Pick a calculation mode, choose the connection type, enter your known values, and click Calculate.
Real (P), reactive (Q), and apparent (S) power form the power triangle: S² = P² + Q². A lower power factor means a larger reactive-power slice for the same real-power output.
Results are engineering estimates. Balanced three-phase formulas, Wye/Delta phase relationships, and the current/voltage-unbalance percentage definition have been confirmed against IEEE and NEC references. Actual system behavior varies with real-world conditions. Verify with a licensed electrician before any electrical work.
Common North American three-phase line-to-line voltages, and typical power factor ranges by load type — starting points only, always prefer a nameplate or measured value.
| Common Line Voltage | Typical Context |
|---|---|
| 208 V | Commercial buildings (Wye, 120/208V) |
| 240 V | Small commercial (Delta, 120/240V) |
| 480 V | Industrial motors and equipment (Wye, 277/480V) |
| 600 V | Heavy industrial, some Canadian standard |
| Load Type | Typical Power Factor |
|---|---|
| Resistive heating / incandescent lighting | ≈1.00 |
| Fully loaded induction motor | 0.85 – 0.90 |
| Lightly loaded induction motor | 0.60 – 0.80 |
| Mixed industrial/commercial (unknown) | 0.85 (common placeholder) |
Three real-world scenarios, one per mode. Click "Load This Example" to run it in the calculator above.
The balanced three-phase power formula
Using line quantities, real power P = √3 × line-to-line voltage × line current × power factor. Apparent power S = √3 × line-to-line voltage × line current (no power factor applied), and reactive power Q = S × sin(φ), where φ is the angle whose cosine is the power factor. These three values form the power triangle: S² = P² + Q². This relationship holds for both Wye and Delta connections when using line (not phase) voltage and current.
Wye (Star) vs. Delta
In a Wye connection, the three phase windings share a common neutral point; phase voltage is the line-to-line voltage divided by √3, while phase current equals line current. In a Delta connection, the windings form a closed loop with no neutral; phase voltage equals line-to-line voltage, while phase current equals line current divided by √3. Wye is common in commercial/industrial distribution (e.g. 277/480V), where the neutral supplies single-phase loads; Delta is common in some industrial and utility contexts and in motor winding configurations.
Power factor and the power triangle
Power factor is the ratio of real power to apparent power, and reflects how much of the supplied current does useful work versus how much is exchanged with the system's magnetic fields (reactive power) without being consumed. Resistive loads run near unity power factor; inductive loads like motors and transformers pull the power factor below 1.0, increasing the apparent power (and therefore the current) needed to deliver the same real power. A lower power factor means a wider angle φ and a larger reactive-power leg of the triangle.
Understanding current vs. voltage imbalance
Current imbalance across phases is common and usually benign in origin — it simply means single-phase loads (lighting, receptacles, small equipment) aren't perfectly evenly distributed across the three phases of an otherwise healthy, balanced supply. NEMA/IEEE guidance treats meaningful current unbalance (commonly flagged above roughly 5–10%) as worth correcting because it increases losses and uneven heating, but it is not itself evidence of a supply fault. Voltage imbalance is different in kind: it means the supply voltage itself differs measurably from phase to phase, which points to a wiring, connection, or utility-side issue rather than normal load distribution, and is generally treated as a condition to investigate and verify with a meter before relying on the circuit as designed.
When to use each mode
Use Balanced for planning and sizing work where the supply and load are both assumed even — the normal case for new circuit design. Use Unbalanced Current when auditing an existing panel or feeder where you've measured different currents per phase but the supply voltage itself is sound. Use Unbalanced Voltage only after a meter has confirmed the supply voltage itself differs by phase — most often during troubleshooting, not routine design.