Capacitor Bank Sizing Calculation: the kVAr Formula Explained
A capacitor bank sizing calculation gives the reactive power in kVAr that you must add to reach a target power factor. The formula is kVAr = kW × (tan φ1 − tan φ2), where φ1 is your present angle and φ2 the target. A 450 kW load at 0.78 power factor needs about 213 kVAr to reach 0.95.
What you receive: if you send your electricity bill or load list, a written proposal with the kVAr, step layout, standard and price within one working day. Request a quotation
By Eng. Ahmed Ali, Saudi Power Factor Company. Published 9 October 2026.
What inputs does the calculation need?
Three numbers decide the size, and one more decides the type.
- Active power in kW. Use the maximum demand on your bill, or the measured peak, not the connected load. Connected load oversizes the bank.
- Present power factor. Take it from the bill, or measure it at the incomer during normal production.
- Target power factor. Use the figure your tariff requires plus a margin, commonly 0.95. Under the Saudi Electricity Company tariff: 0.90 is the minimum above 1 MVA contract load; we design to 0.95.
- Capacitor voltage and frequency. These matter because a capacitor delivers its kVAr rating only at its rated voltage and frequency.
If the load swings widely or you suspect harmonics, a power quality survey records a week of demand and tells you whether a plain bank is safe.
How do you calculate the kVAr you need?
Use the formula, then divide the result into steps.
- Find the angle tangent at your present power factor: tan φ1 = √(1 − PF²) ÷ PF.
- Find the same value at the target power factor: tan φ2.
- Subtract: the difference is the multiplier.
- Multiply the multiplier by the kW demand to get kVAr.
- Correct for voltage (see the example) and divide the total into steps.
The table gives the multiplier so you can skip steps 1 to 3.
| Present PF | Multiplier to reach 0.90 | Multiplier to reach 0.95 |
|---|---|---|
| 0.70 | 0.536 | 0.692 |
| 0.75 | 0.398 | 0.553 |
| 0.80 | 0.266 | 0.421 |
| 0.85 | 0.135 | 0.291 |
| 0.90 | – | 0.156 |
Read across from your present power factor and multiply by your kW. A 100 kW load moving from 0.80 to 0.95 needs 100 × 0.421 = 42 kVAr.
Worked example: a 450 kW plant at 0.78 power factor
This is an example to show the method; your numbers will differ. The plant has a measured maximum demand of 450 kW at 0.78 power factor on a 380 V, 60 Hz supply. The target is 0.95, and the capacitors are rated 440 V.
| Step | Calculation | Result |
|---|---|---|
| tan φ1 at 0.78 | √(1 − 0.78²) ÷ 0.78 | 0.802 |
| tan φ2 at 0.95 | √(1 − 0.95²) ÷ 0.95 | 0.329 |
| Multiplier | 0.802 − 0.329 | 0.474 |
| kVAr needed at 380 V | 450 × 0.474 | 213 kVAr |
| Voltage factor of a 440 V capacitor on 380 V | (380 ÷ 440)² | 0.746 |
| Nameplate kVAr needed | 213 ÷ 0.746 | about 286 kVAr |
| Selected bank | 6 steps of 50 kVAr at 440 V | 300 kVAr nameplate |
The 300 kVAr nameplate delivers 300 × 0.746 = about 224 kVAr at 380 V. The remaining reactive demand is 450 × 0.802 − 224 = 137 kVAr, which gives a power factor of about 0.96. That clears the 0.95 target with a small margin.
What is the right capacitor bank size when the load varies?
Size the bank for the peak, then split it into steps that match the quiet periods. A bank that is too large at night pushes the plant to a capacitive power factor, so the step size sets how closely the panel can follow the load.
Use these guides:
- Choose step sizes of roughly one-eighth to one-fifth of the total, so 50 kVAr steps suit a 300 to 400 kVAr bank.
- Add one or two smaller steps, for example 25 kVAr, to trim the last few percent.
- Where drives, UPS units or rectifiers feed from the same transformer, add series reactors. A bank sized only on kVAr can resonate with the supply and overheat.
- Include margin for capacitor ageing, because capacitance falls gradually over the life of the unit.
An automatic assembly with a controller switches these steps for you; the range is on our APFC panel page. If you are ordering capacitors alone, check the voltage and kVAr ratings on the LV power capacitors page against your supply.
Where does a capacitor bank sizing calculation go wrong?
Four mistakes appear again and again.
- Using connected load. Motors rarely run at nameplate together, so the calculation overstates the kW.
- Ignoring voltage and frequency. A 440 V capacitor on a 380 V supply delivers about three-quarters of its rating, as the example shows. A capacitor built for a 50 Hz supply also behaves differently on 60 Hz, so state the supply frequency on the order.
- Sizing from one reading. A reading taken during a quiet shift undersizes the bank. A week of logged data avoids this.
- Skipping harmonics. The sum is correct, yet the bank fails early.
Saudi Power Factor Company has worked in Saudi Arabia since 2010 and is approved by Saudi Aramco, SABIC and the Royal Commission for Jubail and Yanbu. We apply this method inside our PFC panel design and sizing service, with the drawings and step layout issued for your approval.
Capacitor bank sizing questions
What is the purpose of a capacitor bank?
A capacitor bank supplies the reactive power that motors and transformers need, so that power no longer has to travel from the utility. This raises power factor, cuts current in your cables, releases transformer capacity and removes reactive-power charges from the bill.
How do I calculate kVAr from kW and power factor?
Multiply the kW by the difference between tan φ at your present power factor and tan φ at your target. For 100 kW moving from 0.80 to 0.95, that is 100 × (0.750 − 0.329) = about 42 kVAr. The multiplier table above gives the same answer.
How much does a 40 kVAr capacitor bank cost?
The price depends on the capacitor type, the voltage rating, whether reactors are included, the switching equipment and the enclosure. A fixed unit costs less than an automatic panel of the same rating. Send your kW and power factor, and the proposal prices the options side by side.
Can I size the bank from my electricity bill alone?
Yes, for a first estimate. The bill gives kW demand and power factor or kVArh, which is enough for the formula. For a final design we also need the supply voltage, transformer rating and any drives, so we confirm those before the drawings are issued.
How long does it take to receive a sized proposal?
You receive the proposal within one working day of sending your bill or load list. Delivery of the panel itself depends on the rating, the step count and drawing approval, and our typical lead time is 2–3 weeks for an APFC panel and 3–4 weeks for a detuned bank.
Need a capacitor bank sizing calculation checked against your own load? Send your bill or load list and receive a sized quotation within one working day.
Email: inquiry@saudipowerfactor.com | Request a quotation