Soap That the Garden Can Forgive: A Sodium Budget for Reusing Bath Water on Plants

This study examines a practical question in everyday hygiene by explicit arithmetic from stated assumptions. The baseline household applied 98.6 g of sodium per square metre per year before leaching, or 69.0 g net, against the stated ceiling of 12 g, an exceedance of 5.8 times. Halving bathing soap events reduced the net load to 34.5 g, still above the ceiling. Switching to potassium-based soap reduced it to 7.7 g net, comfortably inside the budget, and spreading the baseline sodium load thinly enough to comply would have required 115 square metres of garden. On sand, with the ceiling raised to 30 g, the baseline still exceeded the ceiling. The proposed arrangement is as follows. The recommended design pairs greywater reuse with potassium-based soap for bathing and spreads the water over an area sized by the budget formula, with sodium products confined to uses whose water goes to drain. The formula is stated generally so a household can insert its own area, rainfall and wash count. All results are derived from the accompanying simulation script, in which every assumption appears as a named, replaceable value. SIMULATED, NOT MEASURED.