Three Phase Calculator

Calculation Target

Load Power Rating

Power Unit

Line Current (Amperes, I)

Electrical Voltage (V)

Voltage Measurement Type

Power Factor (cos φ)

Efficiency (η %)

Three-Phase Analysis Results

Full Load Line Current 0.00 A

Three-Phase Power Triangle (P, S, Q) —

Wye (Y) vs. Delta (Δ) Circuit Values —

Continuous Duty Ampacity & Conductor Benchmark —

Calculations assume a balanced three-phase AC system: P = √3 × V_LL × I_L × PF × η. Apparent power S = √3 × V_LL × I_L and reactive power Q = √(S² − P²). Minimum conductor ampacity incorporates the 125% continuous duty rule per National Electrical Code (NEC) Article 430/210 standards.

What Is a Three Phase Calculator?

A three phase calculator determines current, power, or voltage in a balanced three-phase electrical system. It uses the relationship between line voltage, line current, power factor, and efficiency. Depending on the selected calculation mode, it also displays real, apparent, and reactive power, Wye and Delta electrical values, and a current-based conductor sizing benchmark.

Three-phase electrical systems use three alternating voltage waveforms. They are commonly used to supply motors and other electrical equipment that requires substantial power.

This calculator offers three calculation targets:

Solve for Current: Find line current from a power rating and voltage.
Solve for Power: Calculate real, apparent, and reactive power from line current and voltage.
Solve for Voltage: Calculate line-to-line voltage from a power rating and line current.

The calculations assume a balanced electrical system. They do not analyze unequal phase loads, voltage drops along conductors, or equipment-specific electrical characteristics.

How the Three Phase Calculator Formulas Work

The calculator uses the three-phase power relationship and rearranges it according to the selected calculation target. The main constants are the square root of three, approximately 1.73205, and the conversion factor of 745.699872 watts per horsepower.

1. Three-Phase Current Formula

When solving for current from a load expressed in watts, kilowatts, or horsepower, the calculator uses:

I_L=\frac{P}{\sqrt{3}\times V_{LL}\times PF\times\eta}

In this formula:

IL: Line current in amperes (A).
P: Entered real power converted to watts (W).
VLL: Line-to-line voltage in volts (V).
PF: Power factor, entered as a decimal.
η: Efficiency expressed as a decimal, such as 0.90 for 90%.

Before using this formula, the calculator converts the entered power rating into watts. Kilowatts are multiplied by 1,000, while horsepower is multiplied by 745.699872.

P_W=P_{kW}\times1000

P_W=P_{HP}\times745.699872

If you select kilovolt-amperes (kVA) as the power unit, the calculator follows a different path. It divides the entered kVA value by efficiency before converting apparent power into line current.

I_L=\frac{S_{kVA}\times1000}{\eta\times\sqrt{3}\times V_{LL}}

In this branch, SkVA is the entered apparent power in kVA. The calculator also reports real power as the resulting apparent power multiplied by power factor.

2. Three-Phase Power Formula

When Solve for Power is selected, the calculator uses entered line current and line-to-line voltage to determine apparent power.

S_{VA}=\sqrt{3}\times V_{LL}\times I_L

It then calculates electrical real power using the entered power factor and multiplies that value by efficiency to produce its displayed real power result.

P_{\text{displayed}}=\sqrt{3}\times V_{LL}\times I_L\times PF\times\eta

Apparent power is divided by 1,000 for display in kVA. Real power is divided by 1,000 for display in kW.

The calculator also reports horsepower using its displayed real power value:

HP=\frac{P_{\text{displayed}}}{745.699872}

3. Three-Phase Voltage Formula

When Solve for Voltage is selected, the calculator determines the required line-to-line voltage from a power rating and line current.

For power entered in watts, kilowatts, or horsepower, the formula is:

V_{LL}=\frac{P}{\sqrt{3}\times I_L\times PF\times\eta}

For power entered in kVA, the calculator instead uses:

V_{LL}=\frac{S_{kVA}\times1000}{\eta\times\sqrt{3}\times I_L}

The primary voltage result is always line-to-line voltage, displayed to one decimal place. The calculator also derives a corresponding line-to-neutral voltage.

4. Real, Apparent, and Reactive Power

The calculator displays three power quantities in its Three-Phase Power Triangle section.

Real Power (P): Displayed in kilowatts (kW) and horsepower (HP).
Apparent Power (S): Displayed in kilovolt-amperes (kVA).
Reactive Power (Q): Displayed in kilovolt-amperes reactive (kVAR).

The calculation for reactive power depends on the selected mode. In Solve for Current and Solve for Voltage, the code calculates reactive power from apparent power and its reported real power value:

Q=\sqrt{\max(0,S^2-P_{\text{displayed}}^2)}

In Solve for Power, the code instead calculates reactive power using electrical real power before the efficiency adjustment:

Q=\sqrt{\max\left(0,S^2-(S\times PF)^2\right)}

These formulas use watts, volt-amperes, and volt-amperes reactive internally. The reactive result is divided by 1,000 for display in kVAR.

Important distinction: When efficiency is below 100%, the calculator’s displayed real power and reactive power do not use the same power-triangle convention across all three modes. In particular, the current and voltage modes use efficiency-adjusted apparent power with the reported load power to calculate reactive power. Treat these outputs as results of the implemented model rather than assuming the displayed P, S, and Q always form a conventional electrical input power triangle.

5. Line-to-Line, Line-to-Neutral, Wye, and Delta Values

The calculator allows voltage to be entered as either line-to-line or line-to-neutral voltage when solving for current or power.

If you enter line-to-neutral voltage, the calculator converts it to line-to-line voltage:

V_{LL}=\sqrt{3}\times V_{LN}

For its displayed circuit values, it calculates:

V_{LN}=\frac{V_{LL}}{\sqrt{3}}

I_{\text{Wye Phase}}=I_L

I_{\text{Delta Phase}}=\frac{I_L}{\sqrt{3}}

The phase-current relationships are based on balanced Wye (Y) and Delta (Δ) connections. The line-to-neutral value represents the corresponding balanced Wye voltage relationship; a Delta connection does not inherently provide a neutral conductor.

6. Continuous Duty Conductor Ampacity Benchmark

The calculator multiplies calculated or entered line current by a fixed factor of 1.25 to provide a minimum conductor rating benchmark.

I_{\text{benchmark}}=I_L\times1.25

For example, a line current of 50 A produces a benchmark of 62.50 A.

The calculator labels this output with a 125% rule and references the National Electrical Code (NEC) in its explanatory text. However, the implemented calculation is only multiplication by 1.25. It does not select wire sizes, verify conductor insulation ratings, or account for installation conditions and equipment-specific code requirements.

Worked Example: Calculate Current for a 30 kW Three-Phase Load

Consider a hypothetical balanced three-phase load with the following inputs:

Input	Example Value
Calculation Target	Solve for Current
Load Power Rating	30
Power Unit	Kilowatts (kW)
Electrical Voltage	480 V
Voltage Measurement Type	Line-to-Line
Power Factor	0.85
Efficiency	90%

First, convert 30 kW to 30,000 W. Next, convert efficiency from 90% to 0.90. The calculator then determines apparent power:

S=\frac{30{,}000}{0.85\times0.90}=39{,}215.69\text{ VA}

Using the apparent power value, calculate line current:

I_L=\frac{39{,}215.69}{\sqrt{3}\times480}\approx47.17\text{ A}

The calculator then calculates the remaining displayed values, including the derived phase currents and 125% conductor benchmark.

Calculated Output	Result
Full Load Line Current	47.17 A
Real Power	30.00 kW
Horsepower Equivalent	40.2 HP
Apparent Power	39.22 kVA
Reactive Power, Using Calculator Formula	25.26 kVAR
Line-to-Line Voltage	480.0 V
Line-to-Neutral Voltage	277.1 V
Wye Phase Current	47.17 A
Delta Winding Phase Current	27.23 A
125% Conductor Rating Benchmark	58.96 A

For the conductor benchmark, the arithmetic is:

47.1691\times1.25\approx58.96\text{ A}

These results follow the calculator’s actual formulas. They are an example of the tool’s calculations, not a conductor selection or installation recommendation.

How to Use the Three Phase Calculator

Start by selecting the electrical quantity you want to calculate. The form changes its visible inputs based on the selected mode.

Select Calculation Target. Choose Solve for Current, Solve for Power, or Solve for Voltage. Solve for Current is selected initially.
Enter Load Power Rating when required. Current and voltage modes use this field. You can enter the value in kW, kVA, horsepower, or watts.
Select Power Unit when required. The default unit is kilowatts (kW). The available options are kW, kVA, HP, and W.
Enter Line Current when required. Power and voltage modes use the Line Current (Amperes, I) field.
Enter Electrical Voltage when required. Current and power modes use the Electrical Voltage (V) field.
Choose Voltage Measurement Type. In current and power modes, select Line-to-Line Voltage or Line-to-Neutral Voltage. Line-to-Line is the default.
Enter Power Factor. The field indicates a range of 0.01 to 1.00. If left blank, the calculation uses 0.85.
Enter Efficiency (%). The field indicates a range of 1% to 100%. If left blank, the calculation uses 100%.
Click Calculate. Review the main answer, power values, phase relationships, and conductor benchmark.
Click Reset to start again. This clears the number fields, returns to Solve for Current, restores the default selections, and hides the results.

The calculator requires positive power, current, and voltage values in whichever fields are used by the selected mode. Its calculation checks also reject power factors at or below zero or above 1, and efficiencies at or below zero or above 100%. Invalid required values trigger an alert rather than a calculated result.

How to Interpret Your Three-Phase Electrical Results

Current, Power, and Voltage Results

The main result changes according to the selected calculation target. Solve for Current displays Full Load Line Current in amperes, rounded to two decimal places. Solve for Power displays Total Real Power Output in kilowatts, also to two decimal places. Solve for Voltage displays Calculated Line-to-Line Voltage to one decimal place.

All three modes also display real power, apparent power, and reactive power. The displayed kW, kVA, and kVAR values use two decimal places. The horsepower equivalent uses one decimal place.

Why Power Factor Matters

Power factor describes the relationship between real power and apparent power in an AC system. In the calculator, a lower power factor increases calculated current when load power, voltage, and efficiency remain unchanged.

For example, changing power factor from 1.00 to 0.85 increases the apparent power needed for the same entered watt or kilowatt load. The resulting line current also increases.

The calculator does not determine power factor from measured electrical waveforms. It uses the value you enter, or 0.85 when the field is blank.

How Efficiency Changes the Calculation

Efficiency represents the relationship between useful output power and electrical input power. The calculator accepts efficiency as a percentage and converts it into a decimal for its formulas.

In current and voltage modes, a lower efficiency increases the modeled apparent power needed for a given load rating. In power mode, efficiency reduces the reported real power output calculated from electrical apparent power and power factor.

The kVA input branch uses its own formula, dividing entered apparent power by efficiency before further calculations. For that reason, kVA should not be treated as interchangeable with kW or horsepower inputs.

Wye and Delta Circuit Relationships

The calculator displays both Wye and Delta phase-current values without requiring you to select a circuit connection.

For a balanced Wye connection, phase current equals line current. For a balanced Delta connection, winding phase current equals line current divided by the square root of three.

These are standard balanced-system relationships. They are not a substitute for checking an actual circuit’s connection and operating conditions.

What the 125% Conductor Benchmark Means

The Continuous Duty Ampacity & Conductor Benchmark section multiplies line current by 1.25 and reports the result in amperes. It also repeats the power factor and efficiency used in the calculation.

The 125% calculation is a simplified benchmark, not a complete electrical code assessment. Actual conductor sizing may depend on conductor material, insulation temperature rating, terminal limitations, ambient temperature, grouping, load classification, and other applicable requirements.

Use the displayed benchmark to understand the calculator’s arithmetic. Verify final conductor and circuit protection requirements using the applicable electrical code and qualified electrical design guidance.

Frequently Asked Questions

How do you calculate current in a three-phase system?

For a balanced three-phase load entered in watts, kilowatts, or horsepower, the calculator divides the power in watts by the square root of three multiplied by line-to-line voltage, power factor, and efficiency. This produces line current in amperes. If you enter kVA instead, the calculator uses its separate apparent-power calculation.

How do you calculate three-phase power from voltage and current?

In Solve for Power mode, apparent power equals the square root of three multiplied by line-to-line voltage and line current. The calculator multiplies apparent power by power factor and efficiency to obtain its displayed real power output. It also calculates reactive power using apparent power and electrical real power before the efficiency adjustment.

What is the difference between kW, kVA, and kVAR?

Kilowatts (kW) measure real power, kilovolt-amperes (kVA) measure apparent power, and kilovolt-amperes reactive (kVAR) measure reactive power. The calculator displays all three quantities in its power results. Their numerical relationship depends on power factor and, in this implementation, the selected calculation mode and efficiency treatment.

Can I enter line-to-neutral voltage instead of line-to-line voltage?

Yes. Solve for Current and Solve for Power include a Voltage Measurement Type selector. When Line-to-Neutral Voltage is selected, the calculator multiplies the entered voltage by the square root of three to determine line-to-line voltage. Solve for Voltage does not display this selector because it directly calculates line-to-line voltage.

What happens if power factor or efficiency is left blank?

The calculator uses a power factor of 0.85 and efficiency of 100% when the corresponding field is blank or cannot be parsed as a number. Entering your own values replaces these fallbacks. Since the two factors can significantly change calculated current, power, and voltage, use equipment-specific information when available.

How does the calculator convert horsepower to kilowatts?

The calculator multiplies entered horsepower by 745.699872 to convert it into watts. It also converts calculated real power back into horsepower by dividing watts by the same factor. The Power Triangle display shows the resulting horsepower value to one decimal place alongside real power in kilowatts.

Can I use the conductor rating result to select wire size?

Not by itself. The calculator provides a conductor ampacity benchmark equal to 125% of line current. It does not select conductor sizes or check the installation details needed for a complete electrical code assessment. Final conductor sizing and circuit protection decisions require the applicable code rules and equipment information.

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