Electrical Theory

AC Power: Single-Phase, Split-Phase and Three-Phase

Why homes get 120/240 V, why many businesses get 208 V or 480 V, and what the square root of 3 has to do with it.

Key takeaways
  • Alternating current reverses direction 60 times a second in North America.
  • “120 V” is an RMS value; the peak is about 170 V.
  • Homes usually get split-phase power: two 120 V legs that add to 240 V.
  • Three-phase wye systems give 120/208 V or 277/480 V because phase-to-phase voltage is √3 times phase-to-neutral.

The power from the utility is alternating current (AC): the voltage swings positive and negative in a smooth wave, 60 times every second in North America. How many of those waves you get, and how they are lined up, decides what voltages are available at your panel.

RMS: what “120 volts” really means

Because AC is always changing, we describe it with an effective value called RMS (root mean square). An AC voltage of 120 V RMS heats a resistor the same as 120 V of steady DC. For a sine wave, the peak is the RMS value times √2, so a 120 V circuit actually peaks near 170 V. Ordinary meters read RMS, which is why your outlet measures around 120 V.

Split-phase: how most homes are fed

A typical home service comes from a utility transformer whose secondary winding has a connection in the middle, called a center tap. The center tap becomes the neutral. Each end of the winding becomes a “leg” or “line”:

  • Either leg to neutral: about 120 V, for lights and receptacles.
  • Leg to leg: about 240 V, for ranges, dryers, water heaters, heat pumps and EV chargers.

The two legs are opposite each other, so their voltages add when you measure across both. People sometimes call this “single-phase three-wire”; it is still one phase from the utility, split in half.

L1NL2L1: 120 VL2: 120 VL1 to N = 120 V · L2 to N = 120 V · L1 to L2 = 240 V
A center-tapped transformer gives two 120 V legs that are opposite each other. Leg to neutral is 120 V; leg to leg is 240 V.

Three-phase power

Three-phase systems use three AC waves, each shifted one-third of a cycle (120°) from the next. The total power delivered stays very steady, which makes motors run smoothly and lets the same size wire carry more power. That is why commercial buildings, shops and farms with big pumps often have three-phase service.

Why 208 and 480 (the √3)

In a wye (Y) system, the three windings meet at a common neutral point. Measure from any phase to neutral and you get the “low” voltage. Measure between two phases and the waves are 120° apart, not opposite, so they don’t simply add. The math works out to the phase-to-neutral voltage times √3 (about 1.732):

  • 120 × 1.732 ≈ 208, so a 208Y/120 V system.
  • 277 × 1.732 ≈ 480, so a 480Y/277 V system. The 277 V is common for commercial lighting.
NABC120 V208 VCommon wye systems208Y/120 V: 120 × 1.732 ≈ 208480Y/277 V: 277 × 1.732 ≈ 480Phase to neutral: lights, receptaclesPhase to phase: motors, big equipment
In a wye system the three phases are 120° apart. Each phase to neutral is 120 V, but phase to phase is 120 × √3, about 208 V. The same math gives 277/480 V.

Why this matters

A piece of equipment rated for 240 V may underperform on 208 V. A heater, for example, puts out roughly 25% less heat at 208 V than at 240 V (power scales with voltage squared). Before any equipment is ordered for a commercial space, we check the nameplate against what the building actually has. Delta systems, high-leg services and power factor are topics for future articles.

Sources and further reading

  1. OpenStax, University Physics Volume 2, 15.2 Simple AC Circuits (RMS values)
  2. Michigan State University, Tech Note 220: Three-Phase AC Systems
  3. PDHonline, The Square Root of 3 in Three-Phase Systems (course E431)

Local rules decide. These articles explain general ideas and point to the code sections we use. They are not legal or engineering advice and don’t replace the code itself. California adopts the NEC with its own amendments, cities and counties can add more, and the local inspector (the AHJ, or authority having jurisdiction) has the final say on any job. Read the code free at NFPA’s free access page.