Backing up iPhone to iCloud?

I'm trying to back up my iPhone contacts and all apps to the iCloud. I've gone through and done so by going to settings, iCloud, back up now and doing that back up. However, when I log into iCloud through my computer not all of my contact information is there. Is everything actually backed up to the iCloud, however, it is just not visible when I am looking at the iCloud through my computer?

Before I upgraded my phone from the 4s to the 6 I recall doing a hard backup and connecting my phone to the computer using the power cord.

If it is not actually doing a full back up since not all of my contacts are showing up when I log onto the computer how can I ensure everything is backed up to iCloud?