Vd=2KIL/Cm or Cm=2KIL/Vd

Vd is voltage drop

2 is to account for the circuit length (there and back). The square root of 3 would be used if it were 3 phase, instead of 2.

K is a constant. 12.9 for copper, 21.2 for aluminium. Based on 75°C

I is the required amperage. For a feeder it can be calculated on the required load or the size of the protecting overcurrent device (the overcurrent device feeding the feeder panel)

L is the one way length of the run

Cm is the circular mils of the conductor

So....what size feeder conductor is required for 125A panel, a distance of 100 feet, 240 volts single phase with a 3% voltage drop? Let's assume a full load of 125 amps, and I threw in 25 extra feet (versus 75) for terminations.

Vd @ 3%=240 times .03=7.2 volts. This is how many volts we can lose.

Cm=2KIL/Vd

Copper: Cm=2(12.9)(125)(100)/7.2= 44792 Cm

Aluminium: Cm=2(21.2)(125)(100)/7.2= 73611 Cm

So we need a 44792 Cm Copper or a 73611 Cm Aluminium conductor to maintain a 3% voltage drop.

A #3 conductor is 52620 Cm, a #1 is 83690 Cm.

Those are the smallest conductors to use in order to maintain a maximum 3% voltage drop. Now, will they handle the 125 amps we're looking to get to the feeder panel?

Let's see what 310.15 (B)(16) says. And mostly likely you're going to be using THWN or XHHW conductors, so let's base it off that.

From the 75° column: Copper #2 @ 115 amps, Aluminium 1/0 @ 120 amps would be appropriate for a 125A panel.

Wait, what?

That can't be. Neither give me 125 amps? Ahh...but there is a 'next size up rule'. In easy terms, The next size higher standard overcurrent device can protect conductors (having an ampacity less than the protecting overcurrent device) IF 3 qualifiers are met.

The protected conductors are not part of a branch circuit supplying receptacles (they're not....it's a feeder circuit).

The ampacity of the conductors do not correspond to a standard amp rating of an overcurrent device

The next higher standard rating does not exceed 800 amps

So I can put a #2 copper or a 1/0 Al on a 125A breaker no problem. Do our conductors then handle the voltage drop we calculated?

Yes. The #2 Cu required for 125A is larger than the #3 we needed for voltage drop. The #1/0 Al we need for 125A is larger than the required #1 for Vd.

So now that we did the voltage drop calculation and comparison, the length makes the Vd irrelevant. (But you may want to consider up sizing the wire one size to help keep the lights in the hose from flickering when the air compressor starts.) I typically don't bother with voltage drop until it's over 150 feet. Even then it's based on the load, not the size of a panel. In other words, when have you seen a typical homeowner install a 125 or 150 amp panel in their barn and actually draw that many amps? Yes it happens but is rare.

To the OP (Maddog)

Are you feeding this barn sub-panel from your existing breaker panel in the house? Meaning you're going to put a breaker in the house panel to feed the barn. Can you get a 125A breaker to fit your house panel? If not and a 100A is the largest you can get to fit the house, then you're limited to 100 amps, no matter what size panel you put in the barn. Your main breaker in the barn will be a disconnect then, which is required for a detached structure anyways. (I'm assuming it's detached as I've never heard of a barn attached to a house, but hey it could happen :laugh

. Being a detached structure it'll require a grounding electrode system also. Driving 2 ground rods at least 6 ft apart, connected with the appropriate size grounding electrode conductor is the easiest.

I just wanted to clarify some things, not pointing fingers. FWIW, I have my Michigan's Master Electrical licence and been studying the NEC for over 15 yrs. BUT, keep in mind, I'm human and make mistakes too (hope my wife didn't hear that :laugh