Three Phase Power Calculator
This three phase power calculator uses the three phase power formula, P = √3 × V × I × PF, to find real, apparent, and reactive power from line voltage, current, and power factor. Enter the values and the three phase power calculator returns kW, kVA, and kVAR. It applies the standard 3 phase power calculation formula, so you get the full result without working the three phase power equation by hand.
Results
The Three Phase Power Calculator is part of our AC & Three Phase collection. Browse more ac & three phase to size, convert, and check your work alongside this tool.
What the three phase power equation gives you
Three-phase systems carry power on three conductors, and the three phase power formula combines them into a single figure. This three phase power calculator takes the line voltage, the line current, and the power factor, then returns the real power in kW, the apparent power in kVA, and the reactive power in kVAR. The √3 factor in the 3 phase power calculation formula accounts for the phase difference between the conductors, which is why three-phase power is not simply three times the single-phase value.
The 3 phase power calculation formula
The 3 phase power calculation formula for real power is:
Apparent power drops the power factor, S = √3 × V × I, and reactive power is Q = √3 × V × I × sin φ. The three phase power calculator computes all three, so the three phase power equation, the apparent power, and the reactive power come from one entry. The √3 (about 1.732) is the constant that makes this a 3 phase power equation rather than a single-phase one.
Formula for three phase power example
A balanced load at 400 V line voltage drawing 20 A at 0.9 power factor. The three phase power formula gives:
The apparent power is 13.86 kVA and the reactive power about 6.04 kVAR. Enter these values and the three phase power calculator returns the same, matching the formula for three phase power worked by hand.
How to use the three phase power calculator
Enter the line-to-line voltage, the line current, and the power factor of the load. The three phase power calculator applies the three phase power formula and returns kW, kVA, and kVAR together. To calculate three phase current instead, rearrange the same relationship; this tool starts from voltage and current, the most common three phase ac power calculation.
Reading the three phase power calculator result
Real power (kW) is the useful power that does work; apparent power (kVA) is what the supply and cables must carry; reactive power (kVAR) is the part that flows back and forth without doing work. The gap between kW and kVA is set by the power factor, so a low power factor means more current for the same useful power. Size cables and breakers from the kVA and current, not the kW, and use the calculate three phase current result to check the load against the supply.
When to use the three phase power calculator
- Finding load power with the three phase power formula
- Sizing supply from apparent power in a three phase ac power calculation
- Checking current draw when you calculate three phase current
- Comparing real and reactive power with the 3 phase power equation
Common three phase power calculator mistakes
- Dropping the √3. The three phase power formula needs it; without it the answer is about 42% too low.
- Sizing on kW. Cables and breakers follow the kVA and current, not the real power.
- Line versus phase voltage. Use the line-to-line voltage in the 3 phase power calculation formula unless the problem states otherwise.
Tips for accurate results
- Use the line-to-line voltage in the three phase power calculator.
- Enter the real power factor of the load, not an assumed 1.0.
- Size the supply from kVA and current, then check with calculate three phase current.
Why the √3 sits in the three phase power equation
The factor that defines the three phase power formula is √3, and understanding it explains the whole calculation. In a three-phase system the three voltages peak at different moments, 120 degrees apart, so the conductors never all carry their maximum at once. Adding the three contributions with that phase shift produces √3, roughly 1.732, rather than a plain 3. This is why a three phase ac power calculation delivers more power than single phase for the same line voltage and current, but not simply triple. Every 3 phase power calculation formula, whether for power, current, or kVA, carries this √3, and leaving it out is the classic error that makes a three-phase answer come out wrong.
Real, apparent, and reactive power in the 3 phase power equation
The three phase power calculator returns three numbers because AC power has three faces. Real power in kW does the actual work, turning motors and heating elements. Apparent power in kVA is the total the supply delivers, the product of voltage and current, and it is what cables, transformers, and breakers are sized against. Reactive power in kVAR flows back and forth to build the magnetic fields in motors and transformers without doing net work. The power factor is the ratio of real to apparent power, so a poor power factor means the supply carries more kVA than the useful kW, wasting capacity. Reading all three from the three phase power equation lets you size the system correctly and spot where power factor correction would help.
3 phase power calculation formula chart
Real power (kW) from the three phase power formula at 400 V, by current and power factor:
| Current | PF 0.8 | PF 0.9 | PF 1.0 |
|---|---|---|---|
| 10 A | 5.54 kW | 6.24 kW | 6.93 kW |
| 20 A | 11.09 kW | 12.47 kW | 13.86 kW |
| 50 A | 27.7 kW | 31.2 kW | 34.6 kW |
Three Phase Power Calculator FAQ
What is the three phase power formula?
The three phase power formula is P = √3 × V × I × PF for real power in watts. The three phase power calculator applies this 3 phase power calculation formula and also returns kVA and kVAR.
Why is there a √3 in the equation?
The √3 (about 1.732) accounts for the 120-degree phase difference between the three conductors. It is what makes the three phase power equation different from a single-phase one.
How do I calculate three phase current?
Rearrange the formula: I = P / (√3 × V × PF). Starting from power and voltage lets you calculate three phase current, while this tool starts from voltage and current.
What is the difference between kW and kVA?
kW is real power that does work; kVA is apparent power the supply must carry. The power factor sets the gap, and the three phase power calculator shows both from one 3 phase power equation.