If you use "Constant Bit Rate" (CBR) encoding, then the file size is easy to calculate fairly accurately.
For CBR encoding, the "bit rate" is specified in kilobits per second. There are 8 kilobits to a kilobyte. So, for example, if the file is 10 seconds duration and the bit-rate is 128 kbps (kilobits per second), then that is 10 x 128 = 1280 kilobits of data, which = 1280 / 8 = 160 kilobytes.
Size in kB = bit-rate (kbps) x duration (seconds) / 8
The actual file size will be a little bigger due to headers and metadata, but the above calculation is pretty close.
CBR encoding and the bit-rate (kbps) can be selected in the file export dialog (see: http://manual.audacityteam.org/man/file ... ialog.html