How do I find how much space the camera roll is using on my iOS device?
For whatever reason, iOS doesn't break out the size of the Camera Roll as well as other data that is potentially in the cloud like mail, contacts, calendars and photos and videos in the camera app. 

If you absolutely must see the size of your Camera Roll without the help of a Mac or PC, you can measure it indirectly by turning on iCloud backup and seeing the space that did/will take on the last/next backup.

Open the Settings app and go to:

iCloud &gt; Storage &amp; Backup &gt; Manage Storage