This work would not be possible without @_Ninji's reverse engineering efforts. This page is based entirely off of their reverse engineering. Thank you, Ninji!
It is highly recommended that you become familiar with the turnip price patterns before using the calculator. Check out the info page for a summary, /u/Edricus's in-depth write-up for a detailed overview, or the decompiled code for the gory details.
Some other people have also made calculators based on Ninji's reverse engineering: mikebryant, elxris. Be sure to check them out!