My first thought, is that a very tiny shift of the laser, would make for a very large shift at the end of the laser beam.

You'd have to wrap tape tightly, many times around the level, and then you couldn't get the level to sit evenly on the surface you're working.

I don't expect it to work well.
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Christopher A. Young
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Has anyone ever taped a laser pointer to a level?
Seems it should work as long as the pointer has smooth sides.

Just curious after another post on here about them.