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Physics

Power Factor Calculator

Enter the voltage, current and real power for an AC circuit and the calculator instantly returns the power factor, apparent power, reactive power, phase angle, impedance and the capacitor required to correct the power factor to a target value. Supports both single-phase and three-phase systems.

Your details

Single-phase: one live + neutral. Three-phase: three live conductors.
RMS line-to-neutral voltage for single-phase; line-to-line for three-phase.
V
RMS current drawn by the load.
A
Actual power consumed and converted to useful work (watts).
W
Supply frequency. 50 Hz (Europe/Asia/Africa) or 60 Hz (Americas).
Hz
The power factor you want to achieve after adding correction capacitors (0.01 - 1.00).
Power factor (PF)Poor
0.7826

Ratio of real power to apparent power (0 to 1)

Apparent power (S)2,300VA
Reactive power (Q)1,431.8VAR
Phase angle (phi)38.5deg
Impedance (Z)23ohm
Resistance (R)18ohm
Reactance (X)14.3178ohm
Correction capacitor50.55uF
Power factor qualityPoor (penalty risk)
0.7826
Very poor<0.7Poor0.7-0.85Acceptable0.85-0.95Excellent0.95+
043.0886.15111
Target power factor
Capacitance (uF)
Target power factorRequired capacitor
0.84.92
0.817.74
0.8210.55
0.8313.37
0.8416.19
0.8519.03
0.8621.89
0.8724.77
0.8827.69
0.8930.66
0.933.7
0.9136.81
0.9240.01
0.9343.35
0.9446.84
0.9550.55
0.9654.56
0.9759.01
0.9864.16
0.9970.72
186.15

Power factor is 0.7826 - Poor (penalty risk).

  • Only 78.3% of the apparent power (2300 VA) is doing actual work. The rest (1432 VAR) is reactive power cycling back and forth in the circuit.
  • Many utilities charge a power factor penalty when PF falls below 0.85 or 0.90. Improving your power factor reduces these charges and lowers current draw, which in turn reduces cable losses and heat.
  • Adding a 50.55 uF capacitor in parallel with the load will raise the power factor from 0.783 to 0.95.
  • For inductive loads (motors, transformers), the current lags the voltage, giving a lagging power factor. Capacitors compensate by providing leading reactive current.

Next stepUse the target power factor field to find the capacitor size needed for correction, then consult an electrician before installing correction equipment.

Formula

PF=P/S,S=V×I (single),S=3×VLL×I (three-phase),Q=S2P2,ϕ=arccos(PF),C=Qc2πfV2PF = P / S,\quad S = V \times I \text{ (single)},\quad S = \sqrt{3} \times V_{LL} \times I \text{ (three-phase)},\quad Q = \sqrt{S^2 - P^2},\quad \phi = \arccos(PF),\quad C = \frac{Q_c}{2\pi f V^2}

Worked example

Single-phase 230 V, 10 A, 1800 W: S = 230 x 10 = 2300 VA. PF = 1800 / 2300 = 0.7826. Q = sqrt(2300^2 - 1800^2) = 1460 VAR. Phase angle = arccos(0.7826) = 38.5 deg. To correct to PF 0.95: Qc = 1800 x (tan(38.5 deg) - tan(18.2 deg)) = 1800 x (0.795 - 0.329) = 839 VAR. C = 839 / (2 x pi x 50 x 230^2) = 50.6 uF.

What is power factor?

Power factor (PF) is the ratio of real power to apparent power in an AC circuit. Real power (P, in watts) does useful work, driving motors, heating elements and electronic loads. Apparent power (S, in volt-amperes) is what the source must supply, including the reactive component that charges and discharges inductive and capacitive elements without doing net work. A power factor of 1.0 means all supplied power is being used productively. A lower value means extra current must flow to deliver the same real power, which wastes energy in cable resistance and can trigger utility penalty charges. The relationship is described by the power triangle: P = S x cos(phi), Q = S x sin(phi), and S^2 = P^2 + Q^2, where phi is the phase angle between the voltage and current waveforms.

Single-phase vs. three-phase circuits

In a single-phase circuit, apparent power is simply S = V x I. In a balanced three-phase circuit, S = sqrt(3) x V_LL x I, where V_LL is the line-to-line voltage. The factor sqrt(3) (approximately 1.732) arises from the 120-degree phase separation between the three current-carrying conductors. Industrial equipment such as large motors and HVAC compressors almost always runs on three-phase power, while household circuits are typically single-phase. Power factor has the same definition in both cases: PF = P / S, and the same correction approach applies. In three-phase systems, correction capacitors are usually installed one per phase, either in a star (Y) or delta configuration.

Impedance, resistance and reactance

Impedance (Z, in ohms) is the total opposition a circuit offers to AC current. It has two components: resistance (R), which dissipates energy as heat, and reactance (X), which stores and returns energy each half-cycle. The three are related by Z^2 = R^2 + X^2. Resistance is in phase with voltage; inductive reactance causes current to lag voltage; capacitive reactance causes current to lead voltage. The power factor equals R / Z = cos(phi), so a circuit that is entirely resistive (X = 0) has a power factor of 1.0, while a purely reactive load has a power factor of 0.

Power factor correction and capacitor sizing

Most industrial loads are inductive (motors, ballasts, transformers), giving a lagging power factor. Adding capacitors in parallel supplies leading reactive current that partially cancels the lagging reactive demand, reducing Q and raising PF toward 1.0. The required reactive correction is Qc = P x (tan(phi1) - tan(phi2)), where phi1 is the existing phase angle and phi2 is the target phase angle. The capacitance is then C = Qc / (2 x pi x f x V^2). Always have a qualified electrician install correction capacitors, as they store charge and must be discharged safely before any maintenance work.

Power factor quality bands

Power factor rangeRatingTypical consequence
0.95 - 1.00 Excellent No utility penalties; minimal line losses
0.85 - 0.94 Good / acceptable Usually within utility tolerance
0.70 - 0.84 Poor Penalty surcharges common; higher line current
Below 0.70 Very poor Significant penalties; overheating risk

General industry thresholds. Exact penalty cut-offs vary by utility and region.

Frequently asked questions

What is a good power factor?

Most utilities and electrical standards consider a power factor of 0.95 or above to be excellent. Values between 0.85 and 0.94 are generally acceptable, while anything below 0.85 may attract penalty surcharges from the utility and increases the current that cables and switchgear must carry.

What is the difference between real power, reactive power and apparent power?

Real power (P, watts) is the power that performs actual work: running motors, producing light and heat, and powering electronics. Reactive power (Q, VAR) is exchanged between the source and inductive or capacitive elements each cycle without doing net work; it is necessary for creating magnetic fields in motors and transformers but adds to the current that cables must carry. Apparent power (S, VA) is the vector sum of the two and represents the total power the supply must provide. Power factor is P divided by S.

What causes a low power factor?

The most common cause is inductive loads: AC motors (especially lightly loaded ones), fluorescent lighting ballasts, welding equipment and transformers all draw lagging reactive current. Variable-speed drives, rectifiers and switch-mode power supplies can also distort the current waveform, causing displacement power factor and harmonic distortion. In domestic settings, low power factor is rarely penalised, but in commercial and industrial premises, utilities typically measure it and bill accordingly.

What is the difference between a leading and a lagging power factor?

A lagging power factor occurs when the load is inductive: current lags behind voltage. This is by far the most common situation in industrial and commercial settings. A leading power factor occurs when the load is capacitive: current leads voltage. Over-correcting an inductive load with too large a capacitor bank can create a leading power factor, which can also cause problems including voltage rise and instability in the supply network.

How does the three-phase formula differ from single-phase?

For single-phase circuits, apparent power S = V x I. For a balanced three-phase circuit, S = sqrt(3) x V_LL x I, where V_LL is the line-to-line voltage and I is the line current. The factor sqrt(3) (about 1.732) arises from the geometry of three phasors separated by 120 degrees. Power factor, reactive power and the correction capacitor formula all use this S, so the three-phase values will be larger in proportion.

Can I use this calculator for DC circuits?

No. Power factor is an AC concept. In a DC circuit there are no alternating fields, no phase angle and no reactive power. All supplied power in a DC circuit is real power, so the "power factor" of a DC circuit is always 1.0 by definition. This calculator is intended for 50 Hz or 60 Hz AC systems.

Sources

Written by Dr. Tomás Okafor, PhD Physicist · Lagos, Nigeria

Physicist specializing in classical mechanics, bringing 17 years of research and applied dynamics expertise to every calculator he reviews.

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