1) The female Cooper's is the largest. If it looks real big, it's a female Cooper's.
2) The male sharp-shinned is real little (relatively). If it looks real little, it's a male sharp-shinned.
Now the problems: the male Cooper's is barely bigger than the female sharpie. And they look a lot alike. But here are some helpful ID tips:
Cooper's Hawks have rounded tail tips while sharpies have squared off tail tips. Also, Cooper's Hawks have big, prominent heads (the birder slang is blockhead), while sharpies have small heads with almost no neck (birder slang is pinhead).
Nevertheless, sometimes the ID can't be definitively made. On my survey form, one of the options is "Unknown Accipiter." Even expert birders will be forced to use that option occasionally.
It seems like it had a smaller head, and I’m almost certain it had the squared off tail. It was smaller than most of the other hawks I see around here, like the Cooper’s or the Red-shouldered ones I see from time to time. It had a few very quick pumps of its wings and then had a short glide when it flew away. I’m not very good at determining size when it’s not close by and there’s not really anything to compare it to close to it. I guess I should work on that. Thanks so much for your expertise.