3.3 Single-Phase, Three-Phase, and Voltage Systems

Read the system before choosing the formula

Many wrong exam answers are produced before the first calculator entry. The candidate sees kVA and voltage, grabs a familiar formula, and ignores whether the system is single-phase or three-phase. The NEC uses many system types, and the question may state the system directly: 120/240-volt single-phase, 120/208-volt three-phase, 277/480-volt three-phase, or another nominal system.

The first discipline is to identify what voltage the load actually uses. A 120-volt receptacle load is line-to-neutral on a grounded system. A 240-volt water heater on a dwelling service is line-to-line. A 208-volt three-phase load uses line-to-line voltage. A 277-volt lighting load on a 480Y/277-volt system uses line-to-neutral voltage. The label on the system tells you the available voltages, not always the voltage of every load.

Single-phase formulas

For a single-phase two-wire load:

VA = E x I

I = VA / E

For a single-phase 3-wire service or feeder, the same apparent-power relationship works when total VA and line-to-line voltage are used for a balanced two-line load calculation. For many NEC load calculations, you total the VA and divide by the service or feeder voltage that supplies the load.

Example: a single-phase 240-volt load is 12 kVA. Current is 12,000 / 240 = 50 A.

Example: a 120-volt load is 1,800 VA. Current is 1,800 / 120 = 15 A.

The trap is mixing the voltage. If the 12 kVA load is truly 240 volts, dividing by 120 gives 100 A, which doubles the correct line current. If the load is truly 120 volts, dividing by 240 gives half the correct current. Read the load connection, not just the service label.

Three-phase formulas

For balanced three-phase apparent power:

VA = 1.732 x Eline x Iline

Iline = VA / (1.732 x Eline)

The number 1.732 is the approximate square root of 3. It appears because three-phase line quantities are separated by 120 electrical degrees. On the exam, use 1.732 unless the question or calculator gives a square-root function and you prefer using sqrt(3). Do not use 3 in place of 1.732 for line current calculations.

Example: a 45 kVA three-phase load is supplied at 208 volts. What is the line current?

Convert kVA to VA: 45 kVA = 45,000 VA.

I = 45,000 / (1.732 x 208) = 45,000 / 360.256 = 124.9 A.

The practical answer is about 125 A before any code sizing rule is applied. A common distractor is 216 A, which comes from 45,000 / 208 and ignores the three-phase factor.

Common voltage systems

Do not assume every three-phase system has a neutral. Do not assume every 240-volt system is single-phase. Do not assume a high-leg delta allows ordinary 120-volt loads from every phase to neutral. When a question asks about a special system, the NEC rules and definitions become important; when it asks for current from kVA, the formula still depends on phase and voltage.

Line-to-line and line-to-neutral

A slash in a voltage rating usually shows line-to-neutral and line-to-line values on a grounded system. In 120/208 V, 120 is line-to-neutral and 208 is line-to-line. In 277/480 V, 277 is line-to-neutral and 480 is line-to-line. A three-phase motor rated 480 V uses line-to-line voltage. A lighting load rated 277 V uses line-to-neutral voltage.

Example: A 9,600 VA 277-volt lighting load draws I = 9,600 / 277 = 34.7 A. Do not divide by 480 because the luminaires are connected line-to-neutral. Example: A 30 kVA 480-volt three-phase load draws I = 30,000 / (1.732 x 480) = 36.1 A. Do not divide by 277 because the load is connected line-to-line across the three-phase system.

Balanced and unbalanced loads

The simple three-phase formula assumes a balanced load. NEC service and feeder calculations often total VA by category and then apply demand factors, neutral rules, or special load rules. A real panel may be unbalanced phase to phase. The exam will usually provide enough information to know whether it wants a balanced three-phase formula or a code load calculation workflow.

If a question gives separate phase currents or line-to-neutral loads, do not force everything into one balanced formula unless it tells you to. Add VA on each phase or follow the stated method. The word balanced is a strong signal that the standard three-phase formula is appropriate.

Calculator and rounding discipline

Write the denominator as one expression: 1.732 x voltage. Then divide VA by that denominator. Avoid entering 45 x 1000 / 1.732 x 208 without parentheses on a basic calculator, because left-to-right entry may multiply by 208 after dividing. Use this sequence: 45,000, divide, open or mentally compute 1.732 x 208, equals. On a four-function calculator, compute the denominator first, write it down, then divide.

Carry one decimal place unless the answer choices are far apart. NEC conductor and overcurrent sizing may require moving to the next standard size or using an ampacity table after the theoretical current is found. Do not round down a load current before applying a 125 percent rule or a table selection.

Exam traps

The largest trap is the missing 1.732. The second is using the wrong voltage from a slash-rated system. The third is treating kVA as amperes. The fourth is applying a motor horsepower conversion when the NEC directs you to motor full-load current tables. The fifth is confusing calculated current with permitted overcurrent protection. Theory gives the current; the NEC determines the installation requirement.