The power factor calculator above ties together the three kinds of power in an alternating current system — real power in kilowatts, reactive power in kilovolt-amperes reactive, and apparent power in kilovolt-amperes — and then sizes the capacitance you would need to move the power factor up to a target value.
Arb Digital builds free tools that pick one job and finish it properly. This page is about the relationship between the three powers and the correction that changes it. The boundary against the site's existing electrical power calculator is that the other page derives power from circuit quantities such as voltage, current and resistance, while this one starts from the powers themselves and answers what a poor power factor costs and how to fix it.
What This Power Factor Calculator Does
Power factor is the ratio of real power to apparent power. Real power is the part that does work — turns shafts, produces heat, emits light. Apparent power is the product of voltage and current that the supply must actually deliver. When they differ, the gap is reactive power, which flows back and forth between the source and the load's magnetic fields without doing any net work.
The three quantities form a right-angled triangle, with real power along the base, reactive power vertical, and apparent power as the hypotenuse. Power factor is the cosine of the angle between real and apparent. That geometry is why any two of the three determine the third, and the tool accepts whichever pair you happen to have.
The correction calculation follows from the same triangle. Adding capacitance supplies reactive power locally, shortening the vertical side while leaving the base untouched. The required capacitor rating is the difference between the reactive power you have and the reactive power your target power factor allows, and converting that into microfarads needs the supply voltage and frequency.
How to Use It
- Pick the input pair you actually measured. Real and apparent power come off most utility bills; voltage, current and power factor come off a clamp meter; real and reactive power come off a logger.
- Set the supply type correctly. Three-phase figures quoted line-to-line carry a factor of the square root of three, and getting this wrong changes the current by 73 per cent.
- Enter the voltage and frequency even in the power-based modes. They are not needed for the power factor itself, but nothing can be said about capacitance without them.
- Choose a target that matches your tariff. Most utilities that apply a reactive charge set the threshold at 0.95, and correcting far beyond that buys little.
- Read the corrected current as the real prize. It is the figure that determines whether an existing cable, transformer or switchboard has capacity left in it.
The Formula: How Power Factor Is Calculated
Power factor is PF = P ÷ S, real power over apparent power. The three powers are related by S2 = P2 + Q2. The US Department of Energy fact sheet "Reducing Power Factor Cost" gives power factor as real power divided by apparent power, works an example where 100 kW of real power alongside 142 kVA of apparent power gives a power factor of 0.70, and notes that utilities usually charge a penalty to customers with power factors below 0.95.
Apparent power from measurements is S = VI for single-phase and S = √3 × VLL × I for three-phase quoted line-to-line. All three quantities share the same SI dimensions — the SI Brochure published by the BIPM defines the watt as the coherent derived unit of power — and the volt-ampere and var are used by convention to signal which component of it is meant.
Correction uses the tangent form. If φ1 is the present phase angle and φ2 the target, the capacitor rating is QC = P(tan φ1 − tan φ2). For a delta-connected three-phase bank the capacitance per phase is QC ÷ (3 × 2πf × VLL2).
Work the defaults. 52 kW of real power alongside 69.28 kVA apparent gives a power factor of 0.751, and reactive power √(69.282 − 522) = 45.78 kvar. Present tan φ is 45.78/52 = 0.880; at a target of 0.95, tan φ is 0.329. The capacitor rating is 52 × (0.880 − 0.329) = 28.69 kvar, which at 400 volts and 50 hertz is 190 microfarads per phase in delta. Current falls from 100 amperes to 79.0.
Why a Poor Power Factor Costs Money
The energy meter records kilowatt-hours, and correcting power factor does not change them at all. The saving comes from three other places, and understanding which one applies to you decides whether correction is worth doing.
The first is a direct charge. Many commercial and industrial tariffs bill either for reactive energy in kilovar-hours or apply a surcharge when the measured power factor falls below a threshold, commonly 0.95. Where such a term exists, correction removes it outright and the payback is straightforward arithmetic against the capacitor cost.
The second is maximum demand. Where a tariff charges for peak kVA rather than peak kW, the bill tracks apparent power directly, so cutting apparent power cuts the charge in proportion. At the default figures, moving from 0.751 to 0.95 reduces apparent power from 69.3 kVA to 54.7 — a fifth off a demand charge that recurs every month.
The third is capacity, and it does not appear on a bill at all. Cables, transformers, switchgear and generators are all rated in apparent power because they carry the full current regardless of its phase. Freeing up 21 per cent of the current on a supply that is running out of headroom can defer a transformer upgrade, which is frequently the largest single item in the business case. The wire size calculator and the breaker size calculator work from that current figure.
Why Inductive Loads Cause the Problem
Reactive power is not waste in the way losses are. It is energy borrowed and returned twice per cycle, building the magnetic field an inductive device needs and then collapsing it again. Motors, transformers, welding sets and discharge lighting ballasts all work this way, and they are the bulk of industrial load.
Because that energy is returned, it does no net work over a cycle and does not turn the meter. But it does flow, and while it is flowing it occupies the same conductors as the useful current. The two components add vectorially rather than arithmetically, which is why a power factor of 0.75 means 33 per cent more current than the real power alone would require, not 25 per cent.
Motor loading is the usual culprit behind a bad site power factor. An induction motor at full load might reach 0.85; the same motor at a quarter load can fall to 0.5 or below, because the magnetising current stays roughly constant while the working current falls away. Oversized motors running lightly are therefore expensive twice over — poor efficiency and poor power factor together.
Correction Is Not Free of Risk
A capacitor bank supplies leading reactive power that cancels the lagging reactive power of the load. Size it correctly and the two nearly balance. Size it for full load and leave it connected at light load, and it over-corrects: the power factor swings leading, current rises again, and voltage at the point of connection can climb above the supply.
This is why fixed capacitors are usually sized for the minimum load and automatic banks are used where load varies, switching stages in and out to track demand. Some tariffs penalise a leading power factor exactly as they penalise a lagging one, so over-correction can cost money as well as causing voltage problems.
Harmonics complicate matters further. Variable speed drives, rectifiers and switched-mode supplies draw non-sinusoidal current, and capacitors present a low impedance to high frequencies, so they can attract harmonic currents and overheat. In severe cases the capacitance resonates with the supply inductance and amplifies a harmonic rather than absorbing it, which is why detuned reactors are fitted alongside capacitors on sites with significant electronic load.
Displacement Power Factor and True Power Factor
The calculation on this page is displacement power factor — the cosine of the phase angle between voltage and current, valid when both are clean sine waves. On a modern site they often are not, and the distinction matters.
True power factor is real power divided by apparent power regardless of waveform, and it includes distortion as well as displacement. A load drawing heavily distorted current can show a true power factor well below its displacement power factor, and capacitors will not fix the difference because there is no phase angle to correct. Only filtering or a different rectifier topology addresses distortion.
In practice, if the site is dominated by motors and transformers the two figures are close and this calculation is sound. If it is dominated by electronic loads, a measurement of true power factor from a meter that samples the actual waveform is the only reliable input, and the correction result here should be treated as an upper bound on what capacitors can achieve. The frequency converter and the LC resonant frequency calculator are useful when investigating where a resonance sits.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Expecting correction to cut kilowatt-hours — the energy meter reads real power, which correction leaves unchanged. The saving comes from reactive charges, demand charges and released capacity.
- Mixing line-to-line and line-to-neutral voltage — a three-phase figure quoted line-to-line carries a factor of the square root of three that the single-phase formula does not.
- Sizing capacitors for peak load — a bank fixed at full-load requirement will over-correct when the plant is idling, pushing the power factor leading and raising the voltage.
- Ignoring harmonics — capacitors present low impedance to high frequencies and can overheat or resonate on sites with substantial electronic load.
- Comparing readings taken at different times — power factor changes minute by minute with load, so a kW figure and a kVA figure from different moments give a meaningless ratio.
Related Free Tools From Arb Digital
Derive the powers themselves from circuit quantities with the electrical power calculator, and handle DC relationships with the Ohm's law calculator. For the installation, the wire size calculator, the breaker size calculator and the voltage drop calculator all work from the current figure this page produces. Rescale units with the power converter, the capacitance converter and the frequency converter, look at resonance with the LC resonant frequency calculator, and price consumption with the electricity bill calculator. The full free online tools hub lists everything Arb Digital publishes.
Frequently Asked Questions
It is the ratio of real power in kilowatts to apparent power in kilovolt-amperes. A value of 1 means all the current delivered is doing useful work; lower values mean part of the current is exchanging energy with the load's magnetic fields instead.
No. The energy meter records real power, which correction leaves unchanged. What falls is the current and therefore the apparent power, which is what removes reactive charges, reduces kVA demand charges and frees capacity in cables and transformers.
Because generating and transporting the reactive component still consumes network capacity even though it does no useful work at the customer's end. The US Department of Energy notes that utilities usually charge a penalty to customers whose power factor falls below 0.95.
Inductive loads: motors, transformers, welding equipment and discharge lighting ballasts. An induction motor running lightly loaded is the most common cause, because its magnetising current stays roughly constant while its working current falls away.
The rating in kvar is the real power multiplied by the difference between the tangent of the present phase angle and the tangent of the target angle. Converting that to microfarads needs the supply voltage, the frequency and whether the bank is connected in star or delta.
Yes. Too much capacitance pushes the power factor leading, which raises current again and can lift the voltage at the point of connection. Fixed banks are therefore sized for minimum load, and automatic banks switch stages to follow demand.
It calculates displacement power factor, which assumes clean sine waves. Where electronic loads distort the current, true power factor is lower than the displacement figure and capacitors cannot correct the difference, so the result should be read as an upper bound.
This tool is provided for educational and estimating use. Tariff structures and penalty thresholds vary between suppliers and regions, nothing here is financial advice, and capacitor installation is work for a qualified electrical engineer rather than a calculation on a web page.
