:

• Right-click on the folder name (in left navigation of main Outlook view) and choose Properties from the drop-down menu that appears. Click on the button Folder Size... and it will calculate size with and without any sub-folders.

See also:

How can I manage my mailbox to keep within the quota?
What happens if my Outlook mailbox fills?