Three Phase Calculator — Apparent, Active & Reactive Power | Star & Delta | √3 × V × I

Welcome to the three phase calculator, a comprehensive tool that determines the value of current, voltage, and power in your 3-phase circuit. It can help you with:

• Three-phase power calculation from voltage, current, and power factor (or phase angle);
• Estimating other types of power (apparent, active, reactive) from a given quantity; and
• Finding line quantities and phase quantities for both star (wye) and delta systems.

Below, we also explain how to derive the 3-phase power equations in terms of line quantities for both star and delta systems, the three types of power in an AC circuit, the difference between active and apparent power, and what causes reactive power.

⚡ Note: This calculator deals only with balanced three-phase circuits. A balanced three-phase circuit has the same voltages, currents, and power factors in all three phases. If one of these parameters differs between phases, it is an unbalanced three-phase circuit.

What is apparent power in a three phase circuit?

Apparent power is the total electrical power in a three-phase circuit. We calculate the apparent power in terms of phase current and phase voltage as:

S = 3 × V_ph × I_ph

where S is the apparent power, V_ph is the phase voltage, and I_ph is the phase current. Apparent power is measured in volt-amperes (VA).

How do I calculate apparent power using line voltage and current?

In terms of line-to-line voltage and line current, the apparent power of a three-phase circuit is:

S = √3 × V_line × I_line ≈ 1.732 × V_line × I_line

where V_line is the line-to-line voltage and I_line is the line current. This formula is the same for both star and delta connections.

What is active or real power?

Active power is the actual power that is really transferred to the load and dissipated in the circuit. We calculate active power as the product of the apparent power and the power factor:

P = S × PF

where PF is the power factor and equals cos φ. Here, φ is the phase angle — the angle of lead or lag of the current's phase with respect to the voltage's phase. In terms of phase or line quantities:

P = 3 × V_ph × I_ph × PF
P = √3 × V_line × I_line × PF

Active power is measured in watts (W) as it indicates the useful work done in the circuit.

What is reactive power?

Reactive power is the power that continually bounces back and forth between the source and the reactive components (inductors and capacitors) of the load. It does no useful work but is necessary to sustain the magnetic and electric fields. We calculate it as:

Q = S × sin φ = √3 × V_line × I_line × sin φ

Reactive power is measured in volt-amperes reactive (VAR). The three powers form the power triangle: S² = P² + Q².

Star vs. delta: power consumption

The apparent, active, and reactive power are the same for star and delta connections when expressed in line quantities. The difference lies in how line and phase quantities relate:

Star (Wye, Y):  V_ph = V_line / √3,   I_ph = I_line
Delta (Δ):      V_ph = V_line,        I_ph = I_line / √3

How do I calculate three phase current?

Rearrange the apparent power formula to solve for the line current:

I_line = S / (√3 × V_line)

If you know the active power instead, divide by the power factor as well:

I_line = P / (√3 × V_line × PF)

How to use the three phase calculator

1. Select your connection type — star (wye) or delta.
2. Enter the line voltage (line-to-line) in volts.
3. Enter the line current in amperes.
4. Enter the power factor (cos φ), between 0.01 and 1.00.
5. Read the apparent power (S), active power (P), reactive power (Q), phase angle, and the phase voltage and current.

Sample three phase power calculation

Suppose you have a balanced three-phase circuit with a line voltage of 400 V, a line current of 10 A, and a power factor of 0.9:

S = 1.732 × 400 × 10 = 6928.20 VA ≈ 6.93 kVA
P = 6928.20 × 0.9 = 6235.38 W ≈ 6.24 kW
Q = 6928.20 × 0.4359 = 3020.30 VAR ≈ 3.02 kVAR
φ = arccos(0.9) = 25.84°

FAQs

What is the difference between active power and apparent power?

Apparent power (S, in VA) is the total power supplied to the circuit, the vector sum of active and reactive power. Active power (P, in W) is the portion that actually does useful work. They are related by the power factor: P = S × PF. Apparent power equals active power only when the power factor is 1 (a purely resistive load).

How does apparent power relate to electrical power?

Apparent power is the product of the RMS voltage and RMS current without considering the phase difference between them. It represents the total electrical "demand" the load places on the supply, which is why generators, transformers, and cables are rated in VA or kVA rather than watts.

What causes reactive power in an AC circuit?

Reactive power is caused by reactive components — inductors (motors, transformers) and capacitors. These store energy in magnetic or electric fields during one part of the AC cycle and release it back during another, causing current to lead or lag the voltage. Although reactive power does no net work, it must be supplied and increases the current drawn from the grid.

What is a good power factor?

A power factor of 1.0 (unity) is ideal — all the apparent power is converted to useful work. Most industrial three-phase loads have a power factor between 0.8 and 0.95. A low power factor means more current is required to deliver the same real power, so utilities often charge extra for poor power factor.

Want to learn more?

This calculator is part of our Electronics & Circuits collection. You may also find useful our kVA Calculator, Power Factor Calculator, and AC Wattage Calculator.