3 Phase Power Calculator

sqrt(3) = 1.732 is the ratio of line-to-line voltage to line-to-neutral voltage in a 3-phase wye system: V_L-L = sqrt(3) x V_L-N. The three line currents sum vectorially -- in a balanced system, their phasors are 120 degrees apart and the line current equals the phase current. The total power P = 3 x V_L-N x I x PF = 3 x (V_L-L / sqrt(3)) x I x PF = sqrt(3) x V_L-L x I x PF. The sqrt(3) is not an arbitrary constant -- it is rooted in the trigonometry of the 120-degree phase relationship: cos(30 degrees) = sqrt(3)/2, and the line-to-line voltage is twice the line-to-neutral voltage projected onto the line axis, yielding the sqrt(3) factor. Using 1 instead of 1.732 (single-phase formula for 3-phase loads) underestimates power by 42%, one of the most common and dangerous electrical design errors.

Measure the current in each of the three phases with a clamp meter. The currents should be within approximately 5% of each other. If phase A reads 85 A, phase B reads 88 A, and phase C reads 45 A, the load is severely unbalanced. Unbalanced currents cause: (1) increased neutral current (up to the imbalance amount, potentially overloading the neutral conductor), (2) increased I squared R losses (the losses are proportional to the sum of squares of phase currents -- imbalance always increases total losses for the same average current), (3) voltage unbalance at the motor terminals causing negative-sequence currents that overheat rotor bars. Major unbalance may indicate a single-phasing condition (one fuse blown) -- a motor running single-phased will rapidly overheat and fail, typically within minutes for motors without phase-loss protection.

208V 3-phase is the standard commercial/light industrial voltage in North America, derived from a 120/208V wye transformer -- common in office buildings, retail, and apartment buildings. It provides 120V single-phase for receptacles and lighting from the same transformer. 240V 3-phase (typically delta, often corner-grounded or with a center-tapped 'wild leg' for 120/240V single-phase) is found in older industrial facilities and some rural areas -- it is being phased out for new construction. 480V 3-phase is the standard industrial voltage -- used for motors above approximately 10 HP, large HVAC equipment, and manufacturing plants across North America. Higher voltage = lower current for the same power = smaller conductors and lower losses. A 100 kW load draws 278 A at 208V but only 120 A at 480V -- a dramatic reduction in conductor size, conduit size, and installation cost. 600V is the Canadian industrial standard. 4160V and above are medium-voltage ranges used for very large motors (500 HP+) and campus/utility distribution.

Not directly, but you can approximate it with careful technique. The two-wattmeter method is the standard approach: using two single-phase wattmeters connected to measure power in a three-wire, three-phase system (the Blondel theorem). Connect wattmeter 1 between phases A and B (current probe on A, voltage probes on A-B), and wattmeter 2 between phases C and B (current probe on C, voltage probes on C-B). Total three-phase power = W1 + W2. This works for any balanced or unbalanced three-wire system. For a four-wire wye system, you need three wattmeters (one per phase). In practice, modern power quality analyzers and clamp meters with three-phase capability eliminate the need for manual two-wattmeter measurements, but understanding the method is essential for verifying instrument readings.

Power factor directly scales the relationship between kW (real power, what does useful work) and kVA (apparent power, what the generator, transformer, and conductors must deliver). At PF = 1.0, kW = kVA -- all current delivers useful work. At PF = 0.7, kW = 0.7 x kVA -- only 70% of the current produces real power; the remaining 30% is reactive current that circulates between the source and the inductive load, heating conductors without doing work. This means a 100 kW load at 0.7 PF requires 143 kVA of system capacity vs 100 kVA at unity. For line current: at 480V, a 100 kW load at 0.7 PF draws I = 100,000 / (1.732 x 480 x 0.7) = 171.5 A; at 0.95 PF it draws only 126.4 A -- a 26% reduction. When estimating PF for an unknown motor load, use 0.85 as a starting point for fully loaded motors and 0.70 for lightly loaded motors (50% load or less). Always measure with a true RMS power analyzer for critical applications.

These three quantities form the power triangle: kW (real power, horizontal axis) is the power that performs useful work -- spinning shafts, producing heat, generating light. kVAR (reactive power, vertical axis) is the power that sustains magnetic fields in motors and transformers but does no net work. kVA (apparent power, hypotenuse) is the vector sum: kVA = sqrt(kW squared + kVAR squared). The power factor PF = kW / kVA = cos(phi), where phi is the phase angle between voltage and current. For a 100 kW load with 60 kVAR of reactive demand: kVA = sqrt(100 squared + 60 squared) = 116.6 kVA, PF = 100 / 116.6 = 0.857. The reactive power does not register on a kilowatt-hour meter but demands system capacity -- conductors, switchgear, and transformers must be sized for kVA, not just kW. This is why utilities penalize low power factor: it costs them real infrastructure to deliver reactive power that generates no revenue.