A long cord does not fail by catching fire. It fails by arriving weak. Every number here is the most a cord of that gauge and length can carry while still delivering usable voltage at the far end, in amps or in watts.
Set the run and the load. The answer is the smallest cord that keeps the sag under 3%, which is the number to use for anything with a motor in it.
The most a cord can carry at a 3% drop, the tight standard. Use this for anything that spins or compresses: saws, drills, pumps, compressors, refrigerators, pressure washers. These loads pull hard on startup and overheat when the voltage sags. Switch the table between amps and watts.
The same cords at a 5% drop, the looser standard most printed cord charts use. It is fine for loads that only make heat or light and do not care about a slightly soft supply: heaters, kettles, work lights, chargers, string lights. Do not use this table for a motor.
Appliances are labeled in watts, so read this one from the nameplate. Find your wattage down the side and the answer is the longest run that gauge can serve at a 3% drop. A 1500 W heater on a 12 gauge cord reaches 70 feet; on 16 gauge it will not run at all, at any length.
The same rule, read backwards. Find your load down the side, your run across the top, and buy that gauge or heavier. Remember that gauge numbers run backwards: 10 AWG is thicker than 14 AWG.
Watts divided by 120 gives amps, which is what the wire actually feels. A 1500 W heater is a 12.5 A load; a 15 A saw is an 1800 W load. Every watt figure here assumes a nominal 120 volts.
At 250 ft a 16 AWG cord pulling 10 A will not melt. It will deliver about 93 volts. A motor fed 93 volts draws extra current to make up the difference, runs hot, and dies young. The cord survives; the tool does not.
Every rating here assumes the cord is laid out flat. Left wound on a reel, a loaded cord traps its own heat and can run 20 to 30 °C hotter. If you cannot uncoil it, drop to the next heavier gauge.
Fifty feet plus fifty feet is a 100 ft run in this chart, with two extra connections that heat up and pull apart. Add the lengths, then look up the total.
The gauge is printed every few feet: 12 AWG 3/C SJTW means 12 gauge, three conductors, thermoplastic jacket, W for wet locations. Trust the print over the packaging.
Percent drop scales with voltage, so the same cord on a 240 V circuit carries twice the amps, and four times the watts, at the same percentage. Welders and RV feeds get far more reach for the copper.
A compressor or pump can pull three to six times its running watts for the first second. That surge is what a long thin cord turns into a stall, so size for the motor, not for the label.
4 and 2 gauge exist as welding cable and generator feeder, not as something with a molded 15 A plug on the end. Once the chart sends you there you are building a temporary feeder, which is a different job with different rules.
These figures are copper. Cheap copper-clad aluminum cords need roughly two gauge sizes heavier for the same job. If a 100 ft 12 gauge cord feels suspiciously light, it probably is.