Hi, I have done some searching and believe my problem may be the fill tube or level setting, but I am not sure what to do next.

This toilet is not used often. I suspected water leak so I changed the flapper, filled the tank, shut the water off, then added blue dye. It has been about 3 weeks and as you can see in the pictures, there is tank water loss. It is not hot so I don't think it is evaporation. The water in the bowl is not blue and there is not water on the floor.

That leads me to believe it is a fill tube or tank water level setting issue. The tanks says set water level 1" below overflow top. And that is where the water level is.

So what do I do next? Adjust the black plastic screw?

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I would venture to say there is absolutely nothing wrong with it... and that you underestimate how much water evaporates in 3 weeks.

 

I'm with XSleeper that it might be evaporation. You can repeat the test but leave the lid off. You should see the water level drop even more.

 

It's just not temperature that effects evaporation, humidity plays a big factor, along with surface area.