Calculation
Q = √3 · U · I · sinφ with sinφ = √(1−cos²φ)
As with real power, the √3 factor applies to line quantities; the sine of the phase angle enters instead of cos φ.
Busch 2006, Abschnitt 5.6 Drehstromleistung
Three-phase reactive power
As with real power, the √3 factor applies to line quantities; the sine of the phase angle enters instead of cos φ.
MINTSI
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Result
Select a target and calculate.
Understand the inputs
- Reactive power Q — Inductive reactive power of the balanced three-phase load, in the same power unit as P, conventionally labelled kvar.
- Line voltage U — RMS voltage between two line conductors of the balanced system.
- Line current I — RMS current in each of the three equally loaded lines.
- Power factor cos φ — Displacement factor of the balanced load; reactive power vanishes at cos φ=1.
Example
400 V, 10 A and cos φ=0.8 give sinφ=0.6 and Q≈2.771 kvar (compare P≈5.543 kW).
Assumptions and limits
Balanced sinusoidal 50 Hz system without harmonics; only inductive (lagging) reactive power is reported, capacitive correction and imbalance are excluded.
Understand Three-phase reactive power
This calculator complements the well-known three-phase real power with the reactive power of a balanced three-phase load, indicating how strongly an inductive load burdens the supply with reactive current before planning correction.
What does this quantity describe?
For a balanced three-phase system, reactive power follows Q=√3·U·I·sinφ, analogous to real power P=√3·U·I·cosφ. U and I are always line quantities. sinφ follows from the entered cos φ via sinφ=√(1−cos²φ) and is positive for 0≤φ<90°.
Formula and variables
Q = √3 · U · I · sinφ with sinφ = √(1−cos²φ)
Q = √3·U·I·sinφsinφ = √(1−cos²φ)S = √3·U·I
| Symbol / input | Meaning |
|---|---|
| Reactive power Q | Inductive reactive power of the balanced three-phase load, in the same power unit as P, conventionally labelled kvar. |
| Line voltage U | RMS voltage between two line conductors of the balanced system. |
| Line current I | RMS current in each of the three equally loaded lines. |
| Power factor cos φ | Displacement factor of the balanced load; reactive power vanishes at cos φ=1. |
Choose the inputs correctly
U is the RMS voltage between two line conductors, not the phase voltage. I is the RMS current in each of the three equally loaded lines. cos φ is the load's displacement factor from a nameplate or measurement.
How to use the calculator
Record line voltage and line current at the same operating point as the power factor. If cos φ is unknown, determine it first with a power meter or the power-factor calculator from measured real power.
Worked example
400 V, 10 A and cos φ=0.8 give sinφ=0.6 and Q≈2.771 kvar; the same load gives P≈5.543 kW and apparent power S=√3·U·I≈6.928 kVA.
Understand the result and units
The closer cos φ is to 1, the smaller Q becomes relative to P. High reactive power increases line current for the same real power, raising losses upstream in the network.
U is a voltage, I a current and cos φ dimensionless. Q is shown in the same power unit as real power, conventionally labelled kvar in practice.
Typical applications
Estimating network loading from motors, transformers and other inductive three-phase loads, and preparing reactive-power correction.
Assumptions, limits and common mistakes
Balanced sinusoidal 50 Hz systems only, without harmonics. Only inductive (lagging) reactive power is reported; capacitive loads, imbalance and distortion reactive power are excluded.
Common mistake: Do not substitute phase voltage for line voltage. Do not confuse cos φ with the total power factor under harmonics, which also includes a distortion component.
Frequently asked questions
What is “Three-phase reactive power” used for?
Estimating network loading from motors, transformers and other inductive three-phase loads, and preparing reactive-power correction.
Where do the input values come from?
U is the RMS voltage between two line conductors, not the phase voltage. I is the RMS current in each of the three equally loaded lines. cos φ is the load's displacement factor from a nameplate or measurement.
What does the result not cover?
Balanced sinusoidal 50 Hz systems only, without harmonics. Only inductive (lagging) reactive power is reported; capacitive loads, imbalance and distortion reactive power are excluded.