Introduction
The voltage-drop formula looks like alphabet soup at first glance — VD = 2 × K × I × L ÷ CM — but every symbol maps to something physical you can picture: how hard the current pushes, how long the road is, and how wide it is. Once you see that, the formula stops being a black box and becomes a tool you can reason with: longer run, bigger drop; bigger wire, smaller drop; more current, bigger drop.
The Wire Size Calculator evaluates this formula (alongside the ampacity check) for your inputs. This guide derives each term, shows where the constants come from, and works the math by hand in both imperial and metric units.
The Formula and What Each Term Means
VD = 2 × K × I × L ÷ CM
- VD — voltage drop in volts, the amount lost between source and load.
- 2 — the round trip. Current flows out on one conductor and back on the other; both have resistance. (For three-phase, this factor becomes √3 with line-to-line voltage.)
- K — the material constant: 12.9 for copper, 21.2 for aluminum (in Ω·circular-mil per foot), representing resistivity at operating temperature.
- I — current in amps, the actual load current (use 125% of continuous loads, per the sizing rules in the code-compliance guide).
- L — the one-way circuit length in feet. The 2 handles the return.
- CM — the conductor’s cross-section in circular mils. A circular mil is the area of a circle 0.001 inch in diameter — the traditional unit for wire area.
Where K comes from
K is just resistivity in convenient units. Copper’s resistivity at operating temperature works out to about 12.9 Ω·CM/ft; aluminum’s is about 21.2. The ratio (21.2 ÷ 12.9 ≈ 1.64) is why aluminum needs roughly 64% more cross-section — about one gauge size up — for the same drop.
The metric form
With area in mm² and length in meters, the same physics reads:
VD = 2 × K × I × L ÷ A, with K ≈ 0.0215 for copper (0.0353 for aluminum), L in meters (one-way), A in mm².
Circular Mils and mm² Reference
| AWG | Circular mils (CM) | mm² |
|---|---|---|
| 14 | 4,110 | 2.08 |
| 12 | 6,530 | 3.31 |
| 10 | 10,380 | 5.26 |
| 8 | 16,510 | 8.37 |
| 6 | 26,240 | 13.3 |
| 4 | 41,740 | 21.2 |
| 2 | 66,370 | 33.6 |
| 1/0 | 105,600 | 53.5 |
| 4/0 | 211,600 | 107 |
Worked Example: Hand-Calculating Voltage Drop
A 30A dryer circuit at 240V, one-way run of 20 m (65.6 ft), copper conductors. Check 10 AWG first (the ampacity minimum for 30A).
Step 1 — Imperial calculation. VD = 2 × 12.9 × 30 × 65.6 ÷ 10,380. Multiply: 2 × 12.9 = 25.8; × 30 = 774; × 65.6 = 50,774.4. Divide: 50,774.4 ÷ 10,380 = 4.89V. Percentage: 4.89 ÷ 240 = 2.04% ✓ (under 3%).
Step 2 — Try 8 AWG to see the effect. 8 AWG = 16,510 CM. VD = 50,774.4 ÷ 16,510 = 3.08V → 1.28%. Upsizing one gauge cut the drop by roughly 37%.
Step 3 — Metric cross-check. 10 AWG = 5.26 mm², L = 20 m, K = 0.0215: VD = 2 × 0.0215 × 30 × 20 ÷ 5.26 = 25.8 ÷ 5.26 = 4.90V → 2.04%, matching the imperial result (rounding accounts for the 0.01V difference).
Step 4 — What if the run were 40 m? Double the length doubles the drop: 4.90 × 2 = 9.80V → 4.08% — over the 3% guidance, forcing 8 AWG (9.80 × 10,380 ÷ 16,510 = 6.16V → 2.57% ✓). The formula’s linearity is the point: length and drop scale together.
Practical takeaway: the formula is most useful as a comparison tool — doubling length doubles drop, and each gauge step up cuts drop by about 37%. For the ampacity side of sizing, see the complete guide.
The Ampacity Formula (Table Lookup)
Ampacity has no neat equation — it’s a lookup in NEC Table 310.16, which lists allowable amps for each gauge at three temperature ratings. The logic behind the table: bigger wire dissipates heat better, and higher temperature ratings tolerate more heat. The calculator-side rules:
- Start from the column matching your termination temperature rating (usually 60°C residential).
- For derating (hot ambient, conduit fill), start from the 90°C column, apply correction factors, and the result must not exceed the termination column’s value.
- Continuous loads (3+ hours) are sized at 125% of the load current.
Mistakes in the Math
- Using round-trip length for L. L is one-way; the 2 covers the return. Doubling L doubles your answer wrongly.
- Reading CM from the wrong row. Off-by-one gauge in the area table skews results by ~60%.
- Using copper K for aluminum. 12.9 vs 21.2 — the wrong constant hides a real problem.
- Computing drop at the breaker rating instead of the load. A 20A circuit carrying 12A drops voltage for 12A — but size the wire for the full rated load for safety margin.
- Forgetting the 125% continuous-load rule. A 16A continuous load is sized and checked as 20A.
- Percentage against the wrong voltage. Drop percent is relative to the circuit voltage (120V or 240V), not the other.
The common mistakes guide covers the non-math errors too.
Related Guides
- Complete Guide — ampacity, voltage drop, and the full sizing workflow.
- Pro Tips — practical sizing judgment from the trade.
- Code Compliance — derating rules and continuous-load requirements.
- Sizing Checklist — verify every calculation step.
- FAQ — quick answers to the most asked questions.
Frequently Asked Questions
What does the “2” in the voltage drop formula mean?
It accounts for the round trip: current travels out on one conductor and back on the other, so the total resistance is twice a single conductor’s. L stays one-way.
What is K in the voltage drop formula?
The material constant: 12.9 for copper, 21.2 for aluminum (Ω·CM/ft). In metric form (mm², meters), K ≈ 0.0215 for copper and 0.0353 for aluminum.
What is a circular mil?
The area of a circle 0.001 inch in diameter — the traditional unit for conductor cross-section. 12 AWG = 6,530 CM; 10 AWG = 10,380 CM.
How do I calculate voltage drop percentage?
Divide the volt drop by the circuit voltage and multiply by 100. A 4.89V drop on a 240V circuit is 2.04%.
Is voltage drop linear with length?
Yes — double the one-way length and the drop doubles. That’s why long runs are the main trigger for upsizing wire.
Why does the metric formula use a different K?
Same physics, different units: K converts resistivity into whatever length/area units you use. 12.9 Ω·CM/ft and 0.0215 Ω·mm²/m describe the same copper.
Get Your Number
The formula rewards intuition: current, length, and resistance each push the drop up; cross-section pushes it down. Work it by hand once, then let the Wire Size Calculator do it instantly — paired with the ampacity check — for every circuit you plan. And as always with electrical work, have a licensed electrician review the final design.
Disclaimer: Calculator results are planning estimates based on the values you enter. Formula results assume standard resistivity constants; actual installations must account for derating, terminal temperature ratings, and local code requirements. Electrical work is regulated in most jurisdictions; consult a licensed electrician and your local authority having jurisdiction (AHJ) before installing or altering wiring.
