Since you're only converting one character, the function atoi() is overkill. atoi() is useful if you are converting string representations of numbers. The other posts have given examples of this. If I read your post correctly, you are only converting one numeric character. So, you are only going to convert a character that is the range 0 to 9. In the case of only converting one numeric character, your suggestion to subtract '0' will give you the result you want. The reason why this works is because ASCII values are consecutive (like you said). So, subtracting the ASCII value of 0 (ASCII value 48 - see ASCII Table for values) from a numeric character will give the value of the number. So, your example of c = c - '0' where c = '5', what is really happening is 53 (the ASCII value of 5) - 48 (the ASCII value of 0) = 5.
When I first posted this answer, I didn't take into consideration your comment about being 100% portable between different character sets. I did some further looking around around and it seems like your answer is still mostly correct. The problem is that you are using a char which is an 8-bit data type. Which wouldn't work with all character types. Read this article by Joel Spolsky on Unicode for a lot more information on Unicode. In this article, he says that he uses wchar_t for characters. This has worked well for him and he publishes his web site in 29 languages. So, you would need to change your char to a wchar_t. Other than that, he says that the character under value 127 and below are basically the same. This would include characters that represent numbers. This means the basic math you proposed should work for what you were trying to achieve.