# Three Phase Calculator

Created by Mehjabin Abdurrazaque
Reviewed by Wojciech Sas, PhD and Rijk de Wet
Last updated: Jun 05, 2023

• 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.

🙋 We deal only with balanced three-phase circuits in this three-phase calculator. A balanced three-phase circuit has the same voltages, currents, and power factors in all three phases. If one of these parameters is different for each phase, 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 of a three-phase circuit in terms of phase current and phase voltage as:

• S = 3 × VPh × IPh,

where:

• S is the apparent power;
• VPh is the phase voltage; and
• IPh is the phase current.

💡 Apparent power is measured in volt-ampere (VA). To learn more about VA and why it is used instead of watts (W), have a look at our kVA calculator.

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

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

• S = √3 × Vline × Iline,

where:

• Vline is the line-to-line voltage; and
• Iline is the line current.

## 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 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 = Vph × Iph × PF

Or, in terms of line voltage and line current:

• P = √3 × Vline × Iline × PF

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

## What is reactive power?

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 × VPh × IPh × sin φ

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

• Q = √3 × Vline × Iline × sin φ

💡 Reactive power is measured in volt-ampere reactive (var).

## What is the difference between power consumption in star and delta connections?

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

• Iline = Iph
• Vline = √3 × Vph

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

• Iline = √3 × Iph
• Vline = Vph

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

• S = √3 × Vline × Iline

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

• P = √3 × Vline × Iline × PF

and the reactive power formula in both connections is:

• Q = √3 × Vline × Iline × sin φ

⚠️ Though we can use the same power equations for both three-phase systems, the line quantities are not the same.

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

• Star connection:
• VL = √3 Vph = 693 V
• IL = Iph = 10 A
• S = √3 VL IL = 12 kVA
• P = √3 VL IL cos φ = 10.4 kW
• Q = √3 VL IL sin φ = 6 kVAr
• Delta connection:
• VL = Vph = 400 V
• IL = √3 Iph = 17.3 A
• S = √3 VL IL = 12 kVA
• P = √3 VL IL cos φ = 10.4 kW
• Q = √3 VL IL 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.

## How do I calculate three phase current?

The formulas to find three phase current from the power.

Known parameter

Formula to find current

Apparent power

Apparent power / (V × 1.73)

Active power

Active power / (V × PF × 1.73)

Reactive power

Reactive power / (V × sin(acos(PF)) × 1.73)

## How to use three phase calculator for AC power calculation?

Example: The real power to a three-phase AC motor is 5 kW. If the voltage and current to the motor are 400 V and 8.6 A, respectively, determine the power factor of the delta system.

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.

## FAQ

### What are the differences between active power and apparent power?

There are many differences between active and apparent power. Here are some of them, listed side-by-side in a table for easy comparison.

Apparent power

Active power

Known as "imaginary power"

Known as "real power"

Measured in volt-amperes (VA, kVA, MVA)

Measures in watts (W, kW, etc.)

The theoretical maximum power delivered by a voltage source during a specific time interval

The portion of electric power converted into useful work

The combination of active and reactive powers

A component of apparent power

### What does reactive power cause in an AC circuit?

In any AC circuit, reactive power causes a phase shift between voltage and current curves and reduces the overlap between the two curves. This results in delivering less power to the loads.

### What are the advantages of reactive power?

The important advantage of reactive power is that it helps maintain voltage levels to deliver active power through transmission lines. Transmission lines act as capacitors at very low levels of load and increase voltage. When they have high loads, transmission lines absorb reactive power and lower voltages.

### How do I find the power delivered to a motor working at 4 kV and 462 A?

The apparent power represents the power delivered. To find the exact answer, multiply voltage (4 kV) by current (462 A), which gives 1848 kVA.

💡 Also, check out our Ohm's law calculator to understand how to calculate the electric power. :)

Mehjabin Abdurrazaque
Connection type
Delta (D)
Phase current (Iₚₕ)
A
Phase voltage (Vₚₕ)
V
Line current (Iₗᵢₙₑ)
A
Line voltage (Vₗᵢₙₑ)
V
Phase angle (φ)
deg
Power factor
Apparent power (S)
kVA
Active power (P)
kW
Reactive power (Q)
kvar
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