As you already pointed out in your question, it's a matter of intervals. Of course, turning it off-and-on like a cars indicator light is more power consuming than simply leaving it on – and turning it off for 12 hours does really save juice. The matter is to find the right "interval".
Not quite up-to-date anymore, but still sufficient for the "raw estimate": About two years ago I've posted a table with some consumption data, using two devices as reference. Let's average the values a little and assume they've changed "for the better", so we can say:
- WiFi in standby uses about 10 mW
- WiFi downloading uses about 800 mW
- WiFi uploading uses about 400 mW
WiFi searching for a nearby AP to connect to, including the entire process, must be somewhere in between (no values in my table or their sources), but I'd assume at least 200..400 mW here – as like with cell signal, it needs to fully power up to scan the area for available SSIDs. Let's further assume the connect process takes about 5..10s, just to have some numbers to juggle with:
- 5s × 200 ms = 1.000 units (minimum power-up consumption)
- 10s × 400 ms = 4.000 units (maximum power-up consumption)
- 10s × 10 ms = 100 units (maximum standby consumption)
By those numbers (being just raw estimates, not scientific calculations!), results would be:
100..400 seconds are the minimum "disconnected time" for your described "toggle" to not consume more juice than staying in standby. Toggling would thus make sense only for breaks of about 10 minutes and up.
For a similar calculation, you might be interested in 2G versus 3G: Does it really save battery? :)
To avoid misunderstandings:
As Dan correctly pointed out in the comments, I've omitted a lot of details here. I was aware of that: the above is nothing but an idealized number-juggling, which should show that even at best circumstances permanent toggling is no good idea. Calculating "exact numbers" which are at the same time "absolute" is impossible, as too many factors play a role here:
- noone expects WiFi idling at 10 mW with the connection lost. It will certainly "power up" on a search for available networks.
Plus the points Dan mentioned:
- many apps that perform network operations in the background use a broadcast receiver to run when the network connection comes up. If you're actually connecting to a network each time you turn the Wi-Fi on, all these apps will run, drawing more power. On each "toggle on and connect", that is – while they wouldn't do so at all otherwise, or at least at very lower intervals
- if the Wi-Fi was on all the time, the same apps might run more or fewer times to update or sync data. This very much depends on the apps installed/used
- if you're waking the device up and/or turning the screen on just to turn on Wi-Fi and check for messages, that'll use more power than the Wi-Fi itself.
So please read my conclusion as "it makes no sense for time-frames smaller than 10 min". The longer the interval, the more likely it makes sense – and the shorter, the less.