Bicycle Helmet: Icelandair

You get both a carryon ( fits in the overhead) and personal item ( fits under the seat). Maximum dimensions for the personal item: 15.7x11.8x5.9 inches.

Thanks but that was not my question. I already know the sizes of carry-on and personal item. What I was wondering was whether I could bring it on the plane just like you might bring your hat or jacket or pillow and have it not count as my "carry-on" or "personal item."

Sorry, you only mentioned the carryon not the personal item so I wasn't sure if you knew. Assuming you're taking both, where do you plan to put the helmet as well?

Wear it. If the check-in hassles you, just tell them you will sue the airline if you suffer a concussion as a result of turbulence and no head protection. Seriously, I would consider it as clothing. No different than somebody wearing a big Stetson hat or a puffy winter jacket. Good luck.

Wear it. Have the helmet on your head when you check-in, and as you board the plane. If anyone questions you about it, you can say it's religious headwear. (I know some serious bicyclists for whom this would be true.) As long as you make it through security, and get past the gate dragons, once you're on the plane, you can probably remove the helmets and toss them up in the overhead bins (should be easy to find space for that, even if they're "full").

I'm petty sure that whatever you are wearing doesn't count as a carry on – so it doesn't even have to be religious headwear.

The internets have many examples of people donning an excess of "clothing items" to beat carry-on limits. Most common is loading up the pockets of cargo pants.

I haven't done this with any kind of headwear, but I have "worn" an extra layer or two when I had otherwise reached my limits. Once on the plane, find a place to stuff the coat etc. and you're good. Doing a minor post-boarding shuffling of your belongings is nothing unusual.