Line current I
Estimated RMS current in each line conductor at steady state.
Electricity · Industrial electricity
Three-phase motor current — power, efficiency and power factor
Estimate steady-state three-phase motor current from useful shaft power P₂, line-to-line voltage U, efficiency η and power factor.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Electrical input power P₁
Active electrical power absorbed by the motor before losses.
Apparent power S
Three-phase apparent power corresponding to P₁ and the power factor.
Reactive power Q
Reactive power associated with apparent power and power factor.
Relation and numerical substitution
I = P₂ / (√3 · U · η · cosφ)—
P₂ is the useful mechanical output power available at the motor shaft. Efficiency η is entered as a percentage and relates P₂ to absorbed electrical power P₁. U is the RMS line-to-line voltage and 0 < cos φ ≤ 1. This is a steady-state calculation: starting current, VFD behavior, cable sizing, voltage drop, protection and code coordination are not sized.
01Formulas and symbols
Formulas used
P₁
P₂ / ηElectrical input power from mechanical output and efficiencyS
P₁ / cosφApparent power from absorbed active powerQ
S · √(1 − cos²φ)Reactive power from S and power factorI
S / (√3 · U)Line current in a balanced three-phase system02Assumptions and limits
Scope of validity
- P₂ is the useful mechanical output power available at the motor shaft.
- Efficiency η is entered as a percentage and relates P₂ to absorbed electrical power P₁.
- U is the RMS line-to-line voltage and 0 < cos φ ≤ 1.
- This is a steady-state calculation: starting current, VFD behavior, cable sizing, voltage drop, protection and code coordination are not sized.
03Validation example
Reference numerical case
- P₂ = 15 kW ; U = 400 V ; η = 90 % ; cos φ = 0.85
- P₁ = 15 / 0.90 = 16.667 kW
- S = 16.667 / 0.85 = 19.608 kVA
- Q = 19.608 × √(1 − 0.85²) ≈ 10.329 kvar
- I = 19,607.8 / (√3 × 400) ≈ 28.30 A
04References
Technical references
- IEC 60034-1 — Rotating electrical machines: rating and performance.
FAQ
Which power should I enter?
Enter useful mechanical output power P₂, usually the rated shaft power.
What does η mean?
η is motor efficiency: P₂ = η·P₁. The tool accepts efficiency as a percentage.
Why √3?
The √3 factor comes from the balanced three-phase power relation using line-to-line voltage.
Does this include starting current?
No. This is a steady-state current estimate; use manufacturer data for starting current.