You can view your quota and the amount of space that your backed up messages have consumed using the ContentStore Email Viewer in both online and offline modes.
Before You Begin
You must install Outlook Add-in for ContentStore Email Viewer.
Procedure
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Open Microsoft Outlook.
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Expand ContentStore.
Under Quota Distribution, a progress bar indicates the amount of backup storage that you have used, and the quota for your mailbox. The color of the bar indicates whether you are near to or over the quota.