Three Phase Power Calculator

The voltage is the same but the load is not, and that difference is worth several thousand watts. A single-phase 208 V load connected across two of the three lines draws current in one pair of conductors and its power is simply volts times amps times power factor. A three-phase 208 V load uses all three, and its power is √3 times larger for the same current in each line. A shop heater sold as 208 V single-phase and one sold as 208 V three-phase have the same nameplate voltage and completely different breakers.

From the 120° between the phases, through a piece of trigonometry you can do on paper. Two line-to-neutral voltages of equal size separated by 120° subtract to give the line-to-line voltage, and the magnitude of that difference is 2 × sin 60°, which is √3. Everything else follows: 277 V × 1.732 is 480 V, 120 V × 1.732 is 208 V, and the 240 V delta with a center-tapped winding produces its notorious high leg at 208 V to neutral for exactly the same reason. It is a consequence of measuring between two rotating vectors rather than an extra term in the physics.

Line current, always — it is what the conductor feeding the motor carries and what the overload device sees. The winding current inside a delta-connected motor is smaller by √3 and is not a figure you can measure without opening the machine, which is why no plate states it. This matters on a wye-delta starter, where the motor runs delta and starts wye, and the starting current is a third of what the same motor would pull thrown straight across the line.

Because doubling the voltage of the same motor halves its current at the same output power, and no √3 enters that ratio — both columns are three-phase, so the factor is already in both and cancels. The same arithmetic sets the rest of the table: the 200 V column is 1.15 times the 230 V one, the 208 V column 1.10 times, and the 575 V column 0.8 times the 460 V. Those four relations hold across every filled cell of the table, which is how the transcription behind this chart was verified rather than trusted.

Third-harmonic current, which adds in the neutral instead of canceling there. On a balanced linear wye load the three fundamental currents are 120° apart and sum to zero at the neutral, which is the whole reason a neutral can be sized smaller in some systems. The third harmonic of each phase, however, lands in phase with the other two, so three equal harmonic currents arrive at the neutral and add arithmetically. A panel full of switch-mode supplies, LED drivers and single-phase electronic loads can put more current in the neutral than in any phase. This page does not compute it: measuring with a true-RMS clamp on the neutral itself is the only honest way to know.

No, and doing it anyway inflates the answer by 73 %. A load between two lines of a three-phase system is a single-phase load: it has one voltage, one current and no √3 in its power. Use the single-phase arithmetic instead, and note that its current returns on the second line rather than on a neutral, so a 208 V two-pole circuit loads two phases of the panel and not one.

Because those two cells of Table 430.250 could not be confirmed against the ratio the rest of the 575 V column obeys, and an interpolated one would look exactly as convincing as a correct one. Every other figure in the chart was verified twice, against a neighboring column and against the column's own ratio. Two of them were not, so they are blank and the page says to read them from the code book — that current sizes a conductor, a disconnect and a short-circuit protective device, and a plausible wrong number there is worse than no number.