Physics

Verified calculator with a transparent formula

Physics

Capacitive Power Factor Calculator.

Calculates the power factor of a capacitor given its reactive power and the total apparent power in an AC circuit.

Results update live as you type.
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Your inputs

How it works

  1. 1

    Enter the reactive power in VAR.

  2. 2

    Enter the apparent power in VA.

  3. 3

    The calculator computes the power factor as the square root of 1 minus the squared ratio.

  4. 4

    The result is a dimensionless number between 0 and 1.

sqrt(max(1 - (reactive_power / apparent_power)^2, 0))

Frequently asked questions

What does a power factor of 1 mean?

It means the circuit is purely resistive, with no reactive power, so all power is used effectively.

Can the power factor be negative?

No, the power factor is always between 0 and 1. A negative value would indicate a leading power factor, but the magnitude is what matters.

Why is the formula using square root?

Because power factor is the cosine of the phase angle, and from the power triangle, cos(θ) = sqrt(1 - (Q/S)^2).

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How it works

Calculates the power factor of a capacitor given its reactive power and the total apparent power in an AC circuit.

  1. Enter the reactive power in VAR.
  2. Enter the apparent power in VA.
  3. The calculator computes the power factor as the square root of 1 minus the squared ratio.
  4. The result is a dimensionless number between 0 and 1.

Formulas

The math behind this calculator, written out so you can verify the result.

Power Factor from Reactive and Apparent Power

PF = sqrt(1 - (Q/S)^2)

The power factor is the cosine of the phase angle between voltage and current. Given reactive power Q and apparent power S, the ratio Q/S is the sine of the angle, so the cosine is

Real-world use cases

Where this calculation shows up in everyday life.

Capacitor Sizing

Determine the power factor improvement when adding a capacitor to correct a lagging power factor.

Example: A motor with Q=500 VAR and S=1000 VA has PF=0.866.

Circuit Analysis

Quickly evaluate the power factor of a capacitive load in an AC circuit.

Example: Check if a capacitor bank is operating near unity.

Tips and common mistakes

Tips

  • Ensure both powers are in the same units (VAR and VA).
  • If reactive power is zero, the power factor is 1.
  • The result is always between 0 and 1; if you get a negative under the square root, check your inputs.

Common Mistakes to Avoid

  • Using watts instead of volt-amperes for apparent power.
  • Forgetting that the ratio must be squared before subtracting from 1.
  • Assuming the power factor is simply Q/S; it is actually the cosine of the angle.

Assumptions and limitations

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.