The ingredients in cheddar are simply milk, salt, and enzymes. The carbs in cheddar cheese are low, as seen below because the only source of potential carbs is from the milk. Milk contains a natural sugar known as lactose, which is generally the source of the carbs. However, a cheese like cheddar typically ages for quite some time. The aging process causes much of the lactose to break down, therefore, the lactose (sugar) is less of a factor in terms of contributing to the carb count.
Below we have supplied data on the carbs in cheddar cheese. The figures come from the USDA nutrient database which provides general nutrition facts. Based on this nutritional information, the carbs in cheddar cheese are very low at approximately 1-2 grams per ounce. Assuming you limit your cheddar cheese intake, the carbs in cheddar cheese are not a concern for most people. Cheddar cheese can actually be considered as a food choice for those concentrating solely on a low carb diet.