Change entered values to positive or negative values

You can make a new field and the formula would be

- [my data entry field]

>... too dangerous to change the user's actual input ...
>...  never really being sure what the user entered ...

Human input should always be verified and changed if incorrect, in the wrong format or if a typo is detected. Luckily it is simple to do with script. Here is the core code (for use with IOL) for negating the number entered by your human:

$("#_fid_6").on("change", function() {
  $("#_fid_6").val(- parseFloat($("#_fid_6").val()));
});

Using a formula to do this only bloats your application with superfluous fields (assuming there is no need for retaining the human's original keystrokes).