The Air Canada rules only permit a 16cm wide bag which is not a lot. of storage allowance.
RyanAir gives 20cm, United gives 22cm... how big is the sizer for Air Canada?
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I'm sitting at YYZ right now, and managed to scout out a (relatively) not-busy part of T1 to measure the sizers. Almost every sizer is of the old type: composed of metal tubing welded together to form a frame. I also saw a few new sizers that are powder coated black sheet metal, and look much less forgiving. Here's what I found:
These sizers are very forgiving, as one can insert a bag diagonally and straighten it out inside the sizer. With this method, for example, wheels on 4-wheel roller bags should poke out of the frame somewhat. Also, thicker bags that are somewhat compressible can expand once they're past the top bar, by about 25-30 mm.
As the photo indicates, I took measurements between the top bars, side bars, and from the top of the bottom bars to the top of the top bars. This type of sizer measures 545 x 405 x 235 mm for the carry-on bag, and 425 x 330 x 160 mm for the personal item. (But if your bag is at all compressible and above any of these measurements, it's easy to shove it in without much force.)
Most relevant to your question, the new style of sizer only has 4 sides for the personal item: left, right, back, and bottom. The only way to check its thickness is visually, which I suspect won't be very rigorous.
I'll try to find one that I can measure, but they're all in busy areas and not easily accessible. If I find one, I'll update this answer with a photo and proper measurements.
At 0:05 in this video, Measuring up Air Canada's hard line on carry-on luggage, you can see the sizer dimensions.
The Personal Item has a 16cm depth.
At 0:20, you see several close-up shots of the sizer itself.