Are my contacts backed up on icloud

Yes, contacts are included in the iCloud backup unless you are using iCloud Contacts:

What is iCloud Contacts? - Apple Support

In that case, they are already in iCloud. But be aware that if you use iCloud Contacts that if you delete a contact on any device, it will be deleted everywhere (including iCloud).

Also, see the last paragraph in the 'Here’s what iCloud Backup includes' section of:

What does iCloud back up? - Apple Support

Be aware that your contacts may also be backed up via another cloud such as - Google or even Yahoo. You can verify this in your iPhone by doing to Settings- Mail- Accounts and opening up each email account saved to your phone.

For instance my contacts are saved to my Google account, so if I follow the above steps and go to Accounts - then click on my Gmail - then turning contacts off, then all of my contacts will disappear from my phone. This tells me that the contacts are saved via my Gmail Account as well.