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Power Factor Calculator

Find the power factor, the three kinds of power (real, reactive and apparent), the phase angle, and the capacitor size (kVAR) needed to correct it.

Level: Grade 12 to college

Printable worksheet

Power Factor Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Power units

The power that does useful work, as read on a wattmeter.

Volts × amps, before allowing for the current lagging behind the voltage.

Works out the capacitor bank needed to raise a lagging power factor to this value.

Result

Power factor

0.8

Power factor 0.8 (φ = 36.87°): 40 kW real, 30 kVAR reactive, 50 kVA apparent.

Real power (P)
40 kW
Reactive power (Q)
30 kVAR
Apparent power (S)
50 kVA
Phase angle (φ)
36.8699 °
Capacitor bank needed
16.8526 kVAR
Apparent power after correction
42.1053 kVA15.8% less current for the same useful work

See the step-by-step solution ↓

Step-by-step solution

  1. Find the power factor (PF): divide the real power P, which does the work, by the apparent power S

    PF=4050=0.8

  2. Find the reactive power Q. The three powers form a right triangle, so Q is the leftover side

    Q=502−402=30 kVAR

  3. Find the phase angle φ, how far the current lags behind the voltage. Its cosine is the power factor

    φ=arccos(0.8)=36.8698976458 °

  4. Size the capacitor (Qc) to raise the power factor to 0.95. It must supply the reactive power you no longer want from the grid: the angle now (φ₁) versus the target angle (φ₂ = arccos(0.95) = 18.1949°)

    Qc=40×(0.75−0.32868411)=16.8526357928 kVAR

  5. Find the apparent power after correction (S₂): the same real power divided by the target power factor

    S₂=400.95=42.1052631579 kVA

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find out how much of the power your equipment draws actually does useful work. In AC wiring with motors, transformers or similar equipment, the current falls a little behind the voltage. When that happens, only part of the volts times amps does real work. The power factor is that useful share: real power (kW) divided by apparent power (kVA). A power factor of 1 means every amp is doing work. At 0.7, the wiring carries about 43% more current than the work alone needs.

Enter whichever pair of values you have. That can be real and apparent power, real and reactive power, or a voltage, current and wattmeter reading. It can also be a known power factor with either kW or kVA. The calculator works out all three powers and the phase angle. If you add a target power factor, it also finds how much reactive power a capacitor bank must supply to reach it.

Where it's used

Why this math matters outside the classroom:

  • Utility charges. Factories with a low power factor may face utility surcharges, so they add capacitors to bring it closer to 1.
  • Capacitor sizing. Correcting a 100 kW load from PF 0.7 to 0.95 needs about 100 × (1.020 − 0.329) ≈ 69 kVAR of capacitors.
  • Power triangle. A load drawing 80 kW and 60 kVAR has an apparent power of √(80² + 60²) = 100 kVA, a power factor of 0.8.
  • Generator ratings. Engineers size generators in kVA because they must carry the full current, not just the real power the load uses.

Grade level and standards: Grade 12 to college; Common Core State Standards for Mathematics HSG.SRT.C.8. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose which values you know. Then pick whether you're working in kW, kVAR and kVA or in W, VAR and VA.
  2. Enter the values you know. They might come from a power meter, a utility bill or the nameplate on the equipment.
  3. If you want to size a correction capacitor, enter a target power factor, such as 0.95. This step is optional.
  4. Read the power factor, the phase angle and the other powers. If you asked for one, the capacitor rating is shown too.

What the inputs mean

Real power (P)
Real (active) power is the part that does the work. It's what your kilowatt-hour meter bills you for. Enter it in kW or W, matching the unit choice above.
Apparent power (S)
Apparent power is the voltage times the current, using RMS (effective average) readings. It's in kVA or VA, and it's what cables and transformers must be sized to carry.
Reactive power (Q)
Reactive power, in kVAR or VAR, is energy that sloshes back and forth each cycle. It moves between the supply and the magnetic or electric fields inside the equipment, without doing work.
Voltage (RMS)
For the voltage, current and power option, use single-phase RMS readings. For three-phase power, use the electrical power calculator to get kVA first.
Target power factor (optional)
Utilities often ask business customers to stay above a set power factor, commonly somewhere around 0.9 to 0.95. Leave this blank to skip the correction calculation.

Formula and method

PF = P ÷ S = cos φ
S² = P² + Q²
Q = √(S² − P²),   S = √(P² + Q²)
Single-phase:  S = V × I
φ = arccos(PF)
Capacitor:  Qc = P × (tan φ₁ − tan φ₂)

In the formulas, PF is the power factor, P is real power, Q is reactive power and S is apparent power. V is the voltage and I is the current. The Greek letter φ (phi) is the phase angle, how far the current lags behind the voltage. Qc is the reactive power the capacitor must supply.

The three powers form a right triangle, called the power triangle. Real power is the bottom side, reactive power is the upright side, and apparent power is the long sloping side. The phase angle φ sits between real and apparent power. The power factor is the cosine of that angle, so knowing any two values fixes the whole triangle.

For a lagging load, like a motor, a capacitor wired in parallel supplies reactive power right there, so less has to come from the grid. Real power stays the same. The reactive power must drop from P × tan φ₁ to P × tan φ₂, where φ₁ is the angle now and φ₂ is the angle of the target power factor. The difference is the capacitor rating in kVAR.

Worked example

A workshop draws 40 kW of real power and 50 kVA of apparent power. The utility asks for a power factor of at least 0.95.

  1. Power factor: PF = 40 ÷ 50 = 0.8.
  2. Reactive power: Q = √(50² − 40²) = 30 kVAR.
  3. Phase angle: φ = arccos(0.8) = 36.8699°.
  4. Correction: tan φ₁ = 0.75 and tan φ₂ = tan(arccos 0.95) = 0.32868411, so Qc = 40 × (0.75 − 0.32868411) = 16.8526 kVAR.
  5. Apparent power after correction: 40 ÷ 0.95 = 42.1053 kVA.

Result: The power factor is 0.8. About 16.85 kVAR of capacitors would raise it to 0.95 and cut apparent power by about 15.8%.

Understanding the result

A low power factor doesn't waste the energy you're billed for in kWh. But it does mean more current for the same work. That means more heat in cables and transformers and more voltage drop. On some rate plans, it also means extra charges for kVA demand or reactive power.

Capacitor banks come in standard sizes, so round the result up to the next size available. Avoid correcting past 1. An over-corrected (leading) power factor can push voltages up and cause problems when the load is light.

Correcting near the equipment lowers the current in the wiring between the supply and the capacitor. It doesn't lower the current in the wiring past the capacitor, toward the equipment.

Assumptions and limitations

  • Voltages and currents follow a smooth sine wave, and the values you enter are RMS (effective average) readings.
  • The load is inductive (lagging), the usual case for motors and transformers.
  • Real power stays the same when the power factor is corrected.
  • Some loads, such as much power electronics, have heavy harmonic distortion (a choppy, non-smooth current). That adds a distortion part to the power factor. Capacitors don't fix it, and through resonance they can make it worse.
  • It gives the capacitor rating in kVAR, not the capacitance in microfarads. That also depends on the voltage, the frequency and how the capacitor is connected.
  • These are estimates. Power factor correction equipment should be specified and installed by a qualified electrician or engineer, following your local electrical code.

Frequently asked questions

What is a good power factor?

Above about 0.95 is generally considered good. Many utilities set a minimum for business and industrial customers, often in the 0.85 to 0.95 range. They may add charges if you fall below it. Purely resistive loads, such as heaters, have a power factor of 1.

Can power factor be greater than 1?

No. Real power can never be more than apparent power, so the ratio tops out at 1. If your readings give a higher value, they were probably taken at different times, or the units got mixed up.

What is the difference between leading and lagging power factor?

Lagging means the current trails behind the voltage, as in motors and other inductive loads. Leading means the current runs ahead of the voltage, as in capacitive loads. The calculator treats loads as lagging, which is the case where capacitors are used for correction.

Does correcting power factor lower my electricity bill?

Only if your rate plan charges for kVA demand or reactive energy, or penalizes a low power factor. Home bills are usually based on kWh alone, and correction doesn't change that.

How this calculator is checked

Method: The AC power triangle (S² = P² + Q², PF = P/S = cos φ) and the standard correction formula Qc = P(tan φ₁ − tan φ₂). The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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