Atrial fibrillation (AF) is the most common sustained cardiac arrhythmia, characterised by a rapid and irregular electrical activation of the atria. Treatments for AF are often ineffective and few atrial biomarkers exist to automatically characterise atrial function and aid in treatment selection for AF. Clinical metrics of left atrial (LA) function, such as ejection fraction (EF) and active atrial contraction ejection fraction (aEF), are promising, but have until now typically relied on volume estimations extrapolated from single-slice images. In this work, we study volumetric functional biomarkers of the LA using a fully automatic SEGmentation of the left Atrium based on a convolutional neural Network (SEGANet). SEGANet was trained using a dedicated data augmentation scheme to segment the LA, across all cardiac phases, in short axis dynamic (CINE) Magnetic Resonance Images (MRI) acquired with full cardiac coverage. Using the automatic segmentations, we plotted volumetric time curves for the LA and estimated LA EF and aEF automatically. The proposed method yields high quality segmentations that compare well with manual segmentations (Dice scores [ 0.93 ± 0.04 ], median contour [ 0.75 ± 0.31 ] mm and Hausdorff distances [ 4.59 ± 2.06 ] mm). LA EF and aEF are also in agreement with literature values and are significantly higher in AF patients than in healthy volunteers. Our work opens up the possibility of automatically estimating LA volumes and functional biomarkers from multi-slice CINE MRI, bypassing the limitations of current single-slice methods and improving the characterisation of atrial function in AF patients.