Find the power factor of an AC load from real and apparent power or the phase angle, see the reactive power in the power triangle, and size 1-phase or 3-phase correction capacitors.
Presets:
Load values
Actual power doing work — from a nameplate, meter, or spec sheet.
Voltage × current — the total power the circuit must supply.
The angle between the voltage and current waveforms, in degrees (0° to 90°).
Power factor
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Enter real and apparent power (or the phase angle) to compute the power factor.
Power Triangle Diagram
Load values
Reactive power is the non-working leg of the power triangle: Q = √(S² − P²).
Reactive power
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Enter real and apparent power to compute the reactive power.
Real (P)—
Apparent (S)—
Reactive (Q)—
Power factor—
Waveform Phase Shift
Correction inputs
Adding a shunt capacitor bank supplies leading reactive power to offset load demand, raising power factor and freeing distribution capacity.
Correction capacitance
—
Enter real power, current PF, target PF, and voltage to compute the correction capacitance.
Capacitance / Phase—
Total Reactive Qc—
Line Current Drop—
Line Heat Loss Saved—
Released Capacity—
Line Current (Before → After)—
4 min read3 steps7 terms3 examples6 FAQsPF = cosφ = P / S
Power factor tells you how efficiently an AC circuit converts the power a utility supplies into actual useful work.
Enter real and apparent power (or the phase angle)
On the Power Factor tab, switch between "Real & Apparent Power" and "Phase Angle" to match what you know. Real power (P) is what a nameplate or meter reports in watts; apparent power (S) is volts × amps. If you only know the phase angle between voltage and current, use that mode instead.
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Read the power factor and reactive power
The result shows the power factor (PF = cosφ, a number between 0 and 1) along with whether the load is lagging (inductive, the common case for motors and transformers) or leading (capacitive). The detail line also reports the reactive power and apparent power in kVA.
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Check reactive power or size a correction capacitor
Switch to the Reactive Power tab to see the full power-triangle breakdown (P, S, Q, and PF together), or to the Correction tab to enter your current PF, a target PF, the supply voltage, and frequency — the calculator returns the shunt capacitance needed to reach that target.
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Reference
Formula & Methodology
3 formulas▸
Power factor
PF = cosφ = P / S
Power factor is the ratio of real power P (watts, the power that does useful work) to apparent power S (volt-amps, the total power the source must supply). It equals the cosine of φ, the phase angle between the voltage and current waveforms, and always falls between 0 and 1.
Reactive power
Q = √(S² − P²)
Reactive power Q (measured in var) is the power that oscillates between the source and the load's magnetic or electric fields without doing useful work. Real power P, reactive power Q, and apparent power S form a right triangle — the "power triangle" — with S as the hypotenuse.
Correction capacitance
Qc = P(tanφ1 − tanφ2), C = Qc / (2πfV²)
To raise a lagging power factor from an existing angle φ1 to a target angle φ2, a shunt capacitor must supply reactive power Qc. Solving for the capacitance C that supplies Qc at line voltage V and frequency f gives the required capacitor size, applied per phase.
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General reference
Trust, Methodology & Sources
Written by Calculover Editorial Team · Updated 2026-07-31▸
Editorial accountability
Author: Calculover Editorial Team - Editor
Owner: Calculover Editorial Team - Editorial owner
Last reviewed: 2026-07-31
Last verified: 2026-07-31
Methodology
Limitations & guidance
Formulated according to standard AC power definitions in IEEE 1459-2010 (Electric Power Quantities), IEEE 18-2012 (Shunt Power Capacitors), and NEC Article 460.
Designed for educational & preliminary facility estimation. Capacitor bank installation, harmonic resonance risk, and switching contactor sizing should be evaluated by a licensed Professional Engineer (PE).
Professional guidance:
Primary sources
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Glossary
Key Terms Explained
7 terms▸
Power factor (PF) ↗The ratio of real power to apparent power, PF = P/S, ranging from 0 to 1. A PF of 1.0 means all supplied power does useful work; lower values mean more of the current is reactive and wasted as extra heating and demand charges.
Real power (P) ↗Also called active or true power, measured in watts (W). This is the power actually converted into work, heat, or light — what a utility meter bills for.
Apparent power (S) ↗The product of RMS voltage and RMS current, measured in volt-amps (VA) or kilovolt-amps (kVA). It is the total power a source and its wiring must be sized to deliver, real and reactive combined.
Reactive power (Q) ↗Power measured in volt-amps reactive (var) that is exchanged between the source and a load's inductors or capacitors each cycle without performing useful work. Inductive loads (motors, transformers) consume reactive power; capacitors supply it.
Phase angle (φ) ↗The angle, in degrees, by which the current waveform lags or leads the voltage waveform in an AC circuit. PF = cosφ, so a 0° angle gives PF = 1 and a 90° angle gives PF = 0.
kVA ↗Kilovolt-amps — apparent power in units of 1,000 VA. Generators, transformers, and UPS systems are rated in kVA because they must handle the full apparent power, not just the real power.
PF correction ↗Adding capacitors (or, less commonly, synchronous condensers) in parallel with an inductive load to supply local reactive power, reducing the reactive current the utility source has to deliver and raising the measured power factor toward 1.0.
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Scenarios
Real-World Examples
3 worked examples▸
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Facilities engineer
800 W load drawing 1,000 VA
Real power (P) 800 WApparent power (S) 1,000 VA
PF = 800 / 1,000 = 0.80 (lagging). The load's reactive power is Q = √(1,000² − 800²) = 600 var — a typical power factor for an uncorrected induction motor.
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Panel designer checking the power triangle
10 kW load running at PF 0.80
Real power (P) 10 kWApparent power (S) 12.5 kVA
S = P / PF = 10,000 / 0.80 = 12,500 VA (12.5 kVA). Reactive power Q = √(12,500² − 10,000²) = 7,500 var (7.5 kvar) — the source must supply 12.5 kVA to deliver 10 kW of useful work.
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Electrician sizing a correction capacitor
10 kW load, correcting PF 0.75 → 0.95 at 240 V / 60 Hz
Real power (P) 10 kWCurrent PF → target PF 0.75 → 0.95Voltage / frequency 240 V / 60 Hz
Qc = 10,000 × (tan(41.41°) − tan(18.19°)) ≈ 5,530 var of correction is needed, which requires a capacitor of about 254.8 µF per phase at 240 V / 60 Hz.
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Reference
Cite This Calculator
APA & MLA▸
Use either format to cite this calculator in a paper, report, or resource list.
Power factor tells you how efficiently an AC circuit converts the power a utility supplies into actual useful work. A low power factor means extra current flows for no useful output — which shows up as higher demand charges, larger required wiring and transformers, and more heat loss. This calculator computes power factor from real and apparent power (or a phase angle), breaks down the reactive power in the power triangle, and sizes the capacitance needed to correct a low power factor toward a target value.
How the Power Factor Calculator works
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On the Power Factor tab, PF = cosφ = P/S: the calculator divides real power (P, in watts) by apparent power (S, in volt-amps), or takes the cosine of a phase angle you enter directly. On the Reactive Power tab, it derives Q = √(S² − P²) — the Pythagorean relationship between the three sides of the power triangle (P along the real axis, Q along the reactive axis, S as the hypotenuse). On the Correction tab, it computes the reactive power a shunt capacitor must supply to move the load from its current phase angle to a target phase angle, Qc = P(tanφ1 − tanφ2), then solves for the capacitance that supplies that much reactive power at the given voltage and frequency: C = Qc / (2πfV²). These are the standard single-phase power-triangle and PF-correction formulas taught in AC circuit analysis and power systems courses.
Inputs and what they mean
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Real power (P) is the power actually doing work — read it from a nameplate, energy meter, or spec sheet, in W, kW, or MW. Apparent power (S) is voltage × current, in VA, kVA, or MVA; it is always greater than or equal to real power. The phase angle (φ) is an alternative way to specify the same relationship when P and S aren't both known. Load type (inductive/lagging vs. capacitive/leading) doesn't change the magnitude of PF, but it does change whether the load needs capacitive or inductive correction — most real-world loads (motors, transformers, fluorescent ballasts) are inductive and lagging. On the Correction tab, target PF, voltage, and frequency all directly scale the required capacitance: doubling the voltage quarters the required capacitance for the same reactive power, since capacitive reactive power scales with V².
Limits and edge cases
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This calculator models a single-phase (or per-phase) circuit with a linear, sinusoidal load. It does not account for three-phase bank sizing, harmonic distortion (which produces a separate "distortion power factor" component that this tool ignores), or capacitor bank switching transients and resonance risk with existing power-factor-correction equipment — all of which a qualified electrician or power engineer should evaluate before installing correction capacitors on a real system. Real power can never exceed apparent power in an ideal circuit, so the calculator rejects inputs where P > S, and the Correction tab requires the target PF to be at or above the current PF (you cannot "correct" toward a worse power factor).
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Questions
Frequently Asked Questions
6 questions▸
What is the power factor formula?+
Power factor is PF = cosφ = P/S, the ratio of real power (P, in watts) to apparent power (S, in volt-amps). It always falls between 0 and 1, where 1.0 means every watt of apparent power is doing useful work.
What does a lagging power factor mean?+
A lagging power factor means the current waveform lags behind the voltage waveform, which happens with inductive loads such as motors, transformers, and fluorescent ballasts. Lagging is the most common real-world case and is the default load type in this calculator.
How is reactive power calculated?+
Reactive power is Q = √(S² − P²), derived from the power triangle where real power (P) and reactive power (Q) are the two legs and apparent power (S) is the hypotenuse.
How do I correct a low power factor?+
Add capacitance in parallel with the load. A capacitor supplies leading reactive power that cancels part of an inductive load's lagging reactive power, raising the measured power factor toward the target you specify.
What units does the Power Factor Calculator use?+
Real power in watts (W), kilowatts (kW), or megawatts (MW); apparent power in volt-amps (VA), kilovolt-amps (kVA), or megavolt-amps (MVA); reactive power in var or kvar; the phase angle in degrees; and correction capacitance in µF, mF, or F depending on magnitude. Power factor itself is a unitless ratio between 0 and 1.
Why does power factor matter?+
A low power factor forces utilities and building wiring to carry more current than the real power alone would require, which increases demand charges, requires larger transformers and conductors, and wastes energy as resistive heating — correcting it lowers costs and frees up system capacity.
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