If you are asking "how many volts in three phase" based on a standard US commercial 120V line-to-neutral reading, the direct answer is 208 volts line-to-line. For a standard 277V line-to-neutral lighting system, the answer is 480 volts line-to-line. Three-phase is not a single voltage; it is a power delivery architecture. The universal conversion factor from line-to-neutral ($V_{LN}$) to line-to-line ($V_{LL}$) in a balanced Wye (star) system is the square root of 3 ($\sqrt{3}$, approximately 1.732). Substituting standard US nominal values into the formula: 120V_{LN} × 1.732 = 207.84V_{LL} (universally rounded to 208V on equipment nameplates).
The Core Conversion Formula and Neighboring Values
The assumption that fixes this answer is a balanced Wye (star) configuration with a solid neutral bond. In a Wye system, the three phase voltages are 120 electrical degrees out of phase with one another. Because they do not peak at the same time, you cannot simply add them together (120V + 120V ≠ 240V). Instead, you must use vector addition, which yields the $\sqrt{3}$ multiplier.
The formula is: $V_{LL} = V_{LN} × \sqrt{3}$
Utility voltages fluctuate. The National Electrical Code (NEC) and ANSI C84.1 standards generally allow a ±10% tolerance on utilization voltage, but extreme grid conditions can push this to ±20%. Here is how your line-to-line voltage shifts across a ±20% range of a nominal 120V line-to-neutral system:
| Line-to-Neutral ($V_{LN}$) | Multiplier | Line-to-Line ($V_{LL}$) | System Status |
|---|---|---|---|
| 96V (-20%) | × 1.732 | 166V | Severe Brownout (Motors will stall/burn) |
| 108V (-10%) | × 1.732 | 187V | Low Limit (ANSI Range B) |
| 120V (Nominal) | × 1.732 | 208V | Ideal Nameplate Rating |
| 132V (+10%) | × 1.732 | 228V | High Limit (ANSI Range B) |
| 144V (+20%) | × 1.732 | 249V | Severe Overvoltage (Electronics will fail) |
How the Answer Shifts: 120V Single-Phase vs. 230V vs. 3-Phase
Confusion usually stems from mixing up single-phase residential power with commercial three-phase power. Here is how the voltage landscape shifts depending on the service entrance:
- 120V (US Single-Phase): This is a line-to-neutral measurement from a standard residential split-phase 120/240V transformer. There is no $\sqrt{3}$ multiplier here because it is single-phase. Line-to-line is simply 240V.
- 230V / 240V (EU Single-Phase vs US Split-Phase): In Europe, 230V is the standard line-to-neutral single-phase voltage. In the US, 240V is the line-to-line voltage of a residential split-phase system. Neither is three-phase.
- 208V (US 3-Phase Wye): Derived from 120V line-to-neutral using the 1.732 multiplier. This is the standard for US commercial office buildings and retail spaces.
- 480V (US 3-Phase Wye): Derived from 277V line-to-neutral ($277 × 1.732 = 480$). This is the standard for US industrial facilities and large commercial HVAC systems.
According to Fluke's power quality guidelines, misidentifying a 208V 3-phase system as a 240V single-phase system is one of the most common causes of premature motor burnout in commercial retrofits. A 240V motor running on 208V operates at 13% below its rated voltage, causing it to draw excess current and overheat.
Decision Tree: Pinpointing Your Exact 3-Phase Voltage
Do not guess your system voltage based on the building type. Use this decision path at the panelboard to terminate in a concrete equipment selection.
| Step | Measurement / Observation | Result / Next Step |
|---|---|---|
| 1 | Measure Phase A to Neutral/Ground. | If ~120V, proceed to Step 2. If ~277V, you have a 480V Wye system. Stop. |
| 2 | Measure Phase A to Phase B (Line-to-Line). | If ~208V, you have a 120/208V 3-Phase Wye. Proceed to Step 3. If ~240V, you have a 240V 3-Phase Delta. Stop. |
| 3 | Verify Phase B to C, and Phase A to C. | All three should read ~208V. If one reads significantly higher (e.g., 208V, 208V, 240V), you have a High-Leg Delta. Stop. |
| 4 | Final Equipment Selection (for 208V Wye). | Concrete Pick: Order a 200V/208V-rated 3-phase motor (e.g., Baldor-Reliance CEVM2333) and use a 3-pole 208V-rated breaker (e.g., Eaton BAB3020). Do not install a 240V-only motor. |
When This Conversion Becomes Meaningless
The $V_{LN} × 1.732 = V_{LL}$ formula is a powerful tool, but it becomes entirely meaningless under three specific conditions:
- Delta Configurations: In a standard 240V Delta system, there is no neutral. The line-to-line voltage (240V) is identical to the phase winding voltage. Applying the 1.732 multiplier to a Delta line-to-line voltage to find a "phase voltage" is mathematically backwards for standard troubleshooting. (Note: In Delta, the $\sqrt{3}$ multiplier applies to current, not voltage: $I_{Line} = I_{Phase} × \sqrt{3}$).
- Severe Neutral Shift (Unbalanced Wye): If the neutral-to-ground bond is broken or the neutral busbar is corroded, the neutral point "floats." A heavily loaded Phase A might drop to 90V line-to-neutral, while an unloaded Phase B spikes to 145V line-to-neutral. The line-to-line voltage might still read 208V, but your $V_{LN}$ conversion will yield chaotic, mismatched numbers. As noted in Schneider Electric's power distribution guides, a floating neutral is an immediate fire and equipment hazard.
- Calculating Power (Watts) without Power Factor: If your actual goal is to find out "how many watts" are in a 3-phase system, knowing the voltage is only half the battle. The 3-phase power formula is $P = \sqrt{3} × V_{LL} × I_{Line} × PF$. If you do not know the Power Factor (PF) of the load (which is rarely exactly 1.0 for motors), any wattage conversion is meaningless.
FAQ: Three-Phase Voltage Quick Answers
Can I run a 240V 3-phase motor on a 208V 3-phase panel?
Generally, no. While some premium inverter-duty motors have a 208-230V nameplate rating, a standard 240V motor running on 208V will draw roughly 10-15% more amperage to produce the same mechanical work. This excess current trips thermal overloads and degrades winding insulation. If you must do this, you need to install a step-up transformer or use a Variable Frequency Drive (VFD) configured to output 240V from a 208V input.
Why do I read 0V between two phases on a 3-phase panel?
If your meter reads 120V from Phase A to Neutral, and 120V from Phase B to Neutral, but 0V between Phase A and Phase B, you do not have 3-phase power. You have a single-phase split-phase system (or a single-phase 120/208V tap) where both breakers are connected to the exact same phase leg. Move one breaker to an adjacent slot to land on the opposite phase busbar.
What is the "High Leg" or "Stinger" in a 3-phase system?
In a 240V Delta High-Leg system (common in older US commercial buildings), two phases read 120V to neutral, but the third phase (the wild leg, usually colored orange per NEC 110.15) reads 208V to neutral. The line-to-line voltage remains 240V across all three phases. Never connect a 120V single-phase load to the high leg; it will instantly destroy the equipment.
