The common rafter is the basic sloped member of a framed roof, running from the wall plate up to the ridge. Its geometry falls out of the pitch: from a horizontal run to the ridge centre, the rise is run × (pitch/12) and the rafter length is run times the slope multiplier √(1 + (rise/12)²) — a 12 ft run at 6/12 rises 6 ft and needs a 13.42 ft rafter to the ridge centre, plus whatever eave overhang the design adds.
Checking a common rafter against code is a table exercise with one trap: the 2021 IRC prescriptive tables (R802.4.1) measure span along the horizontal projection of the rafter, not along the slope — the distance from wall plate to ridge support, which for a symmetric gable is half the building width. The everyday tables are built for No. 2 grade lumber in four species groups (Douglas fir-larch, hem-fir, southern pine, spruce-pine-fir) at 12, 16, 19.2, or 24 inches on center, and spacing buys span dramatically: a spruce-pine-fir 2x8 under the 30 psf snow table spans 17 ft 5 in at 12 in o.c. but only 12 ft 4 in at 24 in o.c. The prescriptive check assumes ceilings not attached to the rafters and rafter ties at the plate; anything outside the tabulated cases is an engineered design.