Three-Phase Power Calculator
Active and apparent power of a balanced three-phase load, in watts, kW and kVA.
Results
Active power
15,588.5
W
Active power
15.588
kW
Apparent power
17.321
kVA
What this tool does
For a balanced three-phase load measured with line-to-line voltage, the total power is √3 times voltage times current times power factor. Forgetting the √3 is the most common mistake in industrial electrical calculations.
Formula
P = √3 × U × I × cos φ
Variables
| Symbol | Meaning | Unit |
|---|---|---|
u | Line-to-line voltage | V |
i | Current | A |
pf | Power factor | — |
P | Active power | W |
Pk | Active power | kW |
S | Apparent power | kVA |
Worked example
- Line-to-line voltage400 V
- Current25 A
- Power factor0.9
- Active power15,588.5 W
- Active power15.588 kW
- Apparent power17.321 kVA
Limitations
- Electrical installations are governed by national wiring rules. Cable sizing also depends on installation method, grouping, ambient temperature and protection devices, which this calculator does not evaluate.
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.
Frequently asked questions
Why is there a square root of three?
Because the three phases peak at different moments, a third of a cycle apart. The line-to-line voltage is √3 times the phase voltage, and summing the three phase powers gives √3 × U × I × cos φ when U is the line voltage. Using 3 instead of 1.732 overstates the power by 73 %.