Three Phase Calculator

Welcome to the three phase calculator, that can help you with:

• Three-phase power calculation from voltage, current, and phase angle or power factor;
• Estimation of other types of power from the given type of power and phase angle or power factor; and
• Finding line quantities and other phase quantities from a phase quantity, one type of power, and phase angle or power factor.

Our 3 phase calculator is a comprehensive tool — it can determine the value of current, voltage, and power in your 3 phase circuit!

Also, we explain how to derive the 3 phase power equations in terms of line quantities for both star and delta systems.

Not only that, but our calculator is also useful for understanding:

• The three types of power in an AC circuit;
• The differences between active power and apparent power;
• How apparent power relates to electrical power; and
• What causes reactive power in an AC circuit, and the advantages attached.

Ready? Let's GO!

Apparent power is the total electrical power in a three-phase circuit. We calculate the apparent power of a three-phase circuit 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.

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

• S = √3 × V_line × I_line,

where:

• V_line is the line-to-line voltage; and
• I_line is the line current.

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

• P = S × PF,

where:

• P is the active power; and
• PF is the power factor and equals cos φ. Here, φ is the phase angle — the angle of lead or angle of lag of the current's phase with respect to the voltage's phase.

We can therefore calculate the active power using the two phases as:

• P = V_ph × I_ph × PF

Or, in terms of line voltage and line current:

• P = √3 × V_line × I_line × PF

Resistors absorb electrical power and dissipate it as heat or light, while capacitors and inductors return the power received in one half of the cycle to the power supply in the next half. The electric power that flows to and from in the circuit due to capacitors and inductors is the reactive power or wattless power (Q).

We calculate reactive power for a three-phase circuit as the power due to the sine component of the phase current, i.e., the product of apparent power (S) and the sine of the phase angle:

• Q = S × sin φ

So, in terms of phase quantities, reactive power is:

• Q = 3 × V_Ph × I_Ph × sin φ

And in terms of line quantities, the reactive power formula is:

• Q = √3 × V_line × I_line × sin φ

In a star connection, line current and phase current are the same and line voltage is equal to √3 times the phase voltage.

• I_line = I_ph
• V_line = √3 × V_ph

Line voltage and phase voltage are the same in a delta connection, and the line current is equal to √3 times the phase current.

• I_line = √3 × I_ph
• V_line = V_ph

Hence, for both delta and star connections, the apparent power is:

• S = √3 × V_line × I_line

Thus, the active power formula in both star and delta connections is:

• P = √3 × V_line × I_line × PF

and the reactive power formula in both connections is:

• Q = √3 × V_line × I_line × sin φ

For example, if the phase voltage is 400 V, the phase current is 10 A and the phase angle is 30 degrees:

• Star connection:
  • V_L = √3 V_ph = 693 V
  • I_L = I_ph = 10 A
  • S = √3 V_L I_L = 12 kVA
  • P = √3 V_L I_L cos φ = 10.4 kW
  • Q = √3 V_L I_L sin φ = 6 kVAr
• Delta connection:
  • V_L = V_ph = 400 V
  • I_L = √3 I_ph = 17.3 A
  • S = √3 V_L I_L = 12 kVA
  • P = √3 V_L I_L cos φ = 10.4 kW
  • Q = √3 V_L I_L sin φ = 6 kVAr

Hence, delta and star connections of the same phase current, voltage, and angle have the same amount of power in their circuits, though their line quantities are different.

To conduct the correct three-phase power calculation to the problem given above:

1. Identify the given parameters — active power = 5 kW, phase voltage = 400 V and line current = 8.6 A.
2. Choose the connection type. By default, the type of three-phase connection of Omni's three-phase calculator is Delta (D). Since the problem doesn't specify the connection type, you can leave this option as it is.
3. Select the appropriate unit from the drop-down list beside each parameter.
4. Enter the values of the given parameters in the respective input boxes.

Done! The three-phase calculator shows you the values of other parameters:

• Phase current =5 A;
• Line voltage = 400 V;
• Phase angle = 33 deg;
• Power factor = 0.84;
• Apparent power = 5.96 kVA; and
• Reactive power = 3.24 kvar.

You can learn more about this particular example from the 3-phase motor amperage calculator. Additionally, the delta to wye converter can help you expand your knowledge about three-phase systems.