If you understand what carbs are, then you understand that ALL oils are of course completely free of carbs. Carbs are starches and sugars. Oils are made of fat.
Whether you are looking at olive oil, corn oil, canola oil (made from rapeseed) or other types of cooking oil, you are looking at a 100% carb free item. You are in essence getting glycerine and fatty acids. These are components of living plants but are NOT carbohydrates. The four main energy sources for a human body are:
so fats and carbs are quite different from each other.
That being said, just because something is carb-free, it is not necessarily healthy. There are many types of oils - from trans-fatty acids to cold pressed oils. Some oils give best benefits while cold, while other oils retain their healthy benefits while heated up.
Be sure to read up about oils in order to choose the proper oils for your various cooking needs! Here are a number of articles to get you started. Post in the forums if you have any questions and we'll help you sort them out! The key thing to remember though that oils are a LARGE category of foods - all zero carbs, but with a wide range of health impacts. Some oils are super for you. Others, less so.
Low Carb Oil Information
Cooking Oil Type and Use Chart
Good Fats, Bad Fats and Ugly Fats
Polyunsaturated and Monounsaturated Good Fats
Good Fats are REALLY Good
Omega-3 Fats, Fish Oil, DHA and EPA
Olives and Olive Oil
Avoid Soybean Oil
McDonalds and Partially Hydrogenated Oils
Trans Fats, Deep Frying and Atkins
Healing the Damage of Trans Fatty Acids
Lisa Shea's Library of Low Carb Books