Google lets you Backup Contacts on your Android device to your Google Account which makes it easier to Transfer the Contacts to a new device. When you Sign in using your Google Account on any new phone, it automatically synchronizes all the contacts and other settings from your old device to your new device. This also lets you revive contacts from any lost smartphone. All this is possible only when you have backed up all your contacts on your Android device to your Google account.
You can access the website or you can go to the Google Contacts Application to cross check whether all your Contacts have been Synced or not. If you keep the Sync Contacts Option turned On, any new contact which you might save on your Android device will be Synced to your Google Account automatically.