Water expands when it freezes. Ice takes up more space than water. Where do I find the formula?

If it’s not homework, use your common sense. Leave an inch or so unfilled. Less is more initially, so freeze the first batch with slightly less than seems safe and observe the results.

Remember your experiences with the ice tray and how the cubes expand.

Ice is about 8% less dense than liquid water. Conversely a given amount of liquid water occupies about 8% more volume when it freezes. [See also my avatar!] Plastic water bottles can usually handle the expansion, though I’ve seen some burst. (It depends in part on how much air is present before freezing.) Aluminum soda cans are designed to pop out the concave bottoms rather than burst when frozen.

I’d recommend filling the bottles, then leaving a little air and squeezing them slightly before sealing so they can further expand when frozen.

Plastic bottles will stretch to accommodate more water (unless the contents are carbonated in which case the gas will be expelled from the liquid causing the bottle to leak.)

Leaving space will not help if it’s glass. The water freezes from the outside in. Once the dye is cast, it cannot reshape itself to fill the bottle. It will break the bottle even if only half full.

You probably can calculate it knowing the coeff of expansion of water and the plastic material.props but that would be a pretty academic pursuit…last time i tried it it just expanded to accommodate the ice but ive noticed that some cos seem to be using different plastics nowadays.