Three Phase Power Calculator

Related Calculators

Table of contents

• How to use
• Common mistakes
• Definitions
• Methodology
• Limitations & assumptions
• Sources

Balanced three-phase: A three-phase circuit where the three phase voltages and currents are the same size and spaced evenly in time.

Line-to-line voltage: Voltage measured between two hot lines. This is the voltage used directly in the standard line-value three-phase formula.

Line-to-neutral voltage: Voltage measured from one hot line to neutral. In a balanced wye system, line-to-line voltage is sqrt(3) times this value.

Line current: Current in one line conductor. It is not the three line currents added together.

Real power: Useful power in kW. It is the part of the electrical power that does work, such as turning a motor shaft or making heat.

Apparent power: Total volt-amp load in kVA that wires, transformers, and generators must carry.

Reactive power: Power in kVAR that moves back and forth because voltage and current are not perfectly lined up.

Power factor: Real power divided by apparent power. It is a number from 0 to 1, where 1 means all apparent power is real power.

Phase angle: The angle in degrees between voltage and current, found from the power factor.

Wye and delta: Common three-phase connection types. They change phase voltage and phase current relationships, but not total balanced three-phase power when line voltage and line current are already known.

Mistake: Using Voltage as line-to-neutral while How is the voltage measured? is set to between two hot lines.
Fix: Change How is the voltage measured? to from hot line to neutral, or enter the true line-to-line Voltage.

Mistake: Adding all three wires and typing the total into Line current.
Fix: Enter the current in one line conductor only; the calculator already includes the three-phase factor.

Mistake: Typing 85 into Power factor when you mean 0.85.
Fix: Enter Power factor as a decimal from 0 to 1, such as 0.85.

Mistake: Entering Apparent power or kVA in Real power.
Fix: Use Real power only for useful power in kW; the calculator computes Apparent power separately.

Mistake: Choosing Show phase values for delta and treating a line-to-neutral Voltage as a delta winding voltage.
Fix: Use the Check note and Line-to-line voltage result; delta Phase voltage equals line-to-line voltage.

Mistake: Picking the wrong Reactive power direction and getting the wrong sign on Reactive power.
Fix: Use lagging for motor-style inductive loads and leading for capacitor-style loads.

• This calculator assumes a balanced three-phase AC load. It does not model unbalanced phase currents, neutral current, harmonics, or waveform distortion.
• Use RMS AC values for Voltage and Line current. Peak values or meter readings from a different reference point will give wrong results.
• Power factor is treated as a single number from 0 to 1. It does not separate displacement power factor from distortion power factor.
• When solving for Power factor, Real power cannot be larger than Apparent power. If it is, the input set is physically inconsistent for this model.
• Wye and delta settings only affect Phase voltage and Phase current outputs. They do not change Real power, Apparent power, or Reactive power when line values are known.
• Reactive power sign follows the selected Reactive power direction: lagging is positive and leading is negative in this calculator.
• Real equipment may need extra margin for starting current, service factor, efficiency, voltage drop, code rules, and manufacturer ratings.

Core line-value method

The calculator first converts the entered Voltage to line-to-line voltage, then applies balanced three-phase power formulas. The real power formula using line-to-line voltage, line current, and power factor is the standard balanced three-phase form [1].

If voltage is line-to-line: V_LL = V_input

If voltage is line-to-neutral: V_LL = sqrt(3) * V_input

S_kVA = sqrt(3) * V_LL * I_L / 1000

P_kW = S_kVA * PF

Here, V_LL is line-to-line voltage in volts, I_L is line current in amps, S_kVA is apparent power, P_kW is real power, and PF is power factor. Apparent power uses kVA, real power uses kW, and reactive power uses kVAR [2].

Solving for the missing value

For Power mode, the calculator uses the entered Voltage, Line current, and Power factor to find Real power. For Current mode, it rearranges the same formula:

I_L = P_kW * 1000 / (sqrt(3) * V_LL * PF)

For Voltage mode, it solves for line-to-line voltage:

V_LL = P_kW * 1000 / (sqrt(3) * I_L * PF)

If How is the voltage measured? is set to line-to-neutral in Voltage mode, the primary voltage answer is:

V_LN = V_LL / sqrt(3)

For Power factor mode, it divides real power by apparent power:

PF = P_kW / S_kVA

If this result is above 1, the calculator shows an error instead of forcing the value down to 1.

Reactive power and angle

Reactive power and phase angle are based on the power triangle relationship between real, reactive, and apparent power [2].

Q_kVAR = direction_sign * S_kVA * sqrt(1 - PF^2)

angle_deg = acos(PF) * 180 / pi

The direction_sign is +1 for lagging and -1 for leading, so leading reactive power is shown as a negative kVAR value.

Optional phase values

When Show phase values for is set to wye or delta, the calculator adds phase voltage and phase current using standard line-to-phase relationships [3].

Wye: V_phase = V_LL / sqrt(3); I_phase = I_L

Delta: V_phase = V_LL; I_phase = I_L / sqrt(3)

These phase values are supporting details. They do not change the total balanced three-phase power result.

Worked mini-example

With 480 V measured between two hot lines, 50 A line current, and a power factor of 0.85, apparent power is:

S_kVA = sqrt(3) * 480 * 50 / 1000 = 41.57 kVA

Real power is:

P_kW = 41.57 * 0.85 = 35.33 kW

For a lagging load, reactive power is about 21.90 kVAR and the phase angle is about 31.79 degrees.