The Cable Size Calculation Formula

Cable sizing is controlled by two independent formulas: one for ampacity (thermal limit) and one for voltage drop (performance limit). Each formula produces a minimum conductor size. You take the larger of the two.

This article walks through the formulas themselves. For the procedural walkthrough that shows how to apply them circuit by circuit, see How to Size a Cable: A Step-by-Step Walkthrough.

The voltage-drop formula

The standard DC-equivalent formula for resistive voltage drop in a cable run is:

V_drop = (2 × K × I × L) / A        [single-phase or DC]

Where:

The factor of 2 accounts for both the line conductor and the neutral (or return) conductor carrying current over the full length.

For three-phase circuits the return path is shared across three conductors, which reduces the effective resistance. The three-phase version is:

V_drop = (√3 × K × I × L) / A       [three-phase]

Because √3 is approximately 1.732, three-phase drops are about 13% lower than single-phase for the same conductor, current, and length.

The K constant: what it means and what values to use

K represents the resistivity of the conductor material expressed in circular-mil units. It appears frequently in the NEC and in engineering references as:

Aluminum's K is about 64% higher than copper's, which is why aluminum wire must be upsized compared with copper for equivalent voltage drop performance. For a full comparison of material tradeoffs, see Copper vs. Aluminum Wire.

These K values assume conductors at or near 75°C. At higher operating temperatures resistivity rises slightly, so the formula is slightly conservative at cooler temperatures and slightly optimistic at very high temperatures. For most design work the standard values are appropriate.

Solving for the required conductor area

In practice you set a voltage drop budget, typically 3% for branch circuits per NEC recommendations, and solve for the minimum conductor area that meets it:

A_required = (2 × K × I × L) / V_drop_max        [single-phase]

A_required = (√3 × K × I × L) / V_drop_max       [three-phase]

Where V_drop_max = (target percentage / 100) × supply voltage.

For example, 3% of 240 V = 7.2 V. For 3% of 480 V = 14.4 V. Once you have A_required in circular mils, you look up the next AWG size with a circular-mil area at or above that number.

Common AWG circular-mil areas for quick reference:

The ampacity side of the calculation

Voltage drop is a performance limit. Ampacity is a safety limit. The NEC defines ampacity as the maximum current a conductor can carry continuously without exceeding its temperature rating.

The starting point is the design current. For continuous loads (operating for 3 hours or more), NEC 210.19 requires sizing the conductor at 125% of the actual load:

I_design = I_load × 1.25     [continuous load]
I_design = I_load × 1.00     [non-continuous load]

With I_design in hand, you look up the minimum AWG that meets or exceeds that current in NEC Table 310.12 (or 310.16 for the full table), at the wire's temperature rating and in the applicable conditions.

For a detailed explanation of how to read those tables and when derating applies, see Ampacity Explained and Wire Derating: Temperature and Conduit Fill.

Worked example: single-phase, 30 A, 100 feet, copper

Voltage-drop check for 10 AWG (A = 10,380 circular mils):

V_drop = (2 × 12.9 × 30 × 100) / 10,380
V_drop = 77,400 / 10,380
V_drop ≈ 7.46 V  →  3.1% of 240 V

That is slightly over 3%. Solve for the required area:

A_required = (2 × 12.9 × 30 × 100) / 7.2
A_required = 77,400 / 7.2
A_required ≈ 10,750 circular mils

10 AWG at 10,380 is just under 10,750 circular mils, so it does not quite pass. 8 AWG at 16,510 circular mils passes comfortably:

V_drop = 77,400 / 16,510 ≈ 4.69 V  →  1.95% of 240 V

The ampacity check at 30 A puts the floor at 10 AWG. The voltage drop check requires 8 AWG. Use 8 AWG.

Worked example: three-phase, 30 A, 100 feet, copper

V_drop = (√3 × 12.9 × 30 × 100) / 10,380
V_drop = (1.732 × 12.9 × 30 × 100) / 10,380
V_drop = 67,008 / 10,380
V_drop ≈ 6.46 V  →  1.6% of 208 V (or 1.35% of 480 V)

Three-phase cuts the drop significantly. For a 208 V three-phase system, 6.46 V is about 3.1%, marginal. For a 480 V system, 6.46 V is about 1.35%, well within limits. The supply voltage matters as much as the formula values.

Applying derating factors

When conductors share a conduit with others or run in high-ambient-temperature environments, the base ampacity from the NEC table must be reduced by a derating factor (often written C_f or simply the NEC adjustment factor). The voltage drop formula does not change with derating. Only the ampacity floor changes. More detail is in Wire Derating: Temperature and Conduit Fill.

How to use the formulas together

  1. Calculate I_design from the load.
  2. Find the ampacity minimum AWG from NEC tables, after any derating.
  3. Calculate voltage drop for that AWG using the appropriate formula.
  4. If drop exceeds the target, solve for A_required and find the next AWG up.
  5. The final conductor size is whichever of the two checks gives the larger conductor.

A cable sizing calculator automates both checks and handles the circular-mil lookups, which is useful when comparing copper versus aluminum or evaluating several run lengths at once.

Conductor sizing should be verified against the current NEC and the code adopted by your local jurisdiction. These calculations are for planning and reference purposes. A licensed electrician should review all permanent installations.