Feeder Calculator Guide: Core Formulas and Sizing Worked Examples

When sizing conductors for a subpanel or heavy load, a feeder calculator relies on the fundamental voltage drop equation to ensure your wire gauge can handle the current without starving the downstream equipment. The direct answer for standard single-phase sizing is the formula VD = (2 × K × I × L) / CM. However, plugging numbers into an online tool without understanding the underlying math, temperature assumptions, and unit conversions is how you end up with melted lugs or nuisance tripping.

This guide breaks down the exact physics of the feeder calculator formula, defines every variable, and walks through two complete worked examples with strict unit tracking so you can verify your own calculations on the bench or in the field.

The Core Feeder Calculator Formula & Symbol Definitions

The standard approximate voltage drop formula used in most basic feeder calculators is derived directly from Ohm’s Law (V = I × R), expanded to account for the physical dimensions and material properties of the wire. For single-phase circuits, the formula is:

VD = (2 × K × I × L) / CM

For balanced three-phase circuits, the multiplier changes from 2 (representing the hot and neutral/return path) to the square root of 3:

VD = (√3 × K × I × L) / CM

When This Formula Applies (and Its Assumptions)

This formula is an approximation that assumes a steady-state DC load or a balanced AC load with a power factor near 1.0. It ignores AC reactance (inductive and capacitive effects). According to ECMWeb's analysis of NEC voltage drop rules, this approximation is highly accurate for conductors smaller than 2/0 AWG. For larger feeders (e.g., 250 kcmil and above), AC reactance becomes significant, and you must use the exact impedance (Z) values from NEC Chapter 9, Table 9, factoring in the specific conduit type (PVC vs. steel) and power factor.

Furthermore, the K values of 12.9 (Copper) and 21.2 (Aluminum) assume an operating temperature of 75°C. If your terminals are rated for 90°C and the wire is THHN, the resistance increases slightly as the wire heats up, but 75°C remains the standard conservative baseline for terminal limitations.

Rearranged Forms for Wire Size, Length, and Current

A robust feeder calculator doesn't just solve for voltage drop; it solves for the missing variable when you are constrained by physical space or breaker sizing. Here are the algebraically rearranged forms:

• Solve for Wire Size (CM): Use this when you know your breaker size and run length, and need to find the minimum AWG.
  CM = (2 × K × I × L) / VD
• Solve for Maximum Length (L): Use this when you have a spool of wire and need to know how far you can run it before exceeding a 3% drop.
  L = (VD × CM) / (2 × K × I)
• Solve for Maximum Current (I): Use this when evaluating an existing feeder to see if it can handle a new piece of equipment.
  I = (VD × CM) / (2 × K × L)

Worked Examples with Unit Tracking

Let’s run two real-world scenarios. We will track the units through the math to prove the dimensional analysis holds up. A realistic answer magnitude for VD on a 120V/240V residential circuit is between 1V and 8V. If your calculator spits out "120V", you forgot a decimal point or used the wrong multiplier.

Problem 1: Finding Voltage Drop on an Existing Single-Phase Feeder

Scenario: You are feeding a detached garage subpanel with a 240V, 60A load. The one-way distance is 150 feet. You pulled 6 AWG Copper THHN wire. What is the voltage drop, and does it pass the 3% NEC recommendation?

1. Identify the variables:
   • K = 12.9 Ω·cmil/ft (Copper at 75°C)
   • I = 60 A
   • L = 150 ft
   • CM = 26,240 cmil (Looked up via NFPA NEC Chapter 9, Table 8 for 6 AWG)
2. Plug into the single-phase formula:
   VD = (2 × 12.9 × 60 × 150) / 26,240
3. Calculate the numerator:
   2 × 12.9 × 60 × 150 = 232,200
4. Divide by the denominator (CM):
   232,200 / 26,240 = 8.85 V
5. Unit Tracking Check:
   ( [Ω·cmil/ft] × [A] × [ft] ) / [cmil]
   The ft cancels out. The cmil cancels out. We are left with Ω × A, which equals Volts (Ohm's Law).
6. Calculate Percentage:
   (8.85 V / 240 V) × 100 = 3.68%

Verdict: At 3.68%, this exceeds the 3% recommended maximum for feeders. While not strictly a code violation in all jurisdictions (NEC 210.19(A) Informational Note suggests 3% for branch, 5% total), it is poor practice for a dedicated subpanel. You should upsize to 4 AWG Copper (41,740 cmil), which drops the VD to 5.56V (2.3%).

Problem 2: Sizing Wire for a Three-Phase Commercial Load

Scenario: You need to feed a 480V, 3-phase, 100A HVAC compressor located 300 feet from the switchgear. You want to limit the voltage drop to exactly 3%. What size Copper wire do you need?

1. Calculate the maximum allowable Voltage Drop (VD):
   480 V × 0.03 = 14.4 V
2. Identify the variables:
   • Multiplier = √3 (1.732) for 3-phase
   • K = 12.9 Ω·cmil/ft
   • I = 100 A
   • L = 300 ft
   • VD = 14.4 V
3. Use the rearranged formula to solve for CM:
   CM = (1.732 × 12.9 × 100 × 300) / 14.4
4. Calculate the numerator:
   1.732 × 12.9 × 100 × 300 = 670,284
5. Divide by VD:
   670,284 / 14.4 = 46,547.5 cmil
6. Unit Tracking Check:
   ( [Ω·cmil/ft] × [A] × [ft] ) / [V]
   Since V = Ω × A, the Ohms and Amps in the numerator cancel with the Volts in the denominator, leaving only cmil.
7. Select the wire size:
   Look at NEC Chapter 9, Table 8. You need a wire with at least 46,547 cmil. 4 AWG is 41,740 cmil (too small). 3 AWG is 52,620 cmil.

Verdict: You must pull 3 AWG Copper conductors. Always verify that 3 AWG is also rated for 100A in the ampacity tables (NEC 310.16) at your specific temperature column and conduit fill derating factors. In the 75°C column, 3 AWG THHN is rated for 100A, making it a perfect match.