What is the formula for inductive reactive power?

Q = U · I · sin(φ), where U and I are RMS voltage and current and φ is the phase angle. Alternatively Q = I² · X_L using the inductive reactance X_L = 2πfL, or Q = √(S² − P²) from the power triangle. The unit is var.

What is the difference between inductive and capacitive reactive power?

Both are reactive power in var, but the current lags the voltage for inductive loads (motors, transformers) and leads it for capacitive loads (capacitors). By convention inductive Q is taken as positive; capacitive Q is negative. They partly cancel, which is why capacitors are used to compensate inductive loads.

How do I get reactive power from the power factor?

With active power P and power factor cos(φ), compute the angle φ = arccos(power factor), then Q = P · tan(φ). For example, at P = 1840 W and cos(φ) = 0.8, φ = 36.87° and Q = 1840 · tan(36.87°) = 1380 var.

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Inductive Reactive Power: The Formula and How to Use It

Stromfee Redaktion · 5. Juli 2026

Inductive reactive power Q is the power that oscillates between the source and inductive loads like motors and transformers without doing useful work. The core formula is Q = U · I · sin(φ), measured in var (volt-amperes reactive).

The Core Formula

Inductive reactive power is Q = U · I · sin(φ), where U is the RMS voltage, I is the RMS current, and φ is the phase angle between them. For a purely inductive load the current lags the voltage by 90°, so sin(φ) = 1 and Q = U · I. The unit is var (or kvar for thousands). Q is called 'inductive' when the current lags the voltage, which is the typical case for coils, motors and transformers.

Calculating Q From Inductive Reactance

If you know the current and the inductive reactance X_L, use Q = I² · X_L. The reactance itself comes from X_L = 2π · f · L = ω · L, where f is the frequency (50 Hz in Europe) and L is the inductance in henry. Equivalently, if voltage across the inductor is known, Q = U² / X_L. These forms are useful when the load is specified by its inductance rather than its phase angle.

Deriving Q From the Power Triangle

Reactive power is one side of the power triangle: S² = P² + Q². So if you already know apparent power S and active power P, you get Q = √(S² − P²). You can also write Q = P · tan(φ). The active power is P = U · I · cos(φ), and cos(φ) is the power factor — so a lower power factor means a larger reactive share for the same active load.

Worked Example

Take a single-phase load at U = 230 V drawing I = 10 A with a power factor cos(φ) = 0.8. The phase angle is φ = arccos(0.8) = 36.87°, so sin(φ) = 0.6. Then Q = 230 · 10 · 0.6 = 1380 var ≈ 1.38 kvar (inductive). Cross-check: S = 230 · 10 = 2300 VA, P = 2300 · 0.8 = 1840 W, and √(2300² − 1840²) = 1380 var — the same result.

Three-Phase Systems

For a balanced three-phase load the formula becomes Q = √3 · U_L · I_L · sin(φ), where U_L is the line-to-line voltage and I_L the line current. The √3 factor accounts for the three phases. The same power-triangle relation Q = √(S² − P²) still holds, with S = √3 · U_L · I_L.

Why It Matters in Practice

Inductive reactive power loads cables and transformers with current that does no useful work, and many grid operators bill a reactive-power component when the power factor is poor. A poor cos(φ) at a generator's grid feed-in point can lead to grid charges. Capacitor banks or controlled compensation offset the inductive Q, raising the power factor toward 1 and cutting those losses and fees.

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Inductive Reactive Power: The Formula and How to Use It

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