How safely does reinstalling Windows wipe old data?
Create a DBAN USB or CD and wipe the drive. This utility is designed to wipe a hard drive by overwriting it. DBAN only works on hard disk drives (HDD), not solid state drives (SSD).
You do not need to do a multipass wipe. A single pass is all you need to prevent others from reading your drive. The 7 pass wipe is a myth that still persists to this day.
Reinstalling Windows can overwrite some, none, or all of the data. Creating a simple DBAN boot disk and using it mitigates all the risk.
As for the Windows licenses, if the license came bundled with the computer, or were bought individually, they can be given to someone else. You can always call Microsoft to confirm the validity of selling a license.
After Windows format and clean re installation of the OS overwrite all free space using the cypher command using the command prompt.
cipher /w:F
F would be the drive letter of the system volume which is usually C
Nothing can be recovered now, by anyone.
To answer your initial question first; you are not safe by just reinstalling Windows, since you cannot guarantee that the data in question will be overwritten.
You may want to overwrite the (deleted) sensitive data using one of some available options;
You can use the DiskPart command - Clean All - but make sure that you know what disk you are working with.
You can (after deleting the sensitive data) use the Cipher command with the /W option.
You can also make yourself a simple BAT file or two - a couple of samples below;
One additional comment: If you wipe the disk/data 2-3 times, thereby alter the magnetic patterns beyond recognition, then even 'incredibly powerful people' will not be able to recover the data.
---
@echo off
rem Simple Disk Wipe Utility - wipedfast.bat
rem ---
rem --- 1) Delete all unwanted content from disk, leaving possibly only the command interpreter to run this script.
rem --- 2) Delete content from trashcan/recycled, if any.
rem --- 3) Run this script until it reports file system full.
rem --- 4) Delete WASH*.TMP files on each drive to reclaim space or to rerun utility.
rem --- Do this for all file systems/drives (C:, D:) on system, at least a couple of times.
rem ---
echo Grow file system test (fast / large increments - less secure). See comments in script file.
echo To be done for each drive (C:, D:) on system.
echo Abort with Ctrl-C when disk full and delete WASH-files
echo - Ideally run wipedfast.bat first - then wiped.bat when disk full - before deleting WASH-files.
pause
echo abcdefghijklmnopqrstuvwxyz0987654321ABCDEFGHIJKLMNOPQRSTUVWXYZ > wash_a.tmp
copy wash_a.tmp wash_b.tmp
:start
copy wash_a.tmp+wash_b.tmp wash_c.tmp
del wash_a.tmp
del wash_b.tmp
copy wash_c.tmp wash_a.tmp
ren wash_c.tmp wash_b.tmp
goto start
---
@echo off
rem Simple Disk Wipe Utility - wiped.bat
rem ---
rem --- 1) Delete all unwanted content from disk, leaving possibly only the command interpreter to run this script.
rem --- 2) Delete content from trashcan/recycled, if any.
rem --- 3) Run this script until it reports file system full.
rem --- 4) Delete WASH*.TMP files on each drive to reclaim space or to rerun utility.
rem --- Do this for all file systems/drives (C:, D:) on system, at least a couple of times.
rem ---
echo Wipe file system (slow / small increments - most secure). See comments in script file.
echo To be done for each drive (C:, D:) on system.
echo Abort with Ctrl-C when disk full and delete WASH-files.
echo - Ideally run wipedfast.bat first - then wiped.bat when disk full - before deleting WASH-files.
pause
echo abcdefghijklmnopqrstuvwxyz0987654321ABCDEFGHIJKLMNOPQRSTUVWXYZ > wash_a.tmp
copy wash_a.tmp wash_b.tmp
:start
copy wash_a.tmp+wash_b.tmp wash_c.tmp
del wash_b.tmp
ren wash_c.tmp wash_b.tmp
goto start