I'd find it useful. Is it similar to OpenOffice Math?
If it would be useful or not depends on what your website is about. Do people who visit your website need it? Or will it be the main attraction?
If it is any good, I say go for it.
However, I beat you to it. I made a huge calculator with a ton of built in functions already:
nixelinc.org
Programmed from scratch by a friend and I.
Check it out. Look at the publications for some examples. If you have ever used matlab or Mathematica, it is very similar.
To make a truly good one, the best thing to do would be to make it at once very powerful and versatile, while still keeping it extremely easy to use and learn to use.
Most of the command-line type calculators I've seen are either too simple; they won't do much useful, or to difficult to use: you have to learn complicated syntax for putting in problems. If you could make a simple to learn, but powerful one, you'd really have something there.
It might be useful, but I think SAGE is good enough for me. But someone else might like it.