How do I get the equivalent of #FC8019 in purple or any other color?
#FC8019 is the HEX notation for an RGB color. The appearance of an RGB color depends on its assigned RGB color profile, so to get a color managed conversion from the web HTML hex code, you would need a color manged application like Adobe Photoshop, and make the conversion from sRGB to the desired destination color space. The Adobe Color web app is not color managed.
Hex coded colors are for the web and use sRGB as the standard color space for the internet. That said, fc8019 is an orange color not a purple. My question would be Equivalent how? Brightness, saturation? If you click on Triads and enter your orang hex value you will get a couple of analogus purples out. #4D22F5 is one of those
The best way to play around with these is using Photoshop's color picker. Or you can enter the hex code right in Adobe Color and get varieties.