I have an empty 512 drive and my Mac only has 224 gb of content, and yet I keep getting a 'not enough space error' and time machine backup fails. I've erased it and formatted it, etc. What am I doing wrong?

You aren't doing anything wrong. You just need a bigger backup drive.

For a long and boringly detailed explanation please review this post: time machine does not delete old backups - Apple Community

mswaldon wrote:

I really think there's something else going on. Now, Im using an empty 1TB drive and it still says not enough space to backup my 224 GB of content? I even erased the drive and reformatted it with disk utility.

What is your internal drive capacity; not its current usage?

Apple is going to be looking at the maximum here; at the necessary storage capacity.

Time Machine doesn’t work very effectively (if at all) near its storage capacity limits.

1 TB internal to 1 TB external isn’t going to work well as that internal 224 GB usage → internal 1 TB usage.

mswaldon wrote:

I have this formatting. yes. no partitions.

Are there any other external drives connected at the same time?

Absent specific exclusions, all connected storage would be included in the TM requirements.

mswaldon wrote:

Thanks! my internal drive is a 250 GB.

That should work, then.

The external drive for Time Machine should be formatted to GUID-partitioned (GPT) Apple Extended Journaled (HFS+), with one big partition.

A good rule of thumb is that your Time Machine backup drive should be at least 3 times the size of the drive that you're backing up.

And, it's GB, not gb.