From iTunes: Backing up, updating, and restoring your iPhone, iPad, or iPod touch software: http://support.apple.com/kb/HT1414
"If you upgrade or otherwise replace your device with a newer device, you may be able to restore the previous backup to the new device. You can upgrade one device with the backup from a different type of device; most settings will transfer to the new device.
Note: During the process of restoring your old backup to a new device, you may see the iTunes progress bar pause. If this occurs, please allow for additional time for the upgrade to complete."
See step 9 in the referenced restore instructions to see how to choose a previous backup.
Were you syncing your contacts with your contacts app on your Mac? I'm not sure if you use Gmail as your email account but you can sync your contacts with Gmail and with your Contacts on your Mac in the future. Then if you any issues occur you have a backup in the cloud (Gmail) and on your Mac.
You can give this app a try: http://www.icopybot.com/itunes-backup-manager.htm
Thanks for the help. Though I think that I didn't explain myself well:
I had an iPhone with lots of contact names and phone numbers. I never synced it with the Address Book on my mac. Now my iPhone is broken and I got a new iPad.
I wanna know if there's a way I can restore my contacts from my iPhone backup straight to my iPad.