Three-Phase Power Calculator Formula
Understand the math behind the three-phase power calculator. Each variable explained with a worked example.
Formulas Used
Real Power
real_kw = real_power / 1000Apparent Power
apparent_kva = apparent_power / 1000Reactive Power
reactive_kvar = sqrt(pow(apparent_power, 2) - pow(real_power, 2)) / 1000Phase Voltage
v_phase = v_line / sqrt(3)Variables
| Variable | Description | Default |
|---|---|---|
v_line | Line-to-Line Voltage(V) | 480 |
i_line | Line Current(A) | 20 |
power_factor | Power Factor | 0.85 |
apparent_power | Derived value= sqrt(3) * v_line * i_line | calculated |
real_power | Derived value= sqrt(3) * v_line * i_line * power_factor | calculated |
How It Works
Three-Phase Power Calculations
Three-phase systems are the standard for industrial and commercial power distribution.
Formulas (Balanced Load)
Apparent Power = sqrt(3) x V_line x I_line
Real Power = Apparent x Power Factor
Reactive Power = sqrt(Apparent^2 - Real^2)
Phase Voltage = Line Voltage / sqrt(3)
The sqrt(3) factor (approximately 1.732) arises from the 120-degree phase separation between the three phases.
Worked Example
480 V three-phase, 20 A line current, 0.85 power factor.
- 01Apparent: sqrt(3) x 480 x 20 = 16,627 VA = 16.63 kVA
- 02Real: 16,627 x 0.85 = 14,133 W = 14.13 kW
- 03Reactive: sqrt(16627^2 - 14133^2) = 8,744 VAR = 8.74 kVAR
- 04Phase voltage: 480 / 1.732 = 277.1 V
Frequently Asked Questions
When is three-phase power used?
For loads above about 5 kW, large motors, industrial equipment, and commercial buildings. It provides constant power delivery and efficient motor operation.
What is the difference between line and phase values?
Line values are measured between phases (L-L). Phase values are measured from one phase to neutral. V_line = sqrt(3) x V_phase for wye connections.
What if the load is unbalanced?
These formulas assume balanced loads. For unbalanced loads, calculate each phase separately and sum the results.
Ready to run the numbers?
Open Three-Phase Power Calculator