I've been looking for a free app like this for the longest time and I've finally found it. It shows how close you are to pitch both numerically and with a needle, and you can calibrate it to A440, 439.5, 441.5, etc, in .5 Hz increments. It's very accurate and sensitive, although it could adjust a little bit faster. I set the refresh level to 5, which gives the best performance. It's definitely quite accurate, but not to .01 Hz; the increments it picks up in are bigger, even though there are two decimal places. You can just watch the larger text that shows you how many 'cents' you are sharp or flat.
Overall it's a great little app that does everything I need it for. When I practice violin, I use it to practice passages slowly, and it's improved my intonation a lot. After practicing with it for a while, it makes my ear keener and then I can play in tune without it.