These will fit into a 1/4" hole (9/32" to be exact) so just a tad over a 1/4". It's 1/2" tall.

This is the specs from the factory:

Size: L x W:12 x 15mm/0.4x0.5 inches

Hole Diameter:3.5mm/0.14 inch

Package content:12pcs bottom rail cord cover buttons

These are found on your horizontals blind bottom rail. Just flip the rail over and you will see the plugs that can be popped off with a standard screwdriver.
The maximum string size this button can hold is 2.4mm.
Fits most blinds.