Reactive Power

Q = S × sin(φ)

Quick answer

This calculator solves Q = S × sin(φ) for Reactive Power. With Apparent Power 22 W, Phase Angle 45 °, the result is 15.56 W. It solves in 3 directions, so you can enter the values you have and get the one you need.

Calculator

Reactive Power (W)
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Formula

Q = S × sin(φ)

Description

Reactive power represents the component of apparent power that oscillates between source and load without performing useful work. It is caused by energy storage elements (inductors and capacitors) that alternately absorb and release energy each half cycle. Inductive loads (motors, transformers) consume positive reactive power, while capacitive loads generate it. The phase angle φ between voltage and current determines the split between real and reactive power. At φ = 0 (purely resistive), Q = 0; at φ = 90° (purely reactive), all power is reactive.

Variables

  • Q — Reactive power in volt-amperes reactive (VAR)
  • S — Apparent power (VA)
  • φ — Phase angle between voltage and current (degrees)

Practical Notes

Power factor correction adds capacitors to cancel inductive reactive power, bringing the net reactive power closer to zero and the power factor closer to unity. Industrial capacitor banks are sized in kVAR. Over-correction (leading power factor) can cause voltage rise and is usually avoided. Some utilities charge separately for reactive power consumption above a threshold.

Symbols and units

Symbol Meaning Default unit Accepted units
Q Reactive Power W µW, mW, W, kW
S Apparent Power W µW, mW, W, kW
phi Phase Angle ° °

Step by step

  1. 1. What you know: Apparent Power 22 W, Phase Angle 45 °
  2. 2. The relation: Q = S × sin(φ)
  3. 3. Substitute: S = 22 W, phi = 45 °
  4. 4. Result: Reactive Power = 15.56 W

Worked examples

Minimum range

Given: Apparent Power 22 mW, Phase Angle 1.5 °

Result: Reactive Power = 0.5759 mW

Low range

Given: Apparent Power 0.22 W, Phase Angle 15 °

Result: Reactive Power = 56.94 mW

Typical

Given: Apparent Power 22 W, Phase Angle 45 °

Result: Reactive Power = 15.56 W

High range

Given: Apparent Power 2.2 kW, Phase Angle 75 °

Result: Reactive Power = 2.125 kW

Maximum range

Given: Apparent Power 22 kW, Phase Angle 750 °

Result: Reactive Power = 11 kW

Solving for each variable

Solve for Reactive Power

Apparent Power 22 mW, Phase Angle 1.5 ° → 0.5759 mW

Solve for Apparent Power

Reactive Power 10 mW, Phase Angle 1.5 ° → 0.382 W

Solve for Phase Angle

Reactive Power 10 mW, Apparent Power 22 mW → 27.04 °

How Reactive Power changes with Apparent Power

Apparent Power (input) Reactive Power (result)
4.84 W 4.78 W
12.1 W 11.95 W
24.2 W 23.9 W
36.3 W 35.85 W
48.4 W 47.8 W
72.6 W 71.71 W
96.8 W 95.61 W
0.1936 kW 0.1912 kW
0.3388 kW 0.3346 kW
0.484 kW 0.478 kW

The same result in other units

Unit Value
mW 15560
W 15.56
kW 0.01556

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Frequently asked questions

How do you calculate Reactive Power?

Use Q = S × sin(φ). With Apparent Power 22 W, Phase Angle 45 °, Reactive Power works out to 15.56 W.

What is the formula for Reactive Power?

The formula is Q = S × sin(φ). Reactive power represents the component of apparent power that oscillates between source and load without performing useful work.

How do you find Apparent Power when you know the other values?

Rearrange for Apparent Power: with Reactive Power 10 mW, Phase Angle 1.5 °, Apparent Power is 0.382 W.

How do you find Phase Angle when you know the other values?

Rearrange for Phase Angle: with Reactive Power 10 mW, Apparent Power 22 mW, Phase Angle is 27.04 °.

What units does Reactive Power use?

Reactive Power is shown in mW, W, kW. Values are held in SI base units internally, so you can mix prefixes without converting by hand.

Related Concepts

All AC Circuits formulas →
Resonant Frequency Impedance (RLC Series) Quality Factor (Bandwidth) Quality Factor (RLC) Power Factor Apparent Power Reactive Power RLC Circuit Bandwidth

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