Every product carries an embodied footprint from raw-material extraction and manufacturing, plus a small footprint each time it's used. A disposable item spends almost all its footprint D up front, once, per use. A reusable item spends a large embodied footprint E only when purchased (or replaced after it wears out), then a small footprint W per wash or reuse:
Disposable, after n uses: C_d(n) = n · D
Reusable, after n uses: C_r(n) = ⌈n / L⌉ · E + n · W
L = durability (uses before the reusable item needs replacing)
Breakeven (ignoring replacement): n* = E / (D − W), valid only if D > W
If the reusable item's per-use washing footprint W ever exceeds the disposable item's per-unit footprint D, the lines never cross — switching never pays off, no matter how many times you reuse it. Otherwise the reusable line starts high (the embodied cost of manufacturing it) but grows slowly, while the disposable line starts at zero but climbs steadily — they cross at n* uses, and the reusable path is quantifiably better for every use after that.
- Uses per day — how often the item is used; only rescales simulated time, not the crossover use-count.
- Reusable durability — how many uses the reusable item survives before it must be replaced (a fresh embodied footprint E); short durability delays or even removes the payoff.
- Wash / upkeep footprint — scales W; hot dishwasher cycles or frequent hand-washing can meaningfully erode the reusable item's advantage.
The illustrative gram-CO₂e values here are order-of-magnitude approximations drawn from published life-cycle-assessment literature on cups, bottles, bags and razors — real figures vary by material, region and manufacturing energy mix, but the breakeven mechanic itself is exactly how LCA researchers compare disposable and reusable products.