3-Phase Power Calculator

The 3-Phase Power Calculator works out three-phase power, line current, or line-to-line voltage for a balanced AC system. Tell it which quantity you want to find, enter the values you already know plus the power factor, and it returns the answer along with the full power breakdown — real power (kW), apparent power (kVA), and reactive power (kVAR) — a to-scale power triangle, the Wye and Delta phase values, an animated three-phase waveform, and a suggested copper wire gauge and breaker size.

Three-Phase Power Formulas

For a balanced three-phase load specified by its line-to-line voltage (V_LL) and line current (I_L), the three power quantities are:

Where PF is the power factor (between 0 and 1) and √3 ≈ 1.732. Rearranging the first two formulas lets you solve for current, I_L = P / (√3 × V_LL × PF), or for voltage, V_LL = P / (√3 × I_L × PF).

Worked Example: 10 kW Motor at 400 V

A three-phase motor delivering 10 kW of real power at 400 V line-to-line with a power factor of 0.9:

The apparent power is 10 / 0.9 = 11.1 kVA, and the reactive power is √(11.1² − 10²) ≈ 4.8 kVAR. Each of the three lines carries about 16 amps, so the circuit needs conductors and a breaker sized for that current with the usual continuous-load margin.

The Power Triangle

Real power (P), reactive power (Q), and apparent power (S) form a right triangle. Real power is the horizontal leg, reactive power the vertical leg, and apparent power the hypotenuse. The angle between P and S is φ, and the power factor is its cosine: PF = cos(φ) = P / S. A power factor of 1.0 collapses the triangle to a flat line (no reactive power); a lower power factor opens the angle and adds reactive power that circulates without doing useful work.

Wye (Star) vs Delta Connections

Three-phase loads are wired in one of two configurations, and each relates the line quantities to the per-winding (phase) quantities differently:

In a Wye connection the line-to-line voltage is √3 times the phase voltage, while line and phase currents are equal. In a Delta connection the line and phase voltages are equal, while the line current is √3 times the phase current. Crucially, the total power is identical for both — only the per-winding voltage and current differ, which matters when sizing motor windings and transformer taps.

kW vs kVA vs kVAR

Three-Phase Current Chart (PF = 0.9)

Approximate line current per phase for a given real power and line-to-line voltage:

Why Three-Phase Uses √3

In a balanced three-phase system the three line-to-line voltages are the vector differences of phase voltages that are 120° apart, which makes each line-to-line voltage √3 (about 1.732) times the phase voltage. When total power is written in terms of the line quantities that engineers actually measure — line voltage and line current — that √3 factor appears. Because the load is split across three conductors, each line carries less current than an equivalent single-phase circuit of the same power, so three-phase distribution uses less copper and delivers smoother power, which is why it dominates industrial and commercial installations.

How to Use This Calculator

1. Choose what to solve for: power, line current, or line-to-line voltage. The form shows only the inputs that answer needs.
2. Enter the known values: the two quantities you already have. When entering power, pick its unit (kW, W, kVA, VA, or hp).
3. Enter the power factor: around 0.9 for typical mixed loads, 0.8–0.85 for motors, or 1.0 for purely resistive loads such as heaters.
4. Click Calculate: read the answer, the full power triangle, the Wye and Delta phase values, and the suggested wire gauge and breaker size.

Frequently Asked Questions

What is the formula for three-phase power?

For a balanced three-phase system using line-to-line voltage, real power is P = √3 × line voltage × line current × power factor (P = 1.732 × V × I × PF). Apparent power is S = 1.732 × V × I, and reactive power is Q = √(S² − P²).

How do you calculate three-phase current from power?

Rearrange the power formula to solve for current: I = P / (√3 × line voltage × power factor), or I = S / (1.732 × V) when you already know the apparent power in kVA.

Why does three-phase power use the square root of 3?

In a balanced three-phase system the line-to-line voltage is the square root of 3 (about 1.732) times the phase voltage. Summing the power delivered by all three phases and expressing it with line quantities produces the factor of 1.732.

What is the difference between kW and kVA in three-phase?

kW is real power, the power that does useful work. kVA is apparent power, the total power the circuit carries. They are related by the power factor: kW = kVA × power factor. The difference is reactive power (kVAR), which circulates without doing work.

What is the difference between Wye and Delta connections?

In a Wye (star) connection the line-to-line voltage is √3 times the phase voltage while line and phase currents are equal. In a Delta connection the line and phase voltages are equal while the line current is √3 times the phase current. Total power is the same for both.

How many amps is a 10 kW three-phase load at 400 V?

With a power factor of 0.9, apparent power is 10 / 0.9 = 11.1 kVA, so line current is 11111 / (1.732 × 400) = 16.0 amps per line.

Additional Resources

• Three-Phase Electric Power - Wikipedia
• AC Power (Real, Reactive, Apparent) - Wikipedia
• Power Factor - Wikipedia