Find the current on the nameplate of the tool or appliance, in amps. If the nameplate gives watts, divide by 120: a 1,500 W heater draws 12.5 A, so read the 13 A row. Then go across to the first column at least as long as the cord. Each cell is the smallest gauge that passes both of the chart's checks, and any thicker gauge passes them too. The longest-cord table works the other way round, giving how far each gauge reaches at a given current.
The first check is the cord's rating. UL 817, the standard for cord sets, rates a finished extension cord separately from the ampacity of its wire. 16 AWG flexible cord is rated 13 A in NEC Table 400.5(A)(1), Column B, and a 16 AWG cord set is rated 13 A up to 50 ft but 10 A over 50 ft. A 14 AWG cord set is rated 15 A up to 50 ft and 13 A beyond, against 18 A for the wire. The plug and connector set the ceiling for the heavier sizes: with 15 A fittings (NEMA 5-15), a 12 or 10 AWG cord set is a 15 A cord at any length, though the wire itself is rated 25 or 30 A. So 16 AWG never appears in the 15 A row, and 14 AWG leaves it past 50 ft.
The second check is voltage drop. Current flows out on one conductor and back on the other, so the drop is 2 × I × R × L, with R taken from NEC Chapter 9 Table 8 for stranded copper at 75 °C. A 10 A load on 100 ft of 14 AWG cord loses 6.28 V, which is 5.23% of 120 V and over the chart's 5% limit. 12 AWG loses 3.96 V (3.30%), so that cell reads 12 AWG. Cord conductors are finer-stranded than the conductor Table 8 describes, so these resistances are an approximation for cords.
The 5% limit is this chart's chosen basis, not a code requirement. The NEC's 3% and 5% figures are informational notes for branch circuits and feeders in premises wiring; they are recommendations, and they don't address cords. A cord plugged into a receptacle adds its own drop to whatever the branch circuit already loses. For a tighter target, the longest-cord table shows the 5% reach, and the voltage drop calculator gives the drop for any length.
The cord's own marking decides. If the jacket or tag gives an amp rating, that is the cord's limit, whatever its gauge. The type letters describe its construction: S is extra-hard service (600 V), J is junior, or hard, service (300 V), W is outdoor (a sunlight-resistant jacket and wet-location conductors), T is thermoplastic, and O is an oil-resistant jacket, with OO meaning the jacket and the insulation both are. An SJTW cord is hard-service thermoplastic cord for outdoor use. The ratings table shows both columns of Table 400.5(A)(1). Column B is for two current-carrying conductors and Column A for three. The grounding conductor isn't counted as current-carrying, so an ordinary three-prong extension cord, two conductors plus a ground, uses Column B.
Cords have limits that no gauge changes. The CPSC says extension cords are for temporary use, advises cords marked for outdoor use outdoors and none under carpets, and advises 16 AWG or larger unless an 18 AWG cord has fuse protection, which is why the chart starts at 16 AWG. NEC 400.12 (2023) doesn't allow flexible cord as a substitute for fixed wiring, run through walls, ceilings, floors, doorways or windows, or attached to building surfaces or concealed.
For exact figures, use the voltage drop calculator: any current and length, at 120 V, 240 V or other voltages, and on 12 V or 24 V DC. It works from solid-wire resistance, a little lower than the stranded values here, so for the same cord its percentages come out slightly lower.