Hi Evan,
It depends on the files and folders that you have on the hard drive.
For Example: If you have 200 GB of worth data in the C drive then to perform a system image you would need minimum of 200 GB of space in the external drive to perform a system image.
To know more about system image in Windows 7, refer the link
What backup settings should I use to maximize my disk space?
Hope this information helps.