A model for Quick Load Analysis of Floating wind turbines (QuLAF) is presented and validated here. The model is a linear, frequency-domain, efficient tool with four planar degrees of freedom: floater surge, heave, pitch and first tower modal deflection. The model relies on state-of-the-art tools from which hydrodynamic, aerodynamic and mooring loads are extracted and cascaded into QuLAF. Hydrodynamic and aerodynamic loads are pre-computed in WAMIT and FAST, respectively, while the mooring system is linearized around the equilibrium position for each wind speed using MoorDyn. An approximate approach to viscous hydrodynamic damping is developed, and the aerodynamic damping is extracted from decay tests specific for each degree of freedom. Without any calibration, the model predicts the motions of the system in stochastic wind and waves with good accuracy when compared to FAST. The damage-equivalent bending moment at the tower base is estimated with errors between 0.2% and 11.3% for all the load cases considered. The largest errors are associated with the most severe wave climates for wave-only conditions and with turbine operation around rated wind speed for combined wind and waves. The computational speed of the model is between 1300 and 2700 times faster than real time.