How are messages larger than 512 bits padded in SHA-256?
You're close; for a message of 550 bits, k=409; remember, k doesn't include the fixed 1 bit that you initially append.

In general, $k=512i + 447 - m$, where $m$ is the length of the message (in bits), and $i$ is the integer value that yields $0 \le k &lt; 512$.  In your example, $m=550$, and $i=1$; this gives us $k=512\times 1 + 447 - 550$