Active power P
Average power converted into useful work or heat.
Electricity · Industrial electricity
Three-phase power, P–Q–S and current
Calculate P, Q and S from line-to-line voltage, line current and power factor, or solve current from kW or kVA.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Reactive power Q
Magnitude of reactive power associated with the entered power factor.
Apparent power S
Balanced three-phase product √3·U·I.
Line current I
RMS current in each line conductor.
Relation and numerical substitution
S = √3 · U · I ; P = S · cosφ ; Q = S · √(1 − cos²φ)—
Balanced three-phase system in sinusoidal steady state. U is RMS line-to-line voltage and I is RMS line current. Power factor is entered as 0 < cos φ ≤ 1. Q is reported as a magnitude; the calculator does not distinguish leading from lagging power factor. Unbalance, harmonics, cable voltage drop and conductor losses are not included.
01Formulas and symbols
Formulas used
S
√3 · U · IThree-phase apparent powerP
S · cosφActive powerQ
S · √(1 − cos²φ)Reactive power magnitudeI
P / (√3 · U · cosφ)Current from active powerI
S / (√3 · U)Current from apparent power02Assumptions and limits
Scope of validity
- Balanced three-phase system in sinusoidal steady state.
- U is RMS line-to-line voltage and I is RMS line current.
- Power factor is entered as 0 < cos φ ≤ 1.
- Q is reported as a magnitude; the calculator does not distinguish leading from lagging power factor.
- Unbalance, harmonics, cable voltage drop and conductor losses are not included.
03Validation example
Reference numerical case
- U = 400 V, I = 32 A and cos φ = 0.85.
- S = √3 × 400 × 32 = 22.1703 kVA.
- P = 22.1703 × 0.85 = 18.8447 kW.
- Q = 22.1703 × √(1 − 0.85²) = 11.6789 kvar.
04References
Technical references
- IEC 60050-131 — International Electrotechnical Vocabulary: circuit theory.
- BIPM — The International System of Units (SI), 9th edition.