Industrial Power Quality Tool

Power Factor Correction & Capacitor Bank Calculator

Size a capacitor bank for power factor correction: enter kW, current and target PF, voltage, phase and connection. Outputs kvar required, µF per phase, rated current and an inrush estimate — with the full derivation chain below.

Power Factor Correction Calculator

kvar compensation, µF per phase, rated current and inrush estimate. Live on every keystroke.

🎯 Step 00 · OverviewTotal steps: 4Core formula: kvar = P × (tanφ₁ − tanφ₂)Accuracy: ±3 % ideal conditions
Quick presets
kvar Compensation Required
69.15kvar
Formula: kvar = P (kW) × (tanφ₁ − tanφ₂)
tanφ₁: 1.0202 · tanφ₂: 0.3287
C per phase
458.58µF
Δ connection per phase
Rated current
151.9A
Capacitor bank nominal
Inrush estimate (rule of thumb)
1 519A peak
10× rated typical · use soft-start or detuned reactor in practice

📌 Key formula.Three-phase Y connection: C_Y = Q / (ω × V²) · Δ connection per phase: C_Δ_per = Q / (3ω × V²) · Single-phase: C = Q / (ω × V²) · ω = 2πf.

⚠️ Engineering disclaimer.This calculator provides preliminary power factor correction sizing only. Real industrial capacitor bank design must consider harmonic resonance (detuned reactors), short-circuit current withstand, switching transients, anti-resonance at upstream capacitor banks, regional grid codes and coordination with a licensed electrical engineer. Do not install an industrial bank based on this tool alone.

The Power Triangle

What Is Power Factor — Real, Reactive & Apparent Power Explained

Every motor, transformer and compressor on an industrial site draws two kinds of power. Real power P (measured in kilowatts, kW) is the useful work — turning a shaft, pumping water, heating air — the power you actually pay for on the electricity bill. Reactive power Q (kilovolt-amperes reactive, kvar) does no work but is essential: it creates the rotating magnetic field inside induction motors and maintains voltage across transformers. Real and reactive power combine through vector addition into apparent power S (kVA), the total current flowing from the grid.

The ratio P/S — the cosine of the angle between voltage and current phasors — is power factor (PF = cos φ). An ideal load has PF = 1.0 (purely resistive); a heavily inductive site without correction sits at PF = 0.65–0.85. The difference between unity and your measured PF is exactly how much reactive power you are importing from the grid instead of generating locally. That reactive power raises supply current, overheats cables and transformers, and often triggers utility PF penalties. The power factor correction capacitor bank — the one this page sizes — supplies that reactive power locally, collapsing the import to near-zero.

Need the full capacitor calculator toolset? Browse the home page for every tool on the site, or jump straight to the Calculators hub where every tool is grouped by job.

Phasor diagram of real (P), reactive (Q) and apparent (S) power forming a right triangle with power factor angle φP² + Q² = S² — the power triangle is always rightPhoto: Unsplash
Step-by-Step Derivation

kvar = kW × (tanφ₁ − tanφ₂) — How to Derive the Capacitor Bank Size

The whole calculator above is four lines of high-school trigonometry dressed up as an industrial engineering problem. Let us walk through each step with the same numbers you typed into the dashboard.

01

Step 01 — Read your site's current and target power factor

Verified

Read PF₁ from your site manager or a data logger on the main distribution board. Common PF₁ values for uncorrected sites: 0.70 (heavy motor load), 0.80 (mixed motor + lighting), 0.85 (mostly lighting / electronic). Target PF₂ is almost always 0.95 — the industry standard — or 0.98 if your utility pays a PF bonus or you import through a dedicated industrial connection. Target PF above 0.99 risks over-correction with some sites and is not recommended.

Input: PF₁ = 0.70 · PF₂ = 0.95
02

Step 02 — Convert each PF to tan φ

Key Formula

PF = cos φ, so φ = arccos(PF). But we do not need arccos — we need tan φ for the reactive side of the power triangle. Use the identity:

tan φ = √(1 / PF² − 1)
tan φ₁ = √(1 / 0.70² − 1) = √(2.0408 − 1) = √1.0408 = 1.0202
tan φ₂ = √(1 / 0.95² − 1) = √(1.1080 − 1) = √0.1080 = 0.3286
03

Step 03 — Multiply by kW to get kvar

Key Formula

The reactive power the capacitors must supply locally is exactly the difference between the original reactive power import and the residual reactive power at target PF. Since P = S × PF and Q = S × sin φ, dividing one by the other gives Q = P × tan φ. So the bank must supply ΔQ = P × (tan φ₁ − tan φ₂):

kvar = P (kW) × (tan φ₁ − tan φ₂)
kvar = 100 × (1.0202 − 0.3286) = 100 × 0.6916 = 69.16 kvar
04

Step 04 — Convert kvar to µF per phase

Key Formula

Reactive power in var relates to capacitance in farads through Q = ω × C × V², where ω = 2πf. Rearranged: C = Q / (ω × V²). Now the connection matters:

ConnectionPer-phase voltageµF per-phase formula
Single-phaseV (same as supply)C = Q / (ω × V²)
3-phase Y (star)V / √3 ≈ 0.577 VC_Y = Q / (ω × V²)
3-phase Δ (delta)V (line voltage)C_Δ_per = Q / (3 × ω × V²)
For 100 kW, PF₁ 0.7 → PF₂ 0.95, 400 V 50 Hz, Δ connection:
ω = 2π × 50 = 314.16 rad/s
C_Δ_per = 69160 var / (3 × 314.16 × 400²) = 69160 / (3 × 314.16 × 160000) = 45.9 µF per phase

💡 Tip — Safety factor.Always buy the next standard capacitor rating above your calculated µF. Industry practice sizes the bank at 1.1–1.2× the theoretical kvar to leave headroom for voltage swells, utility over-voltage events and future motor additions to the site. Derate capacitor voltage by 20% from the rated line voltage.

⚠️ Watch the anti-resonance.Capacitor banks form a resonant circuit with site inductance. If another PFC bank from a neighbouring customer or the utility operates at the same frequency, the two banks can create anti-resonance that amplifies harmonic currents. Always ask the grid operator for their PFC frequency specification before signing off.

❌ Don't skip the detuned reactor.Installing a capacitor bank on a site with significant 3rd harmonic distortion (which most sites with VFDs have) causes the bank to form a resonant tank amplifying 150 Hz/180 Hz current. A detuned reactor (typically 5.5% detuning) is mandatory for sites above ~100 kvar, and the calculation changes — do not copy this page's result blindly.

Reference Table

Standard kvar Compensation — kW × PF₁ to PF₂ = 0.95, 400 V 50 Hz 3-phase Y

Quick-lookup for the most common industrial scenario. All values are 3-phase total kvar; use the calculator above if your target PF, voltage, frequency or connection differ. These numbers match the formula kvar = kW × (tanφ₁ − tan0.95) for PF₂ = 0.95 exactly.

Site PowerCurrent PF₁Total kvar @ PF₂ 0.95Next Standard StepEstimated µF (3-ph Y, 400V 50Hz)
25 kW0.7015.8 kvar50 kvar≈ 314 µF total Y
50 kW0.7031.5 kvar50 kvar (oversize)≈ 627 µF total Y
75 kW0.7047.3 kvar50 kvar (oversize)≈ 941 µF total Y
100 kW0.7063.0 kvar75 kvar≈ 1253 µF total Y
50 kW0.8018.5 kvar50 kvar≈ 368 µF total Y
100 kW0.8037.0 kvar50 kvar (oversize)≈ 736 µF total Y
100 kW0.8528.3 kvar50 kvar≈ 563 µF total Y
100 kW0.9017.7 kvar50 kvar≈ 352 µF total Y
100 kW0.957.4 kvar25 kvar≈ 147 µF total Y

Standard industrial bank kvar steps are almost always 12.5, 25, 50, 100 kvar per step — binary-weighted so 4–8 steps can approximate any total kvar. See the step section below.

Stepped Banks (APFC)

Why Industrial Banks Use Stepped Capacitor Steps

A site's PF varies hour by hour — peak morning start-up is low, night shift is high — so a fixed capacitor bank is either under-correcting at peak or over-correcting at night. Stepped banks split the total kvar into binary-weighted steps (e.g. 12.5 + 25 + 50 + 100 kvar) and an automatic PF controller switches steps in and out to hold PF at 0.95 ± 0.02.

Rule of thumb: largest step ≤ 25% of total kvar. For 200 kvar total, max step is 50 kvar, giving four steps at 12.5 + 25 + 50 + 100 = 187.5 kvar — round up to 200 by adding another 12.5 kvar, or accept the coverage and let the controller approximate between steps.

Each step needs its own contactor and (on industrial sites) its own detuned reactor and discharge resistor. The discharge resistor bleeds remaining voltage from the capacitor to within 50 V of ground in 3 minutes after switch-off — a mandatory safety requirement because a 400 V capacitor can still hold a lethal charge long after the site is powered down.

Inrush & Harmonics

The Two Things That Destroy Capacitor Banks — Inrush & Harmonics

When an uncharged capacitor bank switches in, the inrush is limited only by the supply impedance (the transformer impedance plus cabling resistance). On a stiff industrial supply this can be 10–20× the steady-state rated current, blowing contactors and tripping upstream MCCBs. Soft-start circuits — typically a series power resistor in parallel with a contactor — charge the capacitor over one to two cycles before the bypass contactor closes.

The other killer: harmonics. Variable frequency drives (VFDs), LED lighting and office PCs inject 3rd, 5th, 7th harmonic currents. An undamped capacitor bank forms a resonant circuit with site inductance — and if the resonant frequency lands on a harmonic (which happens with 3rd harmonic at 150 Hz on 50 Hz systems), current amplification reaches 10–20×.

Rule of thumb for detuning: 5.5% reactor on 50 Hz (f_r = 135 Hz) and 7% reactor on 60 Hz (f_r = 180 Hz), both below the 3rd harmonic. Add 2% more detuning if VFD penetration exceeds 30%. Harmonic simulation is mandatory above 100 kvar.

Power Factor Correction FAQ

What is power factor and why does it need correction?▼

Power factor (PF, or cos φ) is the ratio of real power (kW, the useful work you pay for) to apparent power (kVA, what the grid sees). A low PF means your equipment draws reactive power (kVAR) back and forth that never does useful work, raising supply current, overheating cables and transformers, and often triggering utility penalties. Correction adds capacitors that supply reactive power locally instead of importing it from the grid.

How do I calculate capacitor bank size for power factor correction?▼

Measure your total real power P in kW, measure or estimate your current power factor PF₁, pick a target PF₂ (0.95 is standard, 0.98 is aggressive), then apply: kvar needed = P × (tanφ₁ − tanφ₂), where tanφ = √(1/PF² − 1). Example: 100 kW at PF 0.7 → PF 0.95: tan0.7 ≈ 1.02, tan0.95 ≈ 0.329, difference = 0.691, so kvar = 69.1. Enter the same four numbers in the calculator above — it returns kvar, µF per phase, rated current and an inrush estimate.

How do I convert kvar to microfarads (µF)?▼

First convert kvar to var (× 1000). The reactive power Q = ω × C × V² relates var, frequency ω = 2πf, capacitance C in farads and voltage V. Rearranged for three-phase Y connection: C_Y = Q / (ω × V²) in farads, × 10⁶ for µF. For Δ connection (each phase sees line voltage): C_Δ_per_phase = Q / (3 × ω × V²). Single-phase simplifies to C = Q / (ω × V²). The calculator above handles all three configurations.

Why do Y and Δ connections give different µF values?▼

In Y (star) connection each capacitor sees the phase voltage V/√3, so to produce the same total kvar it needs more microfarads (roughly 3× the per-phase µF of a Δ bank for the same line voltage). In Δ (delta) each capacitor sees the full line voltage. Y banks are common for medium-voltage systems with 230/400 V supplies because 400 V capacitors can be used on the phase voltage of ~230 V. Δ banks are common for 400/690 V supplies where each phase sits at full 400 V.

What is capacitor bank inrush current?▼

When the first step of capacitors switches in, the bank is uncharged and acts almost like a short — the inrush current is limited only by the supply impedance, the transformer and the capacitor's own ESL. Typical inrush is 5–20× rated current, which can damage switchgear contacts and create transients that trip protective relays. Industrial banks use soft-start circuits (series resistor that shortouts after charge) or detuned reactors (L-C series) to limit inrush and suppress harmonics.

What is a detuned reactor and do I need one?▼

A detuned reactor adds an inductor in series with each step capacitor, forming a tuned L-C pair. Typical detuning frequencies are 135 Hz (for 50 Hz systems, detuned below the 3rd harmonic at 150 Hz) and 180 Hz (for 60 Hz systems). The reactor prevents anti-resonance with upstream capacitor banks and limits inrush. If your site already has a power factor correction bank from the utility or a neighbouring facility, anti-resonance is a real risk that must be simulated — do not copy a bank design blindly.

How many steps should my capacitor bank have?▼

A stepped capacitor bank (APFC — Automatic Power Factor Correction) splits the total kvar into 4–12 binary-weighted steps (e.g. 12.5, 25, 50, 100 kvar) so the controller can approximate any required kvar. The finer the steps, the less PF oscillates around the target. Rule of thumb: the largest step should be ≤ 25% of total kvar, giving at least 4 steps. Low-power sites (≤ 50 kvar) often use a single fixed step.

Why won't the calculator let me enter PF₂ lower than PF₁?▼

Because capacitors can only add reactive power — they raise PF toward unity, never lower it. If PF₂ < PF₁ you are asking the capacitors to undo something, which they cannot. If you actually need PF₂ < PF₁ your real problem is over-correction from a previous bank or site capacitors, and you should disconnect some of them rather than add more.

Related Capacitor Calculators

🧪

Cylindrical & Spherical

Calculate capacitance of coaxial cylindrical and concentric ...

🎵

Speaker Crossover Cap

Compute series capacitor (tweeter high-pass) and parallel in...

🎚️

DC Link Capacitor

Size DC bus capacitors for 3-phase inverters, VFDs and motor...

⏳

Capacitor Lifetime

Estimate capacitor life from rated lifetime (e.g. 105°C/2000...

📈

ESR & Ripple Current

Compute equivalent series resistance from tanδ/DF/Q, dissipa...

⚙️

PFC & Capacitor Bank

Size kvar compensation for industrial power factor correctio...

⚖️

Cap Voltage Divider

Split voltage across 2–4 series capacitors instantly: Vn = Q...

🔌

Power Supply Cap

Size rectifier bulk, buck-converter output and hold-up capac...

📻

LC Resonance

Get f₀ = 1/(2π√LC) for parallel or series LC tanks, plus Q f...

📉

RC Filter Cap

Solve C = 1/(2πfR) for low-pass, high-pass, band-pass and no...

🔊

Coupling & Bypass

Size AC coupling, input/output, emitter and cathode bypass c...

💎

Crystal Load Cap

Calculate C1 and C2 for a crystal oscillator: C = 2CL − Cstr...

🔧

Motor Capacitor Sizing

Size start and run capacitors for split-phase, cap-start, ca...

🎨

Capacitor Color Code

Decode 3-band, 4-band and 5-band capacitor color codes to pF...

📶

Capacitive Reactance

Compute Xc in Ω/kΩ/MΩ from frequency and C, with parallel-R ...

🔋

Capacitor Charge

Calculate stored charge Q = CV in C, mC, µC, nC, pC from cap...

⏱️

RC Time Constant

Get τ in seconds, ms, µs, ns from any R and C pair, plus the...

⚡

Capacitor Energy

Compute energy stored in any capacitor from E = ½CV² with li...

❄️

HVAC Capacitor Under Load

Test an HVAC run capacitor under load: enter amps, volts and...

📐

Parallel Plate Capacitor

Compute capacitance from plate area, separation and dielectr...

🔗

Series & Parallel Capacitors

Combine up to 12 capacitors in series or parallel with per-c...

🔄

Capacitance Converter

Convert capacitance between pF, nF, µF, mF and F live, and t...