Skip the math — use a voltage drop calculator.
The formula is easy enough: voltage drop = (2 × length × current × resistance per foot) / 1000. But you don’t need to memorize it. Just Google “voltage drop calculator” and plug in the numbers—gauge, length, amps, voltage.
If you want the manual way: for copper wire, each gauge has a known resistance per 1000 feet (e.g., 12 AWG is about 1.6 ohms/1000 ft). Multiply by your length (in feet) divided by 1000, double it for the round trip, multiply by the current (amps), and you get volts dropped. On a 120V circuit, a drop up to 3% (3.6V) is fine. Over 5% and you’ll notice dim lights or slow tools.
Reality check: for most extension cord uses under 100 feet with typical household loads (15A