Power Factor Calculator
Calculate AC power factor, phase angle, apparent power, and reactive power. Size correction capacitors to improve PF for single-phase or three-phase systems.
Choose a solve mode, enter the known values, and select single-phase or three-phase. In correction mode, enter the current and target PF to size a compensation capacitor.
- PF = cos(φ) = P / S
- √(P² + Q²) = S
- Q = P × tan(φ)
- φ = arccos(PF)
- S = V × I
How It Works
- 1
Choose a solve mode
From P & S: enter the real power (W or kW) and apparent power (VA or kVA) read from a meter or nameplate. From V, I, P: enter line voltage, line current, and real power for single-phase or three-phase. PF Correction: enter the load's real power, its current PF, the target PF, line voltage, and frequency to size a correction capacitor.
- 2
Set single-phase or three-phase
Single-phase uses S = V x I. Three-phase (line-to-line voltage) uses S = sqrt(3) x V x I. Choose the one that matches your measurement point.
- 3
Read the results and power triangle
The calculator returns PF, phase angle, S, and Q for all modes. In correction mode it also gives the required reactive compensation Q_c in VAR and the capacitor value in microfarads. The SVG power triangle updates in real time, with old and corrected triangles overlaid in correction mode.
AC power factor, the power triangle, and why utilities care
Every AC circuit has two kinds of power flowing through it simultaneously. Real power P, measured in watts, performs useful work: turning shafts, producing heat, emitting light. Reactive power Q, measured in volt-amperes reactive (VAR), shuttles energy back and forth between the source and the magnetic or electric fields inside motors, transformers, and capacitors without doing any work. The vector sum of P and Q is apparent power S, measured in volt-amperes (VA), and the ratio P/S is the power factor. Charles Proteus Steinmetz, a mathematician and electrical engineer at General Electric, popularized the use of complex numbers (phasors) for AC circuit analysis in the 1890s, giving engineers the algebraic framework to separate real and reactive components. A purely resistive load like an incandescent lamp has PF = 1.0: all current does work. A typical induction motor at full load runs at PF 0.80 to 0.87; at half load it can fall below 0.70. The extra current needed to supply reactive power heats cables, overloads transformers, and wastes generation capacity. Utilities respond by billing industrial customers for kVA demand rather than kW alone, or by imposing surcharges when PF drops below a threshold, usually 0.90 or 0.95. The standard correction method is connecting shunt capacitors that supply leading reactive current to offset the lagging current drawn by motors. IEEE Std 1459-2010 extended the classical power triangle to non-sinusoidal systems with harmonic distortion, introducing distortion power D, but for the fundamental-frequency correction sizing that this calculator performs, the classical sinusoidal model remains accurate.
Common pitfalls
Confusing kW and kVA. The utility transformer and your wiring must carry kVA, not kW. A 10 kW motor at PF 0.7 draws 14.3 kVA; size the feeder, breakers, and transformer for 14.3 kVA. Demand charges on industrial tariffs (IEEE 1159) are billed in kVA or with a PF penalty above the standard tariff.
Over-correcting to leading PF. A capacitor bank sized with the motor under load will over-compensate at no-load, creating leading PF and voltage rise that stresses equipment and trips capacitor fuses. Size for average operating condition, not nameplate; use automatic contactor banks for varying loads.
Ignoring harmonics. True PF = displacement PF × distortion factor. A VFD drive with THD of 35% has a distortion factor of 0.943, so even at displacement PF = 1.0 the true PF caps at about 0.94. Classical capacitor correction cannot fix distortion; use a harmonic filter or line reactor per IEEE 519.
Installing capacitors upstream of the VFD. Capacitors and motor-drive rectifier diodes form a resonant tank that magnifies harmonic currents. PF correction capacitors belong on the utility-side of a VFD, not between the VFD output and the motor.
Assuming single-phase PF meters read correctly on three-phase unbalanced loads. Three-phase PF requires measuring line-to-neutral voltage and current on each phase or using the two-wattmeter method (Blondel's theorem). A single clamp on one phase of an unbalanced load gives a misleading number.
Frequently Asked Questions
What is power factor and why does it matter?
Power factor (PF) is the ratio of real power (watts) doing useful work to apparent power (volt-amperes) drawn from the supply. A PF of 1.0 means all current delivers useful work. Industrial motors, fluorescent lighting, and variable-speed drives typically run at PF 0.7–0.85, forcing utilities to supply extra current that heats cables and transformers without performing work. Most commercial electricity tariffs penalize customers whose PF drops below 0.90–0.95.
What is the difference between leading and lagging power factor?
Lagging PF means current lags voltage, caused by inductive loads such as motors, transformers, and solenoids. Leading PF means current leads voltage, caused by capacitive loads such as long cable runs, power-factor correction banks, and lightly loaded UPS systems. Most industrial facilities have a lagging PF because motors dominate the load. Correction capacitors inject leading current to cancel the lag.
How do I correct a low power factor?
The standard method is adding shunt capacitors across the load. The required reactive compensation is Q_c = P × (tan(φ_old) − tan(φ_new)), and the capacitor value is C = Q_c / (2π × f × V²). For large plants, automatic capacitor banks switch stages in and out to track varying loads. Synchronous condensers and active filters are used when the load is highly non-linear or harmonics are a concern.
Why does three-phase use a √3 multiplier?
In a balanced three-phase system, the total apparent power is S = √3 × V_LL × I_L, where V_LL is the line-to-line voltage and I_L is the line current. The √3 factor comes from the 120° phase displacement between the three conductors. If you measure phase voltage (V_LN) and phase current directly, S = 3 × V_LN × I_L, which gives the same result because V_LL = √3 × V_LN.
What PF does a typical motor have?
NEMA standard induction motors at full load run at PF 0.80–0.87. At partial load the PF drops: a motor loaded at 50% might fall to 0.65–0.72, and at 25% load it can be as low as 0.40–0.55. This is why oversized motors are a common cause of poor facility PF. Selecting a motor sized close to the actual mechanical load or adding individual correction capacitors at the motor starter are standard remedies.
What is apparent power and why is it measured in VA, not watts?
Apparent power S (volt-amperes) is the product of RMS voltage and RMS current. It includes both the real component P (watts, doing useful work) and the reactive component Q (VAR, shuttling energy back and forth between source and load). Utilities size generators, transformers, and cables based on S, not P, because the conductors carry the full current regardless of how much of it does useful work. That is why transformers are rated in kVA, not kW.
Does IEEE Std 1459-2010 change anything for this calculator?
IEEE 1459-2010 defines separate power components for non-sinusoidal and unbalanced systems, introducing distortion power D and harmonic-adjusted quantities. This calculator assumes sinusoidal, balanced conditions, which covers the vast majority of PF correction sizing. For variable-frequency drives, LED drivers, and other highly non-linear loads, a full harmonic power analysis per IEEE 1459 is recommended, typically done with a power-quality analyzer.
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