As far as I know there is no way to reformat a disc that you are currently using as the boot disc from which you are running Windows. Way back when you used to be able to open Command Prompt and do a "format C:" and it would work, for some value of work, because it demolished Windows in the process. There's probably a way to override the protection that does not allow this to be done now, but I wouldn't.
As someone else has already suggested, the only way I know of to achieve your goal is to hook up the disc drive that you'd like to format to another computer as a secondary/external drive and do the format from there.
For myself, a straight install of Windows (whether 10 or earlier) using install media is going to replace anything that needs replacing and is starting afresh, for all practical intents and purposes. It will not remove things like the recovery partition that's probably on your drive and that was placed there by the computer manufacturer. If you want to blow all of that away you will definitely need to reformat and repartition the drive. And if you're doing this on an old drive that had employed MBR and you're installing Windows 8 or Windows 10 you might want to consider using GPT instead.
Brian - Windows 10 Home, 64-Bit, Version 1703, Build 15063 (dot level on request - it changes too often to keep in signature)
The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth.
~ Niels Bohr