/21 Subnet Mask (255.255.248.0): 2,046 Hosts Explained

How many /21 networks fit

A /21 holds 8 × /24. Two /21s make a /20.

A phone on campus Wi-Fi got 10.60.13.250 from DHCP. The Wi-Fi VLAN is a /21. What is its range, and is 10.60.13.250 near the end of it?

The mask is 255.255.248.0. The third octet (248) is the "interesting" one — the first that is not 255.
Block size = 256 − 248 = 8. Networks start at multiples of 8 in the third octet: 0, 8, 16, …
The third octet of 10.60.13.250 is 13. 13 ÷ 8 = 1 remainder 5, so the block starts at 1 × 8 = 8.
Network = 10.60.8.0 (octets after the third become 0). Broadcast = 8 + 8 − 1 = 15, giving 10.60.15.255 (octets after it become 255).
Usable hosts: 10.60.8.1 to 10.60.15.254, which is 2¹¹ − 2 = 2,046 addresses.

Same thing in binary (network bits | host bits):

Address  00001010.00111100.00001|101.11111010
Mask     11111111.11111111.11111|000.00000000
Network  00001010.00111100.00001|000.00000000

Campus and event Wi-Fi

A lecture hall or conference floor can have well over 1,000 devices on one SSID. A /21 gives 2,046 leases. Keep DHCP lease times short (an hour or two) so departed phones free their addresses.
Summarising eight branch /24s

Branches numbered 10.8.0.0/24 to 10.8.7.0/24 summarise to 10.8.0.0/21 at the hub.

Writing 10.60.12.0/21. The third octet must be a multiple of 8, so it becomes 10.60.8.0/21.
Going bigger than /21 for client VLANs. Past about 2,000 devices, broadcast and multicast (mDNS, ARP) traffic hurts Wi-Fi airtime. Split into more VLANs instead.

How many hosts are in a /21?

2,046 usable: 2^11 = 2,048 addresses minus network and broadcast.

What is the wildcard for /21?

0.0.7.255. The block size is 8 in the third octet, so the wildcard there is 8 − 1 = 7, and the whole fourth octet is 255.

What is the range of 10.60.8.0/21?

10.60.8.0 to 10.60.15.255. Usable hosts are 10.60.8.1 to 10.60.15.254.