A deck beam sits on posts and carries the joists. How far apart the posts can be depends on the beam size, the species and how much joist span the beam picks up. The charts reproduce AWC DCA 6 Table 3A for dimension lumber beams and Table 4 for 6x6 post heights and footing sizes.
Reading the beam table
Find the beam (for example 2-2x10, two 2x10s nailed together) under your species group, then read across to the column at or above your joist span. The value is the maximum beam span LB, the distance between post centres. A 2-2x10 Southern Pine beam under 12 ft joists spans 7'-1"; the same beam in the Douglas fir and northern species group spans 5'-8".
Southern Pine has its own column set. Douglas fir-larch, hem-fir, SPF, redwood, western cedars, ponderosa pine and red pine share one, which also lists 3x and 4x solid beams.
Cantilevers and assembly
A beam may extend past its end post by up to LB/4. Built-up beams are nailed or screwed together in the pattern DCA 6 shows in Figure 4, and 3-ply beams must sit in a post cap rather than a notch. Never bolt a beam to the side of a post without a notch or a cap.
If joists hang from the side of the beam, the beam must be at least as deep as the joists.
Posts
DCA 6 requires 6x6 posts minimum. Table 4 limits their height by beam span, joist span and species; 8x8 posts may substitute anywhere up to 14 ft. Corner posts taller than 2 ft get diagonal bracing parallel to the beam.
Footings
Table 4 sizes footings for 1,500 psf soil and 2,500 psi concrete, from an 18" round (16" square, 7" thick) for a short beam span and short joists up to a 42" round for 18 ft on 18 ft. Corner posts may use 90% of the listed size. Every footing bears on undisturbed soil at least 12" down or below your frost line, whichever is deeper.
concrete per footing (cu ft) = π × (diameter ÷ 24)² × thickness ÷ 12 80 lb bag ≈ 0.6 cu ft