Those techniques are spot on for anything 4" and over, but as you drop in pipe size the accuracy starts to go down gradually with each drop in pipe size. It goes down in small increments eventually ending up off by 5/16" with a 1/2" piece of pipe.
.5/2=.25
.25/2=.125
.125/2=.0625
.25+.0625=.3125 or 5/16"
.414*.5*1.5=.3105 or 5/16" in my book ;-)
Actual take off for a 1/2" 45deg fitting is 5/8" so you'd be off 5/16" if you did the short cutt.
Happy pipe fittin!!