Sources & Math

Ohm's Law

V

Volts. The electrical pressure across the thing you're looking at.

I

Current, in amps. The letter is I because the old term was "intensity of current," which is why it isn't a C.

R

Resistance, in ohms: how hard that path fights the current.

P

Power, in watts: the work actually getting done.

Mathematics. Know any two of them and the other two fall out. Every version on the wheel is just V = I · R and P = V · I with one substituted into the other.

Voltage Drop

Vd

The volts you lose getting down the line. This is loss caused by the run itself, not voltage the load is using and not sag from a loaded pot.

K

How hard that metal fights current: copper 12.9, aluminum 21.2 (ohm-cmil/ft). Divide K by CM and you've got that wire's ohms per foot.

I

The amps actually flowing in that conductor. Not the breaker size, not the transformer rating: the real, measured load.

L

One-way length in feet, source to load. Measure it the way you'd pull it: pot to house, not out and back. The formula handles the trip back.

CM

The conductor's cross-section in circular mils, set by its size. #2 AWG is 66,360 cmil, 4/0 is 211,600. Bigger number, less drop.

2 and √3

Single phase, the current goes out and comes back, so it travels twice your one-way run: that's the 2. Balanced three phase has no separate return path, and when you work from line-to-line voltage the math lands on √3 (1.732) instead.

Source: K is the trade-standard rounding of NEC Chapter 9, Table 8: resistance at 75 °C, stranded, times circular mils, divided by 1000, lands between 12.82 and 12.90 for copper and between 21.15 and 21.23 for aluminum across every size this calculator offers. The circular-mil areas come from that same table, and the AWG sizes also check out against the AWG law, d = 5 · 92^((36−n)/39) mils. The 3 % branch / 5 % total guidance the panel mentions is the NEC's own recommendation, not a rule.

XFMR Full Amps

I

Full-load amps. The most current the windings can carry based on the nameplate kVA. Past this you're into overload territory.

kVA · 1000

The nameplate rating converted into plain volt-amps. kVA is thousands of volt-amps, so the 1000x just gets everything down to base units for the formula. A 50 kVA pot is 50,000 volt-amps.

V
Single Phase

The voltage across the winding you're solving for. If the primary wiring is a wye config on a 7,200/12,470 system, you would use 7200. If it's delta it's phase to phase. A delta topside, or phase-to-phase pot for this voltage uses 12470. On the secondary, use 240 for finding the full secondary rating or 120 for half of it.

V_LL
Three Phase

Always phase to phase, the line-to-line voltage: 208, 480, 12470. Three-phase gear is rated line-to-line by convention, so that's what the formula expects.

√3

The bank's kVA is spread across three phases whose voltages sit 120° apart, which is exactly why line-to-line reads √3 (1.732) times phase-to-ground. Since the formula takes that line-to-line number, the √3 has to sit in the denominator, or your answer comes out 1.732 times too big.

Mathematics, and the whole thing is one sentence: a transformer is rated in volt-amps, so divide the volt-amps by the volts and what's left is the amps.
A 50 kVA pot on 7200 carries 50,000 / 7200 = 6.9 amps on the primary, and 50,000 / 240 = 208 amps out the 240-volt secondary. Same 50 kVA, both sides, which is the point.

Pri / Sec Amps

V₁ · I₁

Volts and amps on the primary: the high side.

V₂ · I₂

Volts and amps on the secondary: the low side.

Mathematics: apparent power in equals apparent power out. A transformer doesn't make power, it trades volts for amps. Knock the voltage down by thirty times and the current climbs by thirty times, which is how a handful of amps on the primary becomes a couple hundred on the secondary.

Turns Ratio

a

The ratio itself. A 7200-to-240 pot is 30 to 1, so a = 30.

N₁ · N₂

Turns of wire wound on the primary coil and on the secondary coil.

V₁ · V₂
I₁ · I₂

Volts and amps on each side, primary first.

Mathematics. Notice the current ratio is flipped: I₂ over I₁, not I₁ over I₂. More turns on a side buys you more volts and fewer amps there, and that trade is the whole reason the ratio matters.

Wire Ampacity

Ampacity is the most current a conductor can carry continuously without heating itself past its temperature rating. It isn't a property of the wire by itself: it depends on how fast the surrounding air hauls the heat away, which is why an honest table has to state the conditions it assumed. This is a lookup, not a formula. Here is the basis behind every number in it:

75 °C
conductor

How hot the metal itself is allowed to get, 167 °F.

25 °C
ambient

The air temperature assumed around it, 77 °F. A 100 °F day is not this, and the conductor's ampacity degrades.

2 ft/s wind

A light crosswind, about 1.4 mph, doing the cooling. Dead-still air cools less, so the conductor carries less than the table says.

full sun
0.5 / 0.5

0.5 emissivity (how well it sheds heat) and 0.5 solar absorption (how much sun heat it takes on).

sea level

Thinner air at higher altitudes cools the conductor less.

Bare overhead conductor tables, 47 values across four families, all published on that one basis.

Source: Southwire catalog sheets: ACSR sheet 11-4, AAC sheet 11-2, the AAAC-6201 bare overhead spec, and SPEC 80150 for bare copper. The copper values are additionally cross-checked against Priority Wire & Cable #1110-01; the two vendors publish identical numbers on the identical basis. Real weather and conditions derate these numbers.

Service Wire Size

Two steps, and no formula of its own: work out the full-load amps with the XFMR Full Amps math above, then look up the smallest conductor rated to carry them. The lookup has two install modes, and the panel opens on OVERHEAD. FROM AMPS skips the first step entirely: it sizes wire for an amps number you already trust, like a service rating, a measured demand, or the electrician's load calc. Working out the load itself is NEC Article 220 territory, the electrician's calculation; the panel sizes wire for a number you bring.

OVERHEAD

Triplex or quadruplex hung on a messenger. The insulated phases spiral around the bare neutral, and that neutral is the messenger carrying the weight of the span. NEC Table 310.20 is the messenger table: 75 °C conductors at 40 °C ambient, still air. Vendor drop-cable sheets rate higher because they assume a 2 ft/s wind; the NEC number is the citable, conservative one.

UNDERGROUND

In conduit or direct buried. NEC Table 310.16, 75 °C conductors at 30 °C ambient. Buried conduit counts as raceway and direct burial is named right in the table's title, so one table covers both underground service styles. It is the lower of the two tables, so it is also the conservative answer when in doubt.

CONTINUOUS
×1.25

A load that runs 3 hours or more. The NEC requires conductors at 125 percent of a continuous load (NEC 230.42 for service conductors), so in FROM AMPS mode the panel multiplies your number by 1.25 when you flip this on. Skipping that step is how services get red-tagged.

75 °C column

The temperature rating the charts work from. It isn't only about the wire: the lugs and gear the wire lands on carry their own ratings as well, and a circuit is governed by the lowest-rated piece in it.

no derates
applied

The table value is your starting point, before corrections for hot ambient or for bundling several current-carrying conductors together. Those are yours to apply per NEC 310.15.

Source: OVERHEAD is NEC Table 310.20, 24 values for copper and aluminum, checked against two independent published copies that agree exactly: the 1999 edition, where it is Table 310-20, and a current reprint of the same table. The 2023 edition carries it unchanged. UNDERGROUND is the 75 °C column of NEC Table 310.16, 24 values, checked against the 2023 edition; the same values appear in 2017 and 2020. Ahead of the service point the drop belongs to the utility and the NESC, not the NEC; this panel sizes the customer side.

Ferroresonance

Ferroresonance is what happens when a transformer's magnetizing core and the capacitance of the line feeding it start swapping energy back and forth on their own. It shows up as voltages well above normal, overheating, and it is most often kicked off by switching one phase at a time on certain banks. Underground runs a higher risk because of cable capacitance.

This is the one panel that is deliberately NOT a lookup and not electrical science-backed. There is no published table that scores a bank's ferroresonance risk, so this panel is something I came up with.

Sag & Tension

D

Sag, in feet: how far the low point of the span hangs below a straight line drawn between the two attachment points.

w

How much one linear foot of the conductor weighs.

L

Span length in feet, structure to structure. Sag follows the square of it: double the span at the same tension and you get four times the sag.

T

Horizontal tension in the conductor, in pounds. Pull it tighter and the sag drops, while everything else in that span goes up.

RS · ℓ

Ruling span: the single equivalent span that stands in for a whole multi-span, dead-end to dead-end section, so unequal spans can be sagged off one number. ℓ is each individual span in the section, and Σ just means add them all up.

t · d

Radial ice thickness and bare conductor diameter, both in inches. Ice builds all the way around, so an iced conductor measures d + 2t across.

psf

Wind pressure in pounds per square foot, taken from your loading district.

w'

The loaded weight per foot. Ice pulls straight down and wind pushes sideways, so the two combine like the legs of a right triangle instead of simply adding, and then the district's K constant gets added on.

K

The NESC district constant from the table below, in lb/ft.
NOTE: this is not the same K from the voltage-drop formula up the page. Same letter, unrelated job.

The parabola and ruling span are mathematics. The loading districts are NESC Table 250-1 (Rule 250B), unchanged from the 1997 through the 2023 editions:

Source: NESC Table 250-1 as published in RUS Bulletin 1724E-200 (reprinting IEEE C2-2012) and RUS Bulletin 1724E-153, Exhibit A (1997 NESC). The panel deliberately does not model the district temperatures; sag from temperature change is a different calculation.

kVAR Sizing + Cap Test

Q

Reactive power, in kVAR: the size of the capacitor you need. Reactive power is what magnetizes motors and transformers. It does no work, but it still shows up as current your conductors have to carry.

P

Real power of the load, in kW.

PF₁ · PF₂

The power factor you have now, and the power factor you're aiming for.

acos · tan

acos turns a power factor back into its phase angle, and the tangent of that angle is the ratio of reactive power to real power. Take the difference between where you are and where you want to be, and that's the kVAR you need to add with capacitors.

C · Xc

Capacitance in farads and capacitive reactance in ohms: what a healthy unit should read on a meter.

V · f

The voltage across the capacitor and the system frequency, 60 Hz here.

All mathematics. The test range dresses it in field judgment: per IEEE Std 18-2012 a healthy new unit delivers not less than 100 % and not more than 110 % of rated kVAR at rated voltage and frequency, so it should never meter under the computed capacitance. The default ±10% range is the common field cutoff: low means lost elements or blown internal fuses, and a shorted series group jumps capacitance well past the higher range. The tolerance is adjustable, and your system's acceptance spec wins over the default.

Wire Diameter

cmil

Circular mils, the conductor's area. A mil is a thousandth of an inch, and circular mils are a shortcut for area: square the diameter in mils and that's your area, no π and no radius. A wire 100 mils across (0.1 inch) is 100 × 100 = 10,000 cmil. Squaring a diameter gets you the area, so square-rooting an area gets you back to a diameter, which is all the formula is doing.

strands

How many individual wires are wrapped up to make the conductor. Each carries an equal share of the area.

layers

Concentric layers wrapped around the center strand: 1 layer is 7 strands, 2 layers is 19, 3 layers is 37. Straight across the finished conductor you cross (2 · layers + 1) strands, and that's where the OD formula comes from.

OD

Overall diameter of the finished conductor, in mils.

Every listed diameter re-derives from its own stranding geometry. Areas and stranding follow the vendor catalog sheets above and the AWG law; concentric-lay construction is per the ASTM B-8 family of specs.

The documents

• NFPA 70, the National Electrical Code: Table 310.16 and Chapter 9 Table 8. 2023 edition checked. Free read-only access at nfpa.org.
• The National Electrical Safety Code, IEEE C2: Rule 250B, Table 250-1, via the public federal reprints linked in the sag section. The standard itself is at standards.ieee.org.
• Southwire bare overhead catalog sheets (ACSR 11-4, AAC 11-2, AAAC-6201, and SPEC 80150 bare copper, revision 1.000.003).
• Priority Wire & Cable, Stranded Bare & Tinned Copper, #1110-01, 01-2024 printing.
• USDA Rural Utilities Service Bulletins 1724E-152, 1724E-153 and 1724E-200.
• IEEE Std 18-2012, Standard for Shunt Power Capacitors.
• ASTM B258 (AWG areas) and the ASTM B-8 family (concentric-lay stranding).

Editions and revisions are as I last checked them on 08-27-2026. Standards bodies revise; if you find a newer edition that changes a number here, I want to know: info@digitalapprentice.net.

What this app is, and is not

Lineman's Calculator is field shorthand: the math a journeyman has to call a buddy about, done faster and with the sources and math shown. It is not an engineering study and it does not know your system. Your utility's or employer's standards, the codes and editions adopted where you work, the nameplate in front of you, and your own qualification all come first. When any of them disagree with this app, they win, every time.