Enter an IPv4 address and a CIDR block. Get a clear yes/no, the subnet's network and broadcast bounds, and where the address sits within the range.
Membership is a single bitwise test. Apply the subnet's mask to both the network address and the address you're testing; if the masked results are identical, the address is inside the block.
Formally: (ip & mask) == (network & mask). The mask zeroes out the host bits, leaving only the network portion to compare. This is exactly how a router decides whether a destination is local or needs a next hop.
Knowing an address is "in /24" is more useful alongside the actual first and last addresses, so the result includes the network and broadcast bounds and where your address falls between them.
Yes — the network and broadcast addresses are part of the block. They just aren't normally assignable to hosts (except on a /31 or /32).
Yes. 192.168.1.55/24 is normalized to its network 192.168.1.0/24 before testing.