A universal household size driven mathematical model for indoor water consumption: application to Saudi Arabia and transferability to water-scarce regions

Water scarcity and stress require urgent improvements in household water usage worldwide, including Saudi Arabia. This study develops an activity and fixture-based mathematical model to estimate daily indoor household water use as a function of household size. Outdoor water use, like for gardens, is excluded because it depends on the type of home and other factors. The model accounts for personal water-use activities such as showering, brushing and flushing etc. and household-level activities covering laundry, dishwashing, miscellaneous kitchen use etc. Also, each activity frequency and time is used to reflect realistic household behavior of Saudi Arabian residents. The mathematical model is implemented in Saudi Arabian context but can easily be used by other countries as per their regional contexts by changing the local data for activities, fixtures, and household type. Per-capita water consumption is calculated for household sizes ranging from 1 to \:10⁺ members under two scenarios (current and water-efficient fixtures). Results show that per-capita consumption decreases as household size increases, with single-member households using the most water (431.5 L/day) and \:10⁺ member households the least (329.4 L/day). Upgrading to efficient fixtures reduces consumption by 27.5% to 28.9% across all household sizes. Scaled countrywide results show that Saudi households would save 1.977 million m³/day and non-Saudi households 1.085 million m³/day (offering an average reduction of 28.0% across both segments). Moreover, 1,117.6 million m³ of water will be conserved annually countrywide by both segments using efficient fixtures, offsetting also approximately 3.70 million tonnes of CO₂ emissions each year. Further analysis reveals distinct consumption patterns as water use is concentrated in medium-sized Saudi households (4–8 members) and (1–3 member) non-Saudi households. Validation and sensitivity analyses confirm that these findings are robust to uncertainties and behavioral offsets, with substantial co-benefits for water and climate. The study highlights the importance of integrating household-size distribution into water-demand planning and demonstrates that water-efficient fixtures offer co-benefits for both water security (SDG-6) and climate action (SDG-13).