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Calculator · Power factor
Power factor correction calculator
Capacitors supply the reactive power a load would otherwise draw from the line, and the size comes from the kW and the two power factors. This page takes a load in kW, or a motor in hp with its efficiency, and gives the capacitor kVAR, the multiplier that the published correction tables print, the kVA and line current before and after, and the capacity freed on the same kVA. The EC&M example of a 100 hp motor at 0.85 corrected to 0.95 has an input of 78.8 kW and a multiplier of 0.291, which gives 22.9 kVAR before rounding down to a 22.5 kVAR capacitor. For the current at a given kW, use the kW to amps calculator. The kVA a transformer needs is on the transformer size calculator.
- Give the load in kW, or a motor in hp with its efficiency, the power factor it runs at and the power factor you want. The page opens on 78.8 kW corrected from 0.85 to 0.95.
- The page multiplies the kW by the difference between the tangents of the two power-factor angles, 0.291 here, and gives 22.94 kVAR.
- Take the next smaller standard capacitor, as EC&M does for a motor. The line current falls to 89.5 percent of its value and the same kVA carries 9.27 kW more.
Example result for the default inputs
78.80 kW corrected from a power factor of 0.85 to 0.95.
Capacitor kVAR needed
22.94 kVAR
Table multiplier
0.291
Line current after
89.5 % of before
Capacity freed
9.27 kW
| Load | 78.80 kW |
|---|---|
| Before | PF 0.85: 78.80 kW, 48.84 kVAR, 92.71 kVA |
| After | PF 0.95: 78.80 kW, 25.90 kVAR, 82.95 kVA |
| Multiplier | tan(acos 0.85) - tan(acos 0.95) = 0.6197 - 0.3287 = 0.2911 |
| Capacitor | 78.80 kW x 0.2911 = 22.94 kVAR |
| Line current | 0.85 / 0.95 = 0.895 of the current before, at the same voltage |
| Capacity freed | 92.71 kVA x 0.95 - 78.80 kW = 9.27 kW |
- The kVAR is the exact figure for the stated power factors. A capacitor comes in fixed sizes, and for a motor EC&M rounds down to the next smaller size so that the load is under corrected and not over corrected.
For estimation purposes only. Consult a licensed engineer for final designs.
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How the capacitor kVAR is calculated
Power factor correction adds capacitors that supply the reactive power a load would otherwise draw from the line. The capacitor kVAR is the real power times the difference between the tangent of the power-factor angle before and after, which is the multiplier that the published correction tables print. This page takes the load in kW, or a motor in hp with its efficiency, and gives the kVAR, the kVA and line current before and after, and the capacity freed on the same kVA. It does not size the capacitor bank, apply a utility tariff or check harmonics.
- Real power
kW = hp x 0.746 / efficiencyA motor in hp is converted to input kW, so 100 hp at 94.7 percent is 78.78 kW. Kilowatts typed in are used as they are.- Multiplier
multiplier = tan(acos PF existing) - tan(acos PF target)This is the entry of the published correction tables. From 0.85 to 0.95 it is 0.291, and EC&M prints 0.291. The tangent of the angle is the kVAR per kW at that power factor.- Capacitor kVAR
kVAR = kW x multiplier78.8 kW x 0.291 is 22.94 kVAR. EC&M prints 22.9 kVAR for the 100 hp motor and then rounds down to a 22.5 kVAR capacitor.- kVA before and after
kVA = kW / PFThe same 78.8 kW is 92.71 kVA at 0.85 and 82.95 kVA at 0.95.- Line current
I after / I before = PF existing / PF targetAt the same voltage the current follows the kVA, so it falls to 89.5 percent of its value. EC&M applies this to a 118 A heater current, which becomes 105.6 A.- Capacity freed
freed kW = kVA before x PF target - kWThe kVA the supply already carries can then carry more real power. Electrical Technology gets 350 kW from 1,000 kVA taken from 0.65 to unity.
Worked examples from published power factor data
The default case is the motor input of the EC&M article. 78.8 kW at 0.85 is 92.71 kVA, and at 0.95 it is 82.95 kVA. The multiplier is 0.291, the capacitor is 22.94 kVAR, and the line current falls to 89.5 percent. Another 9.27 kW fits on the same kVA.
Each figure that the sources print sits in the table below beside the value this page computes. Sources round their tangents to three or four digits, so the computed values differ in the last digit. EC&M prints 22.9 kVAR from the hp, and 22.93 kVAR is the unrounded figure.
| Source | Quantity | Printed | This page |
|---|---|---|---|
| EC&M 2009 | 100 hp, 94.7%, input kW | 78.8 | 78.78 |
| EC&M 2009 | Multiplier, 0.85 to 0.95 | 0.291 | 0.2911 |
| EC&M 2009 | Capacitor kVAR | 22.9 | 22.93 |
| EC&M 2009 | Heater current after, A | 105.6 | 105.58 |
| Electrical Technology | 5 kW, 0.75 to 0.90, multiplier | 0.398 | 0.3976 |
| Electrical Technology | 5 kW, 0.75 to 0.90, kVAR | 1.99 | 1.988 |
| Electrical Technology | 650 kW, 0.65 to 1, multiplier | 1.169 | 1.1691 |
| Electrical Technology | 650 kW, 0.65 to 1, kVAR | 759.85 | 759.93 |
| Electrical Technology | 650 kW, 0.65 to 1, kW freed | 350 | 350.0 |
| Electrical Technology | 21.5 kW, 0.86 to 0.94, multiplier | 0.23 | 0.2304 |
| Electrical Technology | 1 kW, 0.71 to 0.97, multiplier | 0.741 | 0.7412 |
Seven cases below run through the same functions the form uses. The last two show that the starting point decides the size: 200 kW from 0.70 to 0.95 needs 138.30 kVAR, and from 0.90 to 0.95 only 31.13 kVAR.
| Case | Setup | Result |
|---|---|---|
| EC&M motor input, 78.8 kW | 78.8 kW, power factor 0.85 to 0.95 | 22.94 kVAR, multiplier 0.291, kVA 92.71 to 82.95, line current 89.5% of before |
| EC&M 100 hp motor, from hp | 100 hp at 94.7% efficiency (78.78 kW), power factor 0.85 to 0.95 | 22.93 kVAR, multiplier 0.291, kVA 92.68 to 82.92, line current 89.5% of before |
| 5 kW motor, 0.75 to 0.90 | 5 kW, power factor 0.75 to 0.9 | 1.99 kVAR, multiplier 0.398, kVA 6.67 to 5.56, line current 83.3% of before |
| 650 kW alternator load to unity | 650 kW, power factor 0.65 to 1 | 759.93 kVAR, multiplier 1.169, kVA 1,000.00 to 650.00, line current 65.0% of before |
| 21.5 kW single-phase motor | 21.5 kW, power factor 0.86 to 0.94 | 4.95 kVAR, multiplier 0.230, kVA 25.00 to 22.87, line current 91.5% of before |
| 200 kW plant, 0.70 to 0.95 | 200 kW, power factor 0.7 to 0.95 | 138.30 kVAR, multiplier 0.692, kVA 285.71 to 210.53, line current 73.7% of before |
| 200 kW plant, 0.90 to 0.95 | 200 kW, power factor 0.9 to 0.95 | 31.13 kVAR, multiplier 0.156, kVA 222.22 to 210.53, line current 94.7% of before |
Standards and data sources
- EC&M, The Basics of PF Correction on Single Induction Motors, June 1, 2009 - The worked example of a 100 hp motor at 94.7 percent efficiency, 0.85 to 0.95, with input 78.8 kW, table multiplier 0.291, 22.9 kVAR, and a 22.5 kVAR capacitor rounded down. It takes 95 percent as the upper limit for a motor and 90 percent as the optimum target, advises under correcting, and says never to use this correction on a motor controlled by a soft-start or a variable-frequency drive.
- Electrical Technology, How to Calculate the Suitable Capacitor Size in microfarads and kVAR for power factor improvement - The relation kVAR = P (tan theta1 - tan theta2) and its printed examples: 5 kW from 0.75 to 0.90 with multiplier 0.398 and 1.99 kVAR, 650 kW from 0.65 to unity with multiplier 1.169 and 759.85 kVAR, and 350 kW gained on 1,000 kVA. Its microfarad answers and one table entry disagree with its own formula and are not used here.
Limitations of this calculator
- The kVAR is the exact figure for the two power factors. Capacitors come in fixed sizes and in switched steps, and no open table of standard sizes was read for this page, so it names none. For a motor, EC&M rounds down to the next smaller size.
- A motor's power factor changes with its load, so the existing power factor must be the one at the load it runs. EC&M advises correcting to the running current and under correcting, with 95 percent as the upper limit and 90 percent the optimum target.
- The conductors and the short-circuit protection of a motor circuit are not sized from the corrected current. NEC Articles 430 and 460 cover the motor circuit and the capacitor, and this page applies neither. A capacitor larger than the motor needs can also raise the voltage at the motor when it is switched off, so ask the capacitor maker for the largest size for that motor.
- Never use this correction at the terminals of a motor controlled by a soft-start or a variable-frequency drive. Ask the drive manufacturer.
- Harmonics are not considered. Capacitors can resonate with a transformer or the line, and a plant with drives or other non-linear loads needs a harmonic study and often detuned reactors. No open source read here gives a number that this page could quote.
- A target near unity can turn the power factor leading when the load drops. Switched banks and controllers are outside this page.
- The microfarad value of a capacitor depends on the connection and the voltage and is not given. Voltage is not an input: the kVAR does not depend on it.
- Utility penalty tariffs, demand charges and capacitor prices are not calculated.
- This is a planning estimate, not a design drawing. A licensed electrician or engineer, the capacitor manufacturer's data and the authority having jurisdiction decide the equipment and the installation.
Common power factor correction mistakes
- Using kVA where kW belongs. The kVAR is the kW times the multiplier. 78.8 kW at 0.85 is 92.71 kVA, and using that figure in place of the kW gives a capacitor about 1.18 times too large.
- Typing a percentage. A power factor is a fraction, so 85 percent is 0.85. The two power-factor fields take values from 0.1 to 1.
- Correcting a motor past the upper limit. EC&M calls 95 percent the upper limit for a motor, with 90 percent the optimum target. Taking 78.8 kW to 0.98, not 0.95, needs 32.83 kVAR, 9.90 kVAR more, for a small drop in line current.
- Taking the power factor at full load for a lightly loaded motor. A motor's power factor falls as it unloads, so the kVAR sized for full load can be too much at light load. Use the power factor at the load it runs and under correct.
- Leaving the overload heaters. Capacitors at the motor terminals reduce the current through the starter. EC&M resizes the heater current by the ratio of the power factors, 118 A to 105.6 A in its example.
- Ignoring the starting point. The gain depends on where you start. 200 kW from 0.70 to 0.95 needs 138.30 kVAR, and from 0.90 to 0.95 only 31.13 kVAR.
Common questions about power factor correction
How do I calculate the capacitor kVAR for power factor correction?
Multiply the real power in kW by the difference between the tangent of the angle at the existing power factor and the tangent at the target. For 78.8 kW from 0.85 to 0.95 the difference is 0.291, so the capacitor is 22.94 kVAR.
What is the power factor correction multiplier?
It is tan(acos existing PF) minus tan(acos target PF), the entry that correction tables print at the row of the existing power factor and the column of the target. From 0.85 to 0.95 it is 0.291. EC&M prints 0.291 for the same pair.
How do I size a capacitor for a motor?
Convert the hp to input kW by hp times 0.746 divided by the efficiency, then multiply by the multiplier. 100 hp at 94.7 percent is 78.78 kW and 22.93 kVAR from 0.85 to 0.95. EC&M rounds down to the next smaller standard capacitor, 22.5 kVAR in its example.
What power factor should I correct to?
For a motor, EC&M takes 95 percent as the upper limit and 90 percent as the optimum target. Unity or a value near it risks a leading power factor at light load, and a building has its own threshold in the utility's tariff.
Does power factor correction reduce the current?
Yes, on the supply side of the capacitor. The line current follows the kVA, so correcting from 0.85 to 0.95 leaves 89.5 percent of the current. Real power drawn by the load stays the same.
How much capacity does power factor correction free?
The same kVA carries more kW at a higher power factor. 78.8 kW at 0.85 is 92.71 kVA, which at 0.95 carries 88.07 kW, 9.27 kW more. Electrical Technology prints 350 kW on 1,000 kVA from 0.65 to unity.
Can I use this with a variable-frequency drive?
No. EC&M says never to use motor-terminal correction with a motor controlled by a soft-start or a variable-frequency drive. Contact the drive manufacturer.
Does the voltage change the kVAR?
No. The kVAR depends on the kW and the two power factors. Voltage matters for the microfarad value and the current, which this page does not give for the capacitor.
Is there a limit on how many times I can run this?
No. This calculator runs in your browser with no daily limit and no signup.
Used on the same job
- Wire size calculator The conductor of a feeder, whose load a better power factor lowers. A motor circuit is sized from the motor tables, not the corrected current.
- Voltage drop calculator Voltage drop falls with the line current.
- Standard breaker and fuse size calculator The standard ratings of Table 240.6(A).
Size the capacitor, then check the line
The kVAR comes first, and the lower line current then shows on the feeder side of the capacitor. A motor circuit is still sized from the motor tables. Take the capacitor sizes and the harmonic limits from the manufacturer's data. The current of a load at a given kW comes from the kW to amps calculator, and the conductor from the wire size calculator. You can also ask the assistant to go over a power factor correction.
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