The manufacture of highly complex and accurate part geometries with reduced costs has led to the emergence of hybrid manufacturing technologies where varied manufacturing operations are carried out in either parallel or serial manner. One such hybrid process being currently developed is the iAtractive process, which combines additive (i.e. fused filament fabrication, which is sometimes called fused deposition modelling. However, the latter term is trademarked by Stratasys Inc. and cannot be used publicly without authorisation from Stratasys) and subtractive (i.e. computer numerical control machining) processes. In the iAtractive process production, operation sequencing of additive and subtractive operations is essential. This requires accurate estimation of production time, in which the fused filament fabrication build time is the determining factor. There have been some estimators developed for fused deposition modelling. However, these estimators are not applicable to hybrid manufacturing, particularly in process planning, which is a vital stage. This article addresses the characteristics of fused filament fabrication technologies and develops a novel and rigorous method for predicting build times. An analytical model was first created to theoretically analyse the factors that affect the part build time and was subsequently used to facilitate the design of test parts and experiments. The experimental results indicate that part volume, interaction of volume and porosity and interaction of height and intermittent factor have significant effects on build times. Finally, the estimation algorithm has been developed, which was subsequently evaluated and validated by applying a wide range of identified influential factors. The major advantage of the new proposed algorithm is its ability to estimate the build time based on simple geometrical parameters of a given part. The key factors that drive the algorithm can be directly obtained from part dimensions/drawings, providing an efficient and accurate way for fused filament fabrication time estimation. Test part evaluations and analysis have clearly demonstrated that estimation errors range from 0.1% to 13.5%, showing the validity, capability and significance of the developed algorithm and its applications to hybrid manufacture.