P = ρ × g × Q × H × η
Hydroelectric power converts the potential energy of water into electricity using the formula P = ρgQHη, where ρ is water density (1000 kg/m³), g is gravitational acceleration (9.81 m/s²), Q is flow rate, H is the net head (vertical drop), and η is turbine efficiency (typically 80-95%). Hydropower is the world's largest source of renewable electricity, generating ~4,300 TWh/year (16% of global electricity). It has the lowest lifecycle emissions of any generation technology: 4 g CO2/kWh versus 820 for coal, 490 for gas, and 12 for wind. The Three Gorges Dam in China has a capacity of 22.5 GW and prevents roughly 100 million tonnes of CO2 annually. Micro-hydro systems (5-100 kW) can power rural communities using small streams. The main environmental concern is habitat disruption: dams block fish migration and alter river ecosystems, though fish ladders and run-of-river designs minimize this impact.