Use 12-gauge or thicker for a 15-amp miter saw at 50 feet.
12 AWG is the minimum. 10 AWG is better if you can find it without spending a fortune.
Here’s the deal: a 15-amp miter saw draws close to the full circuit rating, and electric motors have a high startup surge. At 50 feet, voltage drop becomes real. 14-gauge cord will work—briefly—but it’ll heat up, drop voltage, and could trip breakers or damage the saw over time. I’ve seen 14-gauge cords get noticeably warm with a big miter saw.
Stick to 12 AWG for anything near 15 amps at 50 feet. If you want a margin of safety and less voltage drop, go up to 10 AWG. The price difference isn’t huge, and you’ll never regret having a heavier cord.
Don’t cheap out on extension cords for power tools.