Quick Answer — How Many Uses Until a Reusable Pays Back?
A reusable item costs money up front and a little each time you use it — washing, detergent, energy. A disposable costs nothing up front and a fixed amount each time. The break-even is where the accumulated difference cancels the upfront cost.
Break-even uses = Upfront cost ÷ (Disposable cost per use − Reusable cost per use).
A $28 insulated bottle replacing a $1.45 bottled water, with about 2 cents per use for washing, saves $1.43 every time it is used. That is 19.6 uses to break even — at five uses a week, 27.5 days, or under four weeks.
The carbon break-even is a separate sum and usually a different answer. Carbon break-even = embodied emissions of the reusable ÷ emissions saved per use. That same bottle carries roughly 260 g CO2e of embodied emissions against a disposable bottle's 82 g, with about 4 g per wash, so it repays its carbon in 3.3 uses — much faster than it repays its price.
It does not always run that way round. A stainless steel razor pays back its money in 8.3 uses but its carbon in 19.4 — because a cartridge razor is cheap to make and expensive to buy, while a metal one is the reverse.