Power Factor and the Power Triangle
Power factor formulas: kW, kVA and kVAR from the power triangle, capacitor kVAR to raise power factor, a worked example and a table of multipliers.
The formulas
| To find | Formula |
|---|---|
| Power factor | pf = P / S = cos φ |
| Apparent power | S = P / pf |
| Reactive power | Q = √(S² − P²) = P × tan φ |
| Capacitor to raise pf | Qc = P × (tan φ1 − tan φ2), with φ = arccos(pf) |
P is real power in kW, S apparent power in kVA, Q reactive power in kVAR. The multiplier in the last row is the number you read from a correction table.
Worked example: 100 kW from 0.8 to 0.95
- tan φ1 = tan(arccos 0.8) = 0.75
- tan φ2 = tan(arccos 0.95) = 0.3287
- Qc = 100 × (0.75 − 0.3287) = 42.13 kVAR
- Apparent power falls from 125 kVA to 105.3 kVA, and Q from 75 to 32.87 kVAR
Multiplier: kVAR per kW of load
| Present | Target 0.95 | Target 0.98 | Target 1.00 |
|---|---|---|---|
| pf 0.6 | 1.005 | 1.13 | 1.333 |
| pf 0.7 | 0.6915 | 0.8171 | 1.02 |
| pf 0.8 | 0.4213 | 0.5469 | 0.75 |
| pf 0.9 | 0.1556 | 0.2813 | 0.4843 |
Multiply the kW of the load by the number in the table to get the capacitor size in kVAR.
Frequently asked questions
What is a good power factor?
Many utilities ask for 0.9 or better and may charge a penalty below it. Check your own tariff.
Does a capacitor change the kW?
No. It supplies reactive power locally, so the current from the supply falls, but the real power the load uses is unchanged.
Can I correct to exactly 1.00?
The formula allows it, but a bank sized for unity is easily overcorrected when the load drops. Targets of 0.95 to 0.98 are common.
What if the load has harmonics?
Capacitors can resonate with the supply inductance at a harmonic frequency. On harmonic-rich loads, check for resonance and consider detuned capacitor banks.
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