Calculating f-stop with given focal length and desired depth of field?

I have a varifocal zoom lens set to a desired focal length and at known distance from the subject. I also have a desired depth of field.

Given this information, can I calculate a theoretical f-number to achieve the desired depth of field?

If so, how would this be done?

Is the exposure and sensor size also required to make this calculation?

2) The small angle approximation: $sin(x)$ ~ $x$ for small $x$.