All Office 365 Outlook Web App accounts are by assigned 50GB by default. The following tutorial shows the process of how to check your mailbox usage using the Office 365 Outlook Web App.
On the top right of the page, click on the Gear icon and under My App Settings, select Mail.
Click General to expand the section list then select My account.
On the bottom right hand side of the page you will see your account's usage.
If you need to send large files electronically and are concerned about exceeding the Exchange Online message or account size limit, OIT recommends the following: