A universal two-fifths law of pier scour has been derived, revealing that the equilibrium scour depth to pier diameter ratio follows a consistent scaling law with the introduction of a newly coined pier-scour number. This number encapsulates all key parameters involved in local scour phenomena, including approach flow velocity, threshold shear velocity, approach flow depth, pier diameter, and sediment grain size. The law accounts for the impact of pier shape on equilibrium scour depth through an additional term involving the drag coefficient raised to the power of 2/5. The law is validated using an extensive dataset of experimental measurements on circular pier scour. The derived universal law provides a robust framework for predicting equilibrium scour depth in clear-water scour conditions. The law is applicable to all pier shapes, with the noncircular pier width across the flow equaling the circular pier diameter. The law is supported by extensive experimental data and has practical implications for bridge design and maintenance. The study highlights the importance of considering the pier shape and other key parameters in predicting scour depth, and emphasizes the need for a unified approach to scour prediction. The results demonstrate that the equilibrium scour depth scales with the pier-scour number to the power of 2/5, providing a fundamental understanding of the scour process. The study also discusses the procedure for calculating the maximum scour depth at a circular pier and the role of a factor of safety in pier foundation design. The findings contribute to the development of more accurate and reliable methods for predicting scour depth and improving bridge safety.A universal two-fifths law of pier scour has been derived, revealing that the equilibrium scour depth to pier diameter ratio follows a consistent scaling law with the introduction of a newly coined pier-scour number. This number encapsulates all key parameters involved in local scour phenomena, including approach flow velocity, threshold shear velocity, approach flow depth, pier diameter, and sediment grain size. The law accounts for the impact of pier shape on equilibrium scour depth through an additional term involving the drag coefficient raised to the power of 2/5. The law is validated using an extensive dataset of experimental measurements on circular pier scour. The derived universal law provides a robust framework for predicting equilibrium scour depth in clear-water scour conditions. The law is applicable to all pier shapes, with the noncircular pier width across the flow equaling the circular pier diameter. The law is supported by extensive experimental data and has practical implications for bridge design and maintenance. The study highlights the importance of considering the pier shape and other key parameters in predicting scour depth, and emphasizes the need for a unified approach to scour prediction. The results demonstrate that the equilibrium scour depth scales with the pier-scour number to the power of 2/5, providing a fundamental understanding of the scour process. The study also discusses the procedure for calculating the maximum scour depth at a circular pier and the role of a factor of safety in pier foundation design. The findings contribute to the development of more accurate and reliable methods for predicting scour depth and improving bridge safety.