If the extension cord is short, wrapping it around your arm is OK , but if the extension cord is over 25 feet long, it is best to wrap it up like I am showing you in the video below. I have a water damage cleanup service and I carry a lot of extension cords in my carpet cleaning van and my water damage cleanup trailer to run my dry equipment. Sometimes I have to get power from the upstairs floor so I do not trip a breaker.
If you wind up the extension cord this way it will never get tangled. You can stick your extension cord in a bucket or hang it up on the wall of your truck. No matter how you store it, when it is wound up this way, it will never get tangled and it is really easy to unwind to be used again. So this is my little tip of the day.