The cost is not the allocation per se, the cost is copying the bytes. When concatenating two strings, the bytes from both strings are copied into the new string

The cost is not the allocation per se, the cost is copying the bytes. When concatenating two strings, the bytes from both strings are copied into the new string. If you repeatedly concatenate, the bytes end up getting copied many times. E.g if you concatenate 100 strings by appending one by one, the bytes in the first string is copied 99 times, the bytes in the second string is copied 98 times and so on. Using a StringBuilder, the strings are only copied once when copied into the buffer. If the buffer need to grow, the whole buffer is copied into a larger buffer, but if the buffer grows by say doubling the size, then this cost is amortized, so each string on average is still only copied twice at worst. Faster yet is concatenating an array of strings in a single concat operation. This avoids the buffer resize issue, since the necessary buffer size is known up front. But this leads to the subtle issue where a single concat is faster than using a StringBuilder, while the cost for multiple appends grows exponentially for concat but only lineary for StringBuilder.