How to Calculate Three-Phase Power

Three-phase electrical power can be calculated using line-to-line voltage, line current, and power factor.

For a balanced three-phase AC system, the real power formula is:

Watts = √3 × Volts × Amps × Power Factor

For real power in kilowatts:

kW = (√3 × Volts × Amps × Power Factor) ÷ 1000

For apparent power in volt-amperes:

VA = √3 × Volts × Amps

For apparent power in kilovolt-amperes:

kVA = (√3 × Volts × Amps) ÷ 1000

In these formulas, the voltage should be the line-to-line voltage and the current should be the line current. The value of √3 is approximately 1.732.

Example: 400 V, 10 A, 0.8 Power Factor

Suppose a balanced three-phase electrical load operates at 400 volts line-to-line, draws 10 amps of line current, and has a power factor of 0.8.

First calculate apparent power:

VA = 1.732 × 400 × 10

VA = approximately 6,928 VA

Convert VA to kVA:

kVA = 6928 ÷ 1000

kVA = approximately 6.93 kVA

Now calculate real power:

Watts = 1.732 × 400 × 10 × 0.8

Watts = approximately 5,543 W

Convert watts to kilowatts:

kW = approximately 5.54 kW

Therefore, a balanced 400 V three-phase load drawing 10 A at a power factor of 0.8 uses approximately 5.54 kW of real power and 6.93 kVA of apparent power.

Example: 415 V, 20 A, 0.9 Power Factor

For a balanced three-phase system operating at 415 volts line-to-line, 20 amps, and a power factor of 0.9:

VA = 1.732 × 415 × 20

VA = approximately 14,376 VA

kVA = approximately 14.38 kVA

Watts = 1.732 × 415 × 20 × 0.9

Watts = approximately 12,939 W

kW = approximately 12.94 kW

Three-Phase Power Formula

For a balanced three-phase AC system using line-to-line voltage and line current:

P = √3 × V × I × PF

Where:

P = real power in watts
V = line-to-line voltage in volts
I = line current in amperes
PF = power factor
√3 = approximately 1.732

For apparent power:

S = √3 × V × I

Apparent power is measured in VA or kVA.

Three-Phase Power Reference Table

The following examples use a power factor of 0.8 and line-to-line voltage.

What Is Three-Phase Power?

Three-phase power is an AC electrical system that uses three alternating voltage waveforms separated by 120 electrical degrees.

Three-phase systems are commonly used for commercial buildings, industrial equipment, motors, data centers, large UPS systems, generators, transformers, air-conditioning systems, pumps, and other higher-power electrical loads.

Why Is √3 Used in Three-Phase Calculations?

The value √3, or approximately 1.732, appears in balanced three-phase equations because of the mathematical relationship between the three phase voltages and currents.

When line-to-line voltage and line current are used, apparent power is:

VA = √3 × Volts × Amps

Real power is:

Watts = √3 × Volts × Amps × Power Factor

What Voltage Should I Enter?

For this calculator, enter the line-to-line voltage of the three-phase system.

For example, if a system is described as 400 V three-phase, the 400 V value is typically the line-to-line voltage used by this calculator.

Do not substitute line-to-neutral voltage into this formula unless you convert the calculation appropriately.

What Is Line Current?

Line current is the current flowing through each line conductor supplying the balanced three-phase load.

The calculator assumes the entered current represents the line current of the three-phase system.

Three-Phase Real Power

Real power is the electrical power that performs useful work and is measured in watts or kilowatts.

For balanced three-phase power:

Watts = √3 × Volts × Amps × Power Factor

If you already know the three-phase kW and need to calculate current, use our

kW to Amps Calculator
.

Three-Phase Apparent Power

Apparent power represents the total electrical power supplied to the load and is measured in VA or kVA.

For a balanced three-phase system:

VA = √3 × Volts × Amps

Power factor is not required when calculating apparent power directly from line voltage and line current.

If you want to calculate apparent power directly from amps and voltage, use our

Amps to kVA Calculator
.

Why Is Power Factor Needed for kW but Not kVA?

kW represents real power, while kVA represents apparent power.

The relationship is:

kW = kVA × Power Factor

For example, a three-phase load with an apparent power of 10 kVA and a power factor of 0.8 has:

10 × 0.8 = 8 kW

This is why power factor is included when calculating watts or kW but is not needed to calculate VA or kVA from voltage and current.

Three-Phase kW vs kVA

Kilowatts represent real electrical power, while kilovolt-amperes represent apparent electrical power.

Their relationship depends on power factor:

kW = kVA × Power Factor

At a power factor of 1, kW and kVA have the same numerical value.

At a power factor below 1, the kW value is lower than the kVA value.

Single-Phase vs Three-Phase Power

Single-phase and three-phase electrical systems use different formulas when power is calculated from voltage and current.

For single-phase real power:

Watts = Volts × Amps × Power Factor

For balanced three-phase real power using line-to-line voltage:

Watts = √3 × Volts × Amps × Power Factor

For single-phase calculations, use our

Single-Phase Power Calculator
.

Common Uses of a Three-Phase Power Calculator

A three-phase power calculator is useful for estimating electrical power in commercial, industrial, data center, electrical distribution, and equipment applications.

Common examples include three-phase UPS systems, generators, transformers, motors, pumps, chillers, air-conditioning systems, industrial machinery, electrical panels, servers, data center equipment, and other three-phase loads.

The calculator can help compare voltage, current, power factor, real power, and apparent power values during preliminary planning and electrical analysis.

Frequently Asked Questions

How do I calculate three-phase power?

For a balanced three-phase system using line-to-line voltage:

Watts = √3 × Volts × Amps × Power Factor

How do I calculate three-phase kW?

Use:

kW = (√3 × Volts × Amps × Power Factor) ÷ 1000

How do I calculate three-phase kVA?

Use:

kVA = (√3 × Volts × Amps) ÷ 1000

How do I calculate three-phase VA?

Multiply √3 by the line-to-line voltage and line current.

VA = √3 × Volts × Amps

How many kW is 400 volts three-phase at 10 amps?

The answer depends on power factor.

At a power factor of 1, 400 V three-phase at 10 A is approximately 6.93 kW.

At a power factor of 0.8, it is approximately 5.54 kW.

How many kVA is 400 volts three-phase at 10 amps?

Using line-to-line voltage:

kVA = (1.732 × 400 × 10) ÷ 1000

The result is approximately 6.93 kVA.

How many kW is 415 volts three-phase at 20 amps?

At a power factor of 0.8, the result is approximately 11.50 kW.

At a power factor of 0.9, the result is approximately 12.94 kW.

Do I need power factor to calculate three-phase kVA?

No. When line-to-line voltage and line current are known:

kVA = (√3 × Volts × Amps) ÷ 1000

Do I need power factor to calculate three-phase kW?

Yes. Power factor is required when calculating AC real power from voltage and current.

Why is 1.732 used in the formula?

The number 1.732 is an approximation of √3. It comes from the mathematical relationship between the three phases in a balanced three-phase electrical system.

Should I enter line-to-line or line-to-neutral voltage?

Enter line-to-line voltage for this calculator.

Does this calculator work for an unbalanced three-phase load?

This calculator is intended for balanced three-phase systems. An unbalanced system may require separate calculations or measurements for each phase.

Can I use this calculator for a three-phase UPS?

Yes, it can help estimate real and apparent power when line voltage, line current, and power factor are known.

Actual UPS selection should still use the manufacturer’s kW and kVA ratings, input and output configuration, overload capability, redundancy requirements, battery runtime requirements, and technical specifications.

Can I use this calculator for a three-phase generator?

The calculator can help estimate the electrical power associated with a balanced three-phase load.

Generator sizing may also require consideration of motor starting current, load steps, nonlinear loads, harmonics, environmental conditions, future expansion, and manufacturer requirements.

Electrical Calculation Disclaimer

This Three-Phase Power Calculator is provided for informational, educational, and preliminary planning purposes. Calculated values may be rounded.

The calculator assumes a balanced three-phase AC electrical system and uses line-to-line voltage, line current, and the entered power factor.

Actual electrical conditions may vary because of load imbalance, voltage variation, power factor changes, harmonics, waveform distortion, equipment efficiency, motor starting current, operating conditions, measurement accuracy, and other factors.

Electrical equipment should be selected using manufacturer ratings and specifications. Circuit and conductor design may also require consideration of conductor ampacity, voltage drop, continuous loads, starting currents, protective devices, derating factors, installation conditions, fault current, and applicable electrical codes.

Consult a qualified electrical professional when making final electrical installation, conductor sizing, circuit protection, equipment selection, generator sizing, UPS sizing, or other electrical system decisions.