Hard water stains are mineral deposits, not ordinary dirt. That is why soap and a sponge often do nothing. The most reliable first step is a mild acid, usually white vinegar or a cleaner designed to dissolve calcium buildup.
Spray the glass, let it sit long enough to soften the deposit, then wipe with a microfiber cloth or a non-scratch pad. Rinse well and dry the surface so new spots do not form right away. If the buildup is stubborn, repeat the process instead of switching immediately to an abrasive scrubber that can haze the glass.
The important caveat is that not every cloudy mark is removable. If the minerals have etched the glass, cleaning can improve it but not make it look brand new. In that case, you are dealing with permanent surface damage, not a stain.
The best long-term fix is prevention: squeegee after showers and keep mineral-heavy water from drying on the glass.
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