Power Factor Correction Calculator
Size the capacitor bank: kvar, µF per capacitor, current saved and resonance.
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Results are estimates from the formulas shown, not a professional design or certification. Have a qualified engineer verify anything safety-critical (structures, electrical installations, gas or pressure systems).
About the Power Factor Correction Calculator
Work out the capacitor bank that raises a load’s power factor from its present value to a target. Enter the load as kW, kVA or amps, the supply voltage and frequency, and the two power factors: the calculator gives the kvar the bank must supply, the capacitance of each capacitor for a single-phase, delta or star bank at 50 or 60 Hz, and how much the apparent power, the line current and the I²R losses in the supply cables fall.
It also covers what decides a real bank: capacitors rated above the system voltage (their kvar falls with the square of the voltage, so the nameplate must be larger), an automatic bank built from switched steps (with a check that it never drives the power factor leading), and the parallel resonance between the bank and the supply transformer, which warns when it lands near the 5th, 7th, 11th or 13th harmonic that drives and rectifiers produce.
Without a pass, the free preview works on your own figures and shows each check’s title, the power triangle (watermarked, without its figures) and the first rows of each table by name; the kvar, the capacitance, every other figure, the working, Copy and the CSV and text reports come with a Pro pass.
How to use it
- Choose three-phase or single-phase, the frequency, and how you know the load: real power (kW), apparent power (kVA) or line current (amps).
- Enter the supply voltage (line to line for three-phase) and the present and target power factors. The present one is kW ÷ kVA from a power meter or the bill.
- For a three-phase bank, choose delta or star. Optionally enter the capacitors’ rated voltage, the size of one switched step, and the supply transformer’s kVA and impedance for the resonance check.
- Read the kvar, the capacitance per capacitor and the checks. With a pass, or after unlocking this result, Copy the summary or download it as CSV or a text report.
Examples
100 kW drawing 100 kvar (141 kVA, power factor 0.707), target 0.95
Capacitor 67.1 kvar → 105.3 kVA; the current falls by 25.6%
The DOE fact sheet rounds this to a 67 kvar capacitor, 142 → 105 kVA and 26% less current.
100 kW at 0.75 lagging, target 0.95
tan φ: 0.8819 → 0.3287, Qc = 100 × 0.5532 = 55.3 kvar; 3 × 18.4 kvar capacitors of 366.9 µF each at 400 V; 192.5 A → 151.9 A
55.3 kvar needed at 415 V
Nameplate rating 55.3 × (440 ÷ 415)² = 62.2 kvar
350 kvar bank
S_sc = 1,000 ÷ 0.06 = 16,667 kVA; h = √(16,667 ÷ 350) = 6.9, close to the 7th harmonic: consider a detuned bank
The formula
Real power P stays the same; the bank only supplies reactive power the load would otherwise draw from the supply. With φ = arccos(PF):
- Reactive power before and after: Q₁ = P × tan φ₁, Q₂ = P × tan φ₂
- Capacitor bank: Qc = Q₁ − Q₂ = P × (tan φ₁ − tan φ₂)
- Apparent power: S = P ÷ PF, so the kVA and the line current fall in the ratio PF₁ ÷ PF₂
- Losses in the cables and transformer upstream fall with the square of the current: 1 − (PF₁ ÷ PF₂)²
The factor tan φ₁ − tan φ₂ is the "kvar per kW" figure capacitor tables list.
Capacitance per capacitor
A capacitor of capacitance C at voltage V and frequency f gives Q = 2π f C V², so C = Q ÷ (2π f V²) with Q and V of that capacitor:
- Single-phase: one capacitor of Qc at the supply voltage
- Delta: three capacitors of Qc ÷ 3, each across the line-to-line voltage
- Star: three capacitors of Qc ÷ 3, each at the line-to-neutral voltage V ÷ √3, so each needs three times the capacitance of the delta bank
At 230 V and 50 Hz that is about 60 µF per kvar; at 60 Hz the same kvar needs 5/6 of the capacitance.
Rated voltage and steps
A capacitor’s kvar is quoted at its rated voltage and falls with the square of the voltage it actually sees: Q = Q_rated × (V ÷ V_rated)². Capacitors rated above the system voltage (common where harmonics or detuning reactors raise the voltage across them) therefore need a larger nameplate rating. Never run them above their rating.
An automatic bank switches steps in and out with the load. The calculator rounds the bank up to whole steps and reports the power factor with every step in: if that is leading, the bank is too large for this load.
Harmonics and resonance
A capacitor bank and the inductance of the supply form a parallel resonant circuit. Its resonant frequency, as a multiple of the supply frequency, is about h = √(S_sc ÷ Qc), where S_sc is the short-circuit power at the bank’s bus. With only the transformer limiting it, S_sc ≈ S_T ÷ (z% ÷ 100). If h lands near a harmonic that drives, rectifiers, UPS units or LED drivers inject (the 5th, 7th, 11th and 13th from six-pulse equipment), the harmonic currents are amplified and can overload and destroy the capacitors. The usual answer is a detuned bank, with a series reactor that tunes it below the lowest harmonic, or a harmonic study to IEEE Std 519.
The calculator also gives the steady voltage rise when the bank is switched on, about ΔV% ≈ Qc × z% ÷ S_T.
Sources
- IEEE Std 1459: definitions of active, reactive and apparent power and power factor
- IEEE Std 18: shunt power capacitors
- IEEE Std 1036: guide for the application of shunt power capacitors
- IEEE Std 519: harmonic control in power systems
- US Department of Energy: Reducing power factor cost (fact sheet with the 100 kW example)
- IEC 60831-1 covers self-healing shunt capacitors for systems up to 1,000 V
Limitations
- Sinusoidal supply: the formulas use the displacement power factor. Where harmonics are large, the true power factor is lower and capacitors alone cannot correct it; detuned banks or active filters are needed.
- The resonance check uses the transformer’s impedance only (an infinite source upstream); the real network impedance lowers the resonant frequency somewhat. Several banks, cables and other capacitive loads shift it too.
- One load point at one moment: a bank sized at full load over-corrects at light load unless it is switched in steps.
- Capacitors at a motor’s terminals, switched with it, need their own limits so the motor cannot self-excite as it runs down; in the US, NFPA 70 Article 460 sets rules for capacitors connected with motors.
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Frequently asked questions
What do I get without a pass?
Without a pass, Power Factor Correction Calculator shows each check’s title, a watermarked power triangle and the names of each table’s first rows (up to 3), with the kvar, the working and every figure hidden. Until you unlock it, the result can’t be downloaded or copied. A Pro, Premium or Ultimate pass, a one-time payment that never renews, unlocks the full result. The pricing page lists the passes and their prices.
How do I calculate the kvar needed to correct power factor?
Multiply the real power by the difference of the tangents of the two angles: Qc = P × (tan(arccos PF₁) − tan(arccos PF₂)). For 100 kW from 0.75 to 0.95 that is 100 × (0.8819 − 0.3287) = 55.3 kvar.
How many microfarads are 1 kvar?
C = Q ÷ (2π f V²) for one capacitor. At 230 V and 50 Hz, 1 kvar is 60.2 µF; at 400 V, 50 Hz it is 19.9 µF; at 480 V, 60 Hz it is 11.5 µF. In a delta bank each capacitor sees the line-to-line voltage; in a star bank the line-to-neutral voltage.
Should a three-phase capacitor bank be delta or star?
Both give the same kvar and line current. A delta bank needs one third of the capacitance per capacitor but at the full line voltage; a star bank needs three times the capacitance at the lower phase voltage, which suits capacitors rated below the line voltage.
What power factor should I aim for?
Check your supply tariff: the US Department of Energy notes that many utilities charge an additional fee when the power factor is below 0.95. Aiming slightly below 1 leaves room for load changes; a fixed bank sized for exactly 1 at full load makes the power factor leading at light load.
Why does my capacitor give less kvar than its nameplate?
Its kvar is quoted at its rated voltage and frequency and falls with the square of the voltage: a 440 V, 50 kvar capacitor on 415 V gives 50 × (415 ÷ 440)² = 44.5 kvar. On 60 Hz a capacitor rated for 50 Hz gives 6/5 of its kvar, and the other way round 5/6.
What is a detuned capacitor bank?
A bank with a reactor in series with each step, so that the combination resonates below the lowest significant harmonic. It keeps the bank from amplifying harmonic currents where drives and rectifiers are connected. If the resonance check here lands near a harmonic, ask the supplier for a detuned design.