Abstract A new wake surrogate model based on Reynolds-averaged Navier-Stokes (RANS) single rotor simulations is presented. The model relies on a series of three-dimensional pre-calculated deficit and added turbulence intensity flow fields, stored in a look-up table (LUT) as a function of the thrust coefficient and the ambient turbulence intensity. For any combination of these parameters, the flow around a wind turbine can be predicted by linearly interpolating within the look-up table. Furthermore, the resulting three-dimensional flow fields from different turbine sources can be superposed linearly to calculate the total wind farm flow. The model is implemented in PyWake and benchmarked against other, commonly employed engineering wake models, namely the Gaussian-Bastankhah, the N. O. Jensen and the Zong models, where RANS wind farm simulations are used as reference. In both full and partial wake cases, the surrogate model achieves a higher accuracy than any other model. Besides providing an accuracy comparable to a full RANS solution, the model can compute a flow case in the order of 1 s on a single processor. The main disadvantage is that the generation of the look-up table is time consuming, computationally expensive and can be memory demanding (especially if more inputs, such as the yaw misalignment angle, stability, etc. are added). Nevertheless, generating the LUT only has to be done once per wind turbine type.