No, and for good reason!
NEC is mainly concerned about wire safety. NEC prohibits using wires that are so small that they will overheat - and a great deal of effort goes into that, in the area of 310.15 and its numerous sub-sections, starting with (B)(16) (oh, there's over 20 sections now of just (B)).
For instance, #1 aluminum is good for 100A (assuming 75C wire and terminations). It's good for 100A whether the wire goes 3 feet or 3 miles. Consider a 1-foot segment of that cable. That segment will have the same resistance, and thus, at breaker-trip amperage, the same voltage drop and heat regardless of how far the cable goes. That is all NEC cares about.
NEC does not mandate voltage drop.
However, NEC makes an off-hand "informational note" that suggests in general service, you will get better results if you confine voltage drop over any segment to 3%, and systemwide (service point to outlet) to 8% overall. People wildly misinterpret that, and stupidly overspend on wire. Don't get suckered into that!
Try a thought exercise. I have a driveway 1/2 mile long and I want a 15-watt LED post light every 40', so 66 lights. 66 x 15 watts = 990 watts. Voltage drop over 1/2 mile is gonna be an issue, right? I select modern lights that work totally fine on any voltage from 90V to 306V (that's 100V Japan or 277V USA industrial, +/- 10%.) And then I feed 240V down #14 wire, because I'm Harper. What happens? The farthest light barely gets 100V*. It doesn't care, I don't care, and NEC doesn't care.
The People's Republic of Canada cares. They require "Nanny breakers" to protect you from yourself. You must size for 3% voltage drop, based on (pay attention here) either a) the actual load, or b) 80% of breaker trip. They never require you to size for breaker trip. So don't do that in your own calculations!
So in Canada if you had #1 aluminum going 250' (mind you the wire is good for 100A), you'd need a 70A Nanny Breaker to keep your voltage drop at 2.83% at 56A actual. In the USA you can just use a 100A breaker and "suffer" the 4.04% drop at 80A actual, which literally no appliance anywhere will care about even slightly.
So the rule in the USA is "don't take it to extremes" - if you are neglectful enough with voltage drop to cause serious problems, then you can get red-flagged under NEC 110.12 workmanship. But I'll have no trouble arguing the use-case for my 240V lighting circuit.
Your particular case
I went ahead and crunched your numbers into a voltage drop calc: 250' 120V 13A. Here's what I get for #12 wire:
- 14 AWG: 14.52% (nope)
- 12 AWG: 9.40% (yikes)
- 10 AWG: 5.68% (perfectly acceptable to me)
- 8 AWG: 3.74% (perfectly fine)
I would go straight for a transformer. Plug it into a 240V circuit and use a 240/120 isolation transformer to pump it down to 120V. In an informal toss-it-together scenario, this also gives you passive ground fault protection, in that the tool hot+neutral are totally isolated from ground. Try our numbers now (250', 240V, 6.5A)
- 14 AWG: 3.63% (and we're done)
I can't get it to give me 16 AWG, but that's probably acceptable too. So just daisy-chain 3 common extension cords, but change the plugs and sockets to NEMA 6-15.
1.5 KVA transformers, and even 5 KVA transformers, pop up on Craigslist from time to time.
* I'm "making this up" to show the principle: I haven't actually crunched the numbers, nor do I intend to.