Capacitor Sizing Calculator — Free Online Calculator
Calculate the capacitor kVAR needed for power factor correction. Reduce electricity bills and improve system efficiency.
How to Use This Calculator
Enter your load in kW, current power factor, and target power factor.
The Formula Explained
kVAR = kW × (tan(arccos(PF_current)) - tan(arccos(PF_target))). This is the reactive power that must be supplied by capacitors to improve the power factor.
Capacitor Applications in Electrical Systems
Capacitors are passive energy storage devices that store energy in electric fields between parallel plates. Unlike batteries, they charge and discharge almost instantaneously and have no chemical wear. This makes them ideal for applications requiring fast energy delivery (camera flashes, defibrillators, regenerative braking), frequency filtering (audio crossovers, RF filters), motor starting (single-phase induction motor start capacitors), and power factor correction (industrial facilities).
Three main parameters define a capacitor: capacitance (farads, F, measured in µF for practical values), voltage rating (maximum safe applied voltage), and tolerance (±5%, ±10%, ±20% typical). The energy stored is E = 0.5 × C × V², meaning voltage contributes quadratically — doubling the voltage quadruples the energy. This is why camera flash capacitors operate at 300-450V despite being powered by 3V batteries: the voltage boost dramatically increases energy storage per unit of capacitance.
Worked Example: Motor Start Capacitor
A 1 HP single-phase 230V induction motor typically requires a 100-200 µF start capacitor with 250VAC rating. During startup, the capacitor creates a 90-degree phase shift in the auxiliary winding that produces starting torque. After the motor reaches about 75% speed, a centrifugal switch disconnects the capacitor from the circuit.
Sizing the start capacitor: manufacturer specifications typically give the exact value. For a replacement when the original value is unknown, 40-50 µF per HP is a rule of thumb for start capacitors (different from run capacitors which are 4-10 µF per HP). Voltage rating must exceed the motor line voltage × sqrt(2) plus safety margin: 230V × 1.414 = 325V peak, so use at least 330V or 370V rating.
Failed capacitor symptoms: motor humming but not starting (most common), slow startup, repeated thermal protector tripping. Testing: use a capacitance meter or multimeter with capacitance function. A good 150 µF capacitor reads within 10% of rated value. A failed capacitor reads near zero or shows leakage on the resistance mode.
Worked Example: Industrial Power Factor Correction
A machine shop draws 200 kW of real power at 0.72 power factor (heavy motor load). Apparent power: 200 / 0.72 = 278 kVA. Reactive power: sqrt(278² - 200²) = 193 kVAR lagging.
The utility charges a power factor penalty for PF below 0.90. Target: bring PF to 0.95. New reactive power at 0.95 PF: 200 × tan(acos(0.95)) = 200 × 0.329 = 65.7 kVAR.
Capacitor bank required: 193 - 65.7 = 127 kVAR. At 480V three-phase delta configuration: capacitance per phase = kVAR / (2π × 60 × V² × 10^-6) = 127,000 / (2π × 60 × 480² × 10^-6) / 3 = 486 µF per phase. Most manufacturers sell banks in 25, 50, 100, 150 kVAR steps; choose 150 kVAR to give headroom and round up.
Cost analysis: 150 kVAR capacitor bank at 480V costs about 4,000-8,000 USD installed. Monthly utility penalty savings: typically 200-500 USD for a facility this size. Payback: 12-40 months, depending on specific tariff structure. Additional benefit: reduced wire losses throughout the facility (about 2-4% energy savings from lower current).
Capacitor Calculation Mistakes
1. Mixing up capacitance in different units. 1 F = 1,000,000 µF = 1,000,000,000 nF = 1,000,000,000,000 pF. Losing track of unit prefixes is a common error.
2. Forgetting voltage rating. Operating a capacitor above its voltage rating causes immediate failure, often destructively. Always derate to 80% of rated voltage for long life.
3. Using wrong formula for series vs parallel. Parallel capacitors add: C_total = C1 + C2 + ... Series capacitors combine like resistors in parallel: 1/C_total = 1/C1 + 1/C2 + ... Many people mistakenly do the opposite.
4. Polarity errors on electrolytic capacitors. Electrolytic (aluminum and tantalum) capacitors are polarized and will fail — sometimes explosively — if connected in reverse. Ceramic and film capacitors are non-polarized.
5. Ignoring ESR (equivalent series resistance). Real capacitors have internal resistance that limits ripple current and causes heating. High-ripple applications (power supplies, audio) need low-ESR capacitors, typically costing 3-5x more than standard.
Capacitor Types and Applications
Ceramic: Small values (pF to low µF), non-polarized, wide voltage range. Used in RF, bypass, filter applications.
Electrolytic (aluminum): Large values (1 µF to 10,000+ µF), polarized, for power supply filtering. Most common in power electronics. Life limited by electrolyte dry-out.
Tantalum: Polarized, stable, compact. Used where reliability and temperature stability are critical. Fail by igniting if overvoltaged.
Film (polypropylene, polyester): Non-polarized, stable, long life. Used in motor run capacitors, power factor correction, snubbers.
Supercapacitor (EDLC, Electric Double-Layer Capacitor): Very large capacitance (farads), low voltage (typically 2.7-5.5V per cell). Used for regenerative braking, UPS holdover, memory backup.
Power factor correction capacitors: Large three-phase units designed for continuous AC operation. Typically oil-filled for industrial use.
Standards
IEC 60384 — Fixed capacitors for use in electronic equipment (multiple sub-parts for different types). NEC Article 460 — Capacitor installation including overcurrent protection and grounding for industrial capacitors. UL 810 — Standard for capacitors. IEEE 18 — Shunt power capacitors for power factor correction.
Capacitor sizing: PF correction and motor-start applications
Capacitors in AC power systems serve two main jobs: power-factor correction at industrial sites (to avoid utility PF penalties and reduce conductor current) and motor-start/run on single-phase induction motors. The calculator gives kVAR sizing for PF correction and uF sizing for motor capacitors based on the load profile.
The formula and what it does
The formula calculates how much reactive power (kVAR) you need to add to shift the load from existing PF to target PF. Tables in Schneider and Eaton catalogs let you skip the trig by reading off the multiplier directly.
Worked example
Scenario: Industrial site, 200 kW load at PF 0.78, target PF 0.95 to avoid utility penalty.
Multiplier from PF correction table: 0.802 - 0.329 = 0.473 (or compute: tan(arccos(0.78)) = 0.802, tan(arccos(0.95)) = 0.329). kVAR needed = 200 x 0.473 = 94.6 kVAR. Install a 100 kVAR capacitor bank, which brings PF to about 0.96. Utility penalty avoided: typically $400-1500/month for a 200 kW commercial account.
Common mistakes to avoid
undefinedFrequently asked questions
Why does the utility charge for low PF?
Low PF means more current for the same real power. The utility sizes infrastructure to that current but only gets paid for kWh (real power). The kVAR penalty recoups the cost of oversized infrastructure.
Where should the capacitor bank be located?
At the load (close to the motor or panel) for maximum effect. At the service entrance is simpler but misses the conductor sizing benefit downstream.
Can capacitors over-correct PF?
Yes. Capacitive (leading) PF below 0.95 leading can cause voltage rise, resonance with utility impedance, and equipment problems. Use detuned capacitor banks or harmonic filters in heavy non-linear environments.
How do motor-run capacitors fail?
Heat and age. Oil-filled run capacitors (electrolytic on motor start, oil-filled on run) dry out and lose capacitance. Symptoms: motor runs hot, starts slowly, hums but does not turn. Replace at same uF and same or higher voltage rating.
Are residential PF correction devices worth it?
No. Residential meters measure only real power (kWh). PF correction does not reduce your bill. Industrial PF penalties are based on kVA or kVAR demand, separate billing structure.
What is detuned capacitor?
A capacitor bank with series reactor that shifts the resonance frequency below the 5th harmonic. Prevents capacitor and grid impedance resonance that can amplify harmonics catastrophically.