I said “probably” because I’m not 100% certain about any of my advice, but I can tell you from my own experience, and from watching lots of runners that I think my advice works.
You see people doing all kinds of different things with their arms. Some hold them quite low. Some hold them out from their body. And of course, many experts tell us that we should swing them only forward and back. As distance runners (meaning anything from 5k up to the marathon) we need to find a way of using them that helps us conserve energy, while aiding our forward locomotion. Sprinters like Usain Bolt need to generate lots of power quickly over a short distance, so naturally they will swing their arms quite a bit. We shouldn’t do that.
Let’s start with getting our arm carriage correct. Stand with your proper posture (within yourself, eyes down and ahead 10 ft. or so) and let your arms hang relaxed against your sides. Don’t hold them out from your body at all. Then simply bend your arms at the elbow until your hands are right in front of you chest (nipples). This should feel relaxed. Too many people hold their arms out from their body, and over the course of a race, this adds to fatigue.
Now when we run, we should focus on sweeping our hands down in front of our chest–the left hand sweeps down over the left lung, and the right hand over the right lung. This is much more efficient than thinking of moving our whole arm forward and back. Watch the great Ethiopian runner, Bekele, demonstrate in this video: