Coherent field propagation is an essential computational tool in optics with applications ranging from computational optics and optical design to iterative field reconstructions. An improvement in the computational speed of current propagation methods is therefore highly desired. We describe a scalable angular spectrum (SAS) algorithm with zoom capability for numerical propagation of scalar wave fields in homogeneous media. It allows for propagation models where the destination pixel pitch is larger than the source pixel pitch, requires a computational complexity proportional to the cost of three successive fast Fourier transform operations of the input field, and it is valid for high numerical aperture (NA) propagation geometries. We find that SAS propagation approaches the precision of the computationally far more expensive angular spectrum method in conjunction with zero-padding. This was computationally confirmed by propagation examples. Finally, we discuss the validity of the proposed SAS method, derive practical bandlimit criteria, and state a limit for the propagation distance. The scalability, efficiency, and accuracy at high NA of our proposed wave propagation algorithm yield benefits for a large variety of forward and inverse modeling problems with the ability to apply automatic differentiation. (c) 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement