Formula & Calculator
Power in kW (Three Phase)
Calculates real power in kilowatts for a balanced three-phase AC circuit from line voltage and current.
Interpretation
Power in kW (three‑phase AC): P(kW) = (√3 × V_L × I_L × cosθ) / 1000 for balanced loads.
The √3 factor accounts for the line‑to‑line voltage in a three‑phase system.
Example: V_L=400V, I_L=20A, cosθ=0.85 → P = (1.732×400×20×0.85)/1000 = 11776/1000 ≈ 11.78 kW.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| P | Real power (active power) | kW |
| V_L | Line-to-line RMS voltage | V |
| I_L | Line RMS current | A |
| cos θ | Power factor | dimensionless |
| θ | Phase angle between phase voltage and phase current | ° |
| √3 | Square root of 3 (1.732) — constant for balanced three-phase systems | dimensionless |
What it means
The real power in a balanced three‑phase circuit is P(kW) = (√3 × V_L × I_L × cosθ) / 1000, where V_L is the line‑to‑line voltage, I_L is the line current, and cosθ is the power factor. The √3 factor arises from the relationship between line and phase quantities. This formula is essential for calculating power in industrial motors, generators, and transformers. Example: A three‑phase motor with V_L=400V, I_L=20A, and power factor 0.85 consumes P = √3 × 400 × 20 × 0.85 / 1000 = 1.732 × 400 × 20 × 0.85 / 1000 = 11776 / 1000 ≈ 11.78 kW. This is the actual power drawn by the motor, which determines the electricity cost and required supply capacity.
Worked example
Three‑Phase Power – Practical Example
Real‑World| Parameter | Value |
|---|---|
| VL | 400 V |
| IL | 50 A |
| cos θ | 0.86 |
| Formula | P(kW) = (√3 × VL × IL × cos θ) / 1000 |
Common mistakes
Watch for unit mismatches (W vs kW, single- vs three-phase) and remember to include power factor or efficiency where the formula requires it.Applications
Power in kW (three‑phase): P(kW) = (√3 × V_L × I_L × cosθ)/1000 calculates real power in balanced three‑phase systems. This is used for industrial motors, distribution, and large loads. Engineers use it to design three‑phase systems, to size equipment, and to manage power factor.
- Industrial motor and machinery power calculation
- Three‑phase distribution and transformer sizing
- Power factor correction in industrial plants
- Load flow analysis and system planning
- Educational understanding of three‑phase power
Frequently Asked Questions
Real power is P(kW) = (√3 × V_L × I_L × cos θ) / 1000, where V_L is line‑to‑line voltage, I_L is line current, and cos θ is the power factor.
The √3 factor comes from the relationship between line and phase quantities in a three‑phase system. For a wye connection, V_L = √3 V_ph; for delta, I_L = √3 I_ph.
I_L = (P × 1000) / (√3 × V_L × cos θ).
Common errors: 1) forgetting the √3 factor, 2) using line‑neutral voltage instead of line‑line, 3) using the wrong power factor, 4) applying to unbalanced systems (requires summing phase powers).
Typically 0.7‑0.9 at full load, lower at light loads.
Using a three‑phase wattmeter, or by measuring each phase and summing.
Sizing motors, generators, transformers, and calculating industrial power consumption.
Three‑phase power is more efficient for large loads, provides constant power, and uses less conductor material for the same power.