3 Phase Power Formula Line Voltage

3 Phase Power Formula:

\[ P_{kW} = \frac{V_{line} \times I_{line} \times PF \times \sqrt{3}}{1000} \]

Power (P_kW): kW

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is 3 Phase Power Formula (Line Voltage)?

Definition: This formula calculates the real power in kilowatts (kW) for a balanced three-phase electrical system using line voltage and current.

Purpose: It helps electrical engineers and technicians determine the actual power consumption in three-phase systems, which is essential for system design and analysis.

2. How Does the Formula Work?

The formula is:

\[ P_{kW} = \frac{V_{line} \times I_{line} \times PF \times \sqrt{3}}{1000} \]

Where:

\( P_{kW} \) — Real power in kilowatts
\( V_{line} \) — Line-to-line voltage (volts)
\( I_{line} \) — Line current (amps)
\( PF \) — Power factor (unitless, between 0 and 1)
\( \sqrt{3} \) — Constant for three-phase systems (≈1.732)

Explanation: The formula accounts for all three phases by multiplying by √3, and includes the power factor to calculate real power (not just apparent power).

3. Importance of 3 Phase Power Calculation

Details: Accurate three-phase power calculations are crucial for proper equipment sizing, energy efficiency analysis, and electrical system design in industrial and commercial applications.

4. Using the Calculator

Tips: Enter the line voltage (typically 208V, 480V, etc.), line current, and power factor (default 0.8). Power factor must be between 0 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between line and phase voltage?
A: Line voltage is between any two lines (phases), while phase voltage is between any line and neutral. For wye systems, line voltage = phase voltage × √3.

Q2: Why do we multiply by √3 in three-phase calculations?
A: The √3 factor accounts for the 120° phase difference between the three phases in a balanced system.

Q3: What is a typical power factor value?
A: Motors typically have 0.8-0.9 PF, lighting 0.95+, and heavily inductive loads may be 0.5 or lower.

Q4: How does this differ from single-phase power calculation?
A: Single-phase uses P=VI×PF (no √3 factor) and typically uses phase voltage rather than line voltage.

Q5: What if my system is unbalanced?
A: This formula assumes balanced loads. For unbalanced systems, calculate each phase separately and sum the results.