Spin is a fundamental yet nontrivial intrinsic angular momentum property of quantum particles or fields, which appears within relativistic field theory. The spin density in wave fields is described by the theoretical Belinfante-Rosenfeld construction based on the difference between the canonical and kinetic momentum densities. These quantities are usually considered as abstract and non-observable per se. Here, we demonstrate, both theoretically and experimentally, that the Belinfante-Rosenfeld construction naturally arises in gravity (water surface) waves. There, the canonical momentum is associated with the generalized Stokes drift phenomenon, while the spin is generated by subwavelength circular motion of water particles. Thus, we directly observe these fundamental field theory properties as microscopic mechanical properties of a classical wave system. Our findings shed light onto the nature of spin and momentum in wave fields, demonstrate the universality of relativistic field theory concepts, and offer a new platform for their studies. 2022 The Authors https://creativecommons.org/licenses/by-nc/4.0/ This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial license , which permits use, distribution, and reproduction in any medium, so long as the resultant use is not for commercial advantage and provided the original work is properly cited. Spin is a fundamental yet nontrivial intrinsic angular momentum property of quantum particles or fields, which appears within relativistic field theory. The spin density in wave fields is described by the theoretical Belinfante-Rosenfeld construction based on the difference between the canonical and kinetic momentum densities. As early as in 1909, Poynting ( 13 ) described the intrinsic angular momentum of circularly polarized light (i.e., an electromagnetic wave with rotating electric and magnetic field vectors). This property was later observed via optical torque on matter ( 14 ), and it was associated with the spin of photons (i.e., relativistic massless quanta of light) ( 3 , 15 – 17 ). Thus, the spin angular momentum naturally appears in classical electromagnetic fields ( 16 – 19 ) where it plays an important role in optical manipulation, light-matter interactions, information transfer, etc. ( 16 , 17 , 20 – 22 ). Despite such progress and thorough exploration of spin in various fields, this fundamental physical entity remains nontrivial and is described by rather abstract quantum mechanical and relativistic field theory concepts ( 1 – 7 ). Indeed, the “self-rotation” of the electron described by the Dirac spinors is far from an intuitively clear picture. Furthermore, the canonical momentum and spin densities in the field theory relation Eq. 1 are usually regarded as unobservable per se ( 4 – 6 ), and only their integral values matter. Although there is a number of rather sophisticated Lagrangian and Hamiltonian approaches to fluid dynamics and water waves ( 32 – 35 ), they do not provide a simple unified picture of momentum and angular momentum of surface gravity waves, and, in contrast to their electromagnetic and acoustic counterparts, these fundamental quantities are almost never mentioned in textbooks on fluid dynamics (see the Supplementary Materials) and do not typically appear in experimental observations. Here, we argue that the concepts of spin and kinetic/canonical momenta, originating from relativistic field theory, illuminate and accurately describe the observable dynamical properties of surface gravity waves. In this manner, electromagnetic waves are described by the complex vector electric and magnetic fields, E ( r ) and H ( r ), while acoustic waves are described by the complex vector velocity field v ( r ) and scalar pressure field p ( r ). In both electromagnetic and acoustic cases, the canonical momentum density P is determined by the quadratic form Im[ F * · ( ∇ ) F ] entirely similar to the probability current in quantum mechanics, i.e., the local “expectation value” of the canonical quantum mechanical momentum operator − i This provides the natural similarity between the canonical momentum Eq. 3 and de Broglie momentum in quantum mechanics. Now, substituting the above canonical momentum and spin densities into the Belinfante-Rosenfeld relation Eq. 1 and using the equations of motion for surface water wave fields, we obtain the kinetic momentum density Π = (ρ k /ω) Im( W * V ) (see the Supplementary Materials and Table 1 ). Its form is equivalent to the conserved water wave momentum derived by Peskin ( 46 ). It should be noticed that the energy and momentum conservation laws for water waves are rather nontrivial, because they essentially involve z integrals of generic time-dependent fields ( 46 ). These quantities are precisely described by the relativistic field theory construction by Belinfante-Rosenfeld ( 4 – 6 ), which underpins the spin and momentum of quantum and classical particles and fields. We have shown that the canonical momentum density in acoustic and water waves can be directly associated with the mass transfer due to the generalized Stokes drift, while the spin density originates from the mechanical angular momentum of the medium particles following microscopic elliptical trajectories. We have provided the direct observation of these drift and rotational dynamics of water particles in inhomogeneous gravity wave fields. Nonetheless, the presence of the (2 + 1)D space-time symmetries and microscopic mechanical description of the motion of the medium molecules in water wave fields allows one to obtain meaningful ( x , y ) momentum and z -directed angular momentum of water waves. These quantities involve z -directed spin and are exactly described by the Belinfante-Rosenfeld relation. This hints that the Belinfante-Rosenfeld relation has a more fundamental origin than relativistic field theory. Our results can have a multifold interdisciplinary impact.