<p>Sharp-crested weirs with a contraction ratio (opening width per total width) less than 0.25 are used for low discharge flows. This study investigates how contraction ratio and flow discharge influence relative energy dissipation and residual energy, conducting laboratory tests on models with contraction ratios (<i>b/B</i>) of 1/12, 1/8, 1/6, and 5/24 across various flow conditions. The results show that relative energy dissipation reduces with increasing head over the weir. Additionally, a higher discharge rate is associated with lower relative energy dissipation, indicating more efficient discharge. Higher flow rates and larger contraction ratios result in reduced energy dissipation in rectangular thin weirs, underscoring the importance of weir design and flow conditions on efficiency. Increased discharge rates lead to higher relative residual energy, suggesting improved energy retention downstream. The highest relative residual energy values were observed at higher contraction ratios, indicating that wider thin weirs are more effective in minimizing energy dissipation. An equation was proposed to estimate the relative energy dissipation based on <i>b/B</i> and the ratio of head over the weir to the weir height (<i>h/P</i>) with R² = 0.998, RMSE = 0.0055, MAPE = 0.8466%, NSE = 0.997, SI = 0.0118, and PBIAS (%) = 0.0172. Statistical parameter values indicate very good compatibility of experimental data and calculated values.</p>