If my photos are stored in the icloud, can i erase my photos from my computer? i need to clear space off my disk.

No.

iCloud Photos is a syncing service. Any photo you delete from a device where iCloud Photos is turned on will also be deleted from iCloud and from any other device connected to iCloud Photos. You can potentially reduce the storage space required on a device by turning on Optimize Storage. See: https://support.apple.com/en-us/HT204264

Apple does not currently offer cloud-only storage for photos. If that is what you want or need, you may want to explore 3rd party options such as Google Photos or Dropbox.

iCloud is a sync service. If you delete a photo from your Mac, it's deleted in iCloud too.

If you need storage space on your Mac: you can

• optimize photo storage

https://support.apple.com/en-us/HT206996

Check this: Open Photo's, Go to Photo's, Preferences, iCloud and select 'Optimize Mac storage'

• move your photo library to an external disk

https://support.apple.com/en-us/HT201517

Good to know: you can include an external drive with your photo library in a TimeMachine backup