The iron-pnictide superconductors have a layered structure formed by stacks of FeAs planes from which the superconductivity originates. Given the multiband and quasi three-dimensional(1) (3D) electronic structure of these high-temperature superconductors, knowledge of the quasi-3D superconducting (SC) gap is essential for understanding the superconducting mechanism. By using the k(z) capability of angle-resolved photoemission, we completely determined the SC gap on all five Fermi surfaces (FSs) in three dimensions on Ba0.6K0.4Fe2As2 samples. We found a marked kz dispersion of the SC gap, which can derive only from interlayer pairing. Remarkably, the SC energy gaps can be described by a single 3D gap function with two energy scales characterizing the strengths of intralayer Delta(1) and interlayer Delta(2) pairing. The anisotropy ratio Delta(1)/Delta(2), determined from the gap function, is close to the c-axis anisotropy ratio of the magnetic exchange coupling J(c)/J(ab) in the parent compound(2). The ubiquitous gap function for all the 3D FSs reveals that pairing is short-ranged and strongly constrains the possible pairing force in the pnictides. A suitable candidate could arise from short-range antiferromagnetic fluctuations.