Height: 1.2cm (0.47in)
Black leather version
Levis Woods are a casual plimsole trainer that offers a low profile. If you are looking for trainers that don't give much height, these plimsole styles are the kind to look for. Do bear in mind though, the thinner the sneaker and more closer to the ground your feet are, the greater you'll feel every bump and stone when walking.
In terms of actual thickness, I measured them at USC and found they gave around 12mm, or just under 0.5 inches of height. In the range of trainer thicknesses, that's on the low end.
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Sneaker Heights are estimates.
Measurements are either taken with a stadiometer (barefoot, then in shoes) or using CelebHeights custom-made Shoe Gauge.