Three Phase Power Calculator

Three-phase power is electrical power delivered by three alternating phase conductors whose waveforms are displaced in phase. In a balanced system, the total power can be calculated from one representative line voltage, line current, and power factor. Engineers distinguish real power in watts, apparent power in volt-amperes, and reactive power in var because each describes a different part of AC power.

For a balanced three-phase system using line-to-line RMS voltage, real power is P = √3 × VLL × I × PF. If line-to-neutral voltage is used for a balanced wye system, the equivalent expression is P = 3 × VLN × I × PF. The voltage definition must be explicit because substituting VLL and VLN as though they are the same produces an error.

Choose whether the entered voltage is line-to-line or line-to-neutral. Convert voltage and current to volts and amperes, enter a power-factor magnitude, and apply the correct balanced-system coefficient: √3 for VLL or 3 for VLN. This calculator also derives apparent power and reactive power when the input set is sufficient, while keeping leading and lagging sign conventions explicit.

Calculate real power in watts with P = √3 VLL I PF for line-to-line voltage, or P = 3 VLN I PF for line-to-neutral voltage in a balanced wye system. Divide watts by 1000 for kilowatts. The result assumes a balanced three-phase load represented by one line current and one power-factor magnitude.

Rearrange the balanced three-phase real-power equation. With line-to-line voltage, I = P/(√3 VLL PF). With line-to-neutral voltage in a balanced wye system, I = P/(3 VLN PF). Use real power in watts, voltage in volts, and power factor as a decimal. Motor current calculations may also require motor efficiency if the known power is mechanical output.

Rearrange the same balanced power equation. For a line-to-line result, VLL = P/(√3 I PF). For a line-to-neutral result, VLN = P/(3 I PF). The result is the RMS voltage definition selected in the calculator. Do not compare a calculated VLN result directly with an equipment VLL rating without converting the voltage definition.

Line voltage usually refers to the voltage measured between two phase conductors, while phase voltage can refer to the voltage across an individual phase element. In a balanced wye system, line-to-line voltage is √3 times line-to-neutral voltage. In delta systems, phase winding voltage equals line-to-line voltage, so the relationship depends on connection and measurement points.

Line-to-line voltage, VLL, is the RMS voltage measured between two phase conductors. Common three-phase equipment ratings such as 400 V or 480 V are often line-to-line ratings, although equipment documentation should always be checked. When VLL and line current are used in a balanced three-phase power equation, the coefficient is √3.

Line-to-neutral voltage, VLN, is the RMS voltage from one phase conductor to the neutral point. In a balanced wye system, VLL ≈ √3 × VLN. If a calculator accepts VLN directly, total three-phase real power is P = 3 VLN I PF. This should not be confused with entering VLL into the same formula.

The √3 factor results from the 120-degree phase displacement and vector relationship between line and phase quantities in a balanced three-phase system. Using line-to-line voltage with line current gives S = √3 VLL I. The same total apparent power can be written as 3 VLN I for a balanced wye system because VLL = √3 VLN.

Watts measure real power actually transferred to loads, while volt-amperes measure apparent power, the RMS voltage-current product before power factor is applied. In a balanced three-phase system, S = √3 VLL I or 3 VLN I. Real power is P = S × PF, so W and VA are numerically equal only at unity power factor.

Apparent power S is the magnitude of complex power and is measured in VA, kVA, or MVA. For a balanced three-phase load, S = √3 VLL I when line-to-line voltage is used, or S = 3 VLN I in a balanced wye system. Apparent power combines the real and reactive components through S² = P² + Q².

Reactive power Q represents the AC power component associated with energy exchanged between the source and reactive electric or magnetic fields. It is measured in var, kvar, or Mvar. With apparent power S and real power P, |Q| = √(S² − P²). This calculator uses positive Q for lagging and negative Q for leading as an explicit convention.

Real power P is the average power converted to useful mechanical work, heat, light, or other net energy transfer. It is measured in W, kW, or MW. For a balanced three-phase system, P = √3 VLL I PF or, using balanced wye line-to-neutral voltage, P = 3 VLN I PF. Use measured or manufacturer values whenever the calculation supports equipment selection, loading, protection, or compliance decisions.

Power factor is the ratio of real power to apparent power: PF = P/S. For sinusoidal balanced conditions, its magnitude also corresponds to cos φ, where φ is the phase angle between voltage and current. Power factor is dimensionless and ranges from greater than zero up to one for the magnitude calculations on this page.

At a fixed RMS voltage and current, apparent power S stays the same while real power equals S × PF. Therefore a lower power factor produces less real power for the same voltage-current product. In load planning, a low PF can require higher current or kVA for the same kW, which can affect conductor and equipment loading.

At unity power factor, PF = 1 and real power equals apparent power for the simplified sinusoidal power triangle. The phase-angle magnitude is zero and reactive power Q is zero in that model. Unity power factor does not mean an electrical system has no losses; it only describes the relationship between real and apparent power.

A lagging power factor means current lags voltage under the chosen convention, commonly associated with inductive loads such as motors and transformers. This calculator treats lagging reactive power as positive. Sign conventions can vary among metering standards and applications, so users should confirm the convention required for a specific protection, billing, or power-flow study.

A leading power factor means current leads voltage under the chosen convention, commonly associated with capacitive behavior or overcompensation. This calculator represents leading reactive power as negative while using the positive PF magnitude for real-power calculations. Other systems may define signs differently, so the selected engineering convention should be stated with the result.

For balanced three-phase apparent power, use S = √3 VLL I with line-to-line voltage or S = 3 VLN I with balanced wye line-to-neutral voltage. Divide VA by 1000 to obtain kVA. Power factor is not required to calculate apparent power, although PF is needed if real and reactive power are also desired.

If apparent power S and real power P are known, calculate reactive-power magnitude as |Q| = √(S² − P²). Equivalently, with PF = cos φ, Q = S sin φ. This calculator assigns positive Q for lagging and negative Q for leading. At PF = 1, Q is zero in the simplified sinusoidal power-triangle model.

If the known motor power is electrical real input power, current follows from I = P/(√3 VLL PF) or the corresponding VLN form. If the known value is mechanical shaft output, first divide by motor efficiency to estimate electrical input power. This is why current cannot be determined from motor horsepower alone without voltage, efficiency, and power factor assumptions.

If mechanical motor output power Pout is known, estimated electrical input is Pin = Pout/ηmotor. Convert the mechanical output to watts first if it is entered in horsepower. Once Pin is known, estimated balanced three-phase current can be calculated using the selected voltage definition and power factor. This is an operating estimate, not a motor-sizing recommendation.

No. Motor efficiency compares mechanical shaft output with electrical real input power, while power factor compares real input power with apparent input power. Both affect current, but they describe different physical relationships. A motor can have high efficiency and a moderate power factor, or vice versa, depending on design and operating load.

Convert real power in kilowatts to watts and divide by 745.699872 to obtain mechanical horsepower. If the kW value represents electrical input, the converted horsepower is merely a unit conversion of electrical real power and should not automatically be labeled shaft horsepower. Mechanical output horsepower requires an efficiency relationship between electrical input and shaft output.

There is no single current value for a 10 kW three-phase motor because current depends on line voltage, power factor, motor efficiency, and load. If 10 kW is mechanical output, divide by efficiency to obtain electrical real input before calculating current. Enter the actual voltage and PF rather than relying on a universal amps-per-kW shortcut.

A 20 kW three-phase load can draw very different currents at 208 V, 400 V, 480 V, or higher voltages, and power factor also matters. For a balanced line-to-line system, I = P/(√3 VLL PF). If 20 kW is motor shaft output instead of electrical input, motor efficiency must also be included.

Yes. For a balanced three-phase system, voltage and current determine apparent power, and adding power factor gives real power. With VLL, P = √3 VLL I PF; with balanced wye VLN, P = 3 VLN I PF. If power factor is unknown, voltage and current alone determine kVA but not a unique kW value.

Without power factor, voltage and current can determine apparent power but not real power for a general AC load. In a balanced line-to-line system, S = √3 VLL I. Real power is P = S PF. Assuming PF = 1 without evidence can overstate real power for motors, transformers, and other inductive or capacitive loads.

Use the actual power factor at the operating condition whenever possible, obtained from metering, manufacturer data, or a credible design assumption. Motor PF can vary with load, and system PF can change with capacitor banks, drives, transformers, and other equipment. Do not use one universal PF value for all three-phase loads.

Enter the RMS voltage definition that matches your measurement or equipment data. If the rating is the voltage between phase conductors, select Line-to-Line. If you truly have phase-to-neutral voltage in a balanced wye system, select Line-to-Neutral. The calculator changes the coefficient accordingly and does not treat the two voltages as interchangeable.

Use line voltage when the input value is measured between two phase conductors, which is common for three-phase equipment ratings. Use phase-to-neutral voltage only when that is the quantity actually known and the balanced wye relationship applies. Selecting the wrong voltage definition introduces a factor-of-√3 error in the resulting power, current, or voltage.

Frequency is important for motors, transformers, reactance, speed, and many equipment ratings, but it does not appear directly in the basic balanced three-phase real-power equation P = √3 V I PF. This calculator records frequency as system context only. Equipment must still be operated within its rated frequency and voltage conditions.

The total balanced three-phase line-power equation using VLL and line current remains P = √3 VLL I PF for both common wye and delta systems. Connection type changes the relationship between line and phase voltages or currents. Problems arise when phase quantities are substituted into line formulas without applying the correct wye or delta relationships.

In a wye or star connection, one end of each phase is connected to a common neutral point. For a balanced wye system, line-to-line voltage is √3 times line-to-neutral phase voltage, while line current equals phase current. This makes P = 3 VLN I PF equivalent to P = √3 VLL I PF.

In a delta connection, the three phase windings or impedances form a closed triangle between the line conductors. Phase voltage equals line-to-line voltage, while line current differs from phase current by a √3 relationship in the balanced case. The line-based total-power equation remains P = √3 VLL Iline PF. Use measured or manufacturer values whenever the calculation supports equipment selection, loading, protection, or compliance decisions.

Wye and delta describe different ways of connecting three phase elements. Wye provides a neutral point and has VLL = √3 VLN in the balanced case. Delta places each phase directly across line-to-line voltage and has a different line-to-phase current relationship. Both can use the same balanced line-voltage total-power equation when line quantities are used.

The main calculator is designed for balanced three-phase systems represented by one voltage, one current, and one power factor. It does not reduce a severely unbalanced load to one √3 equation. For unbalanced systems, calculate each phase with its own phase voltage, current, and PF and sum the three real-power contributions.

For an unbalanced system with a known neutral reference, calculate each phase real power separately using PA = VA IA PFA, PB = VB IB PFB, and PC = VC IC PFC, then sum Ptotal = PA + PB + PC. More complex three-wire unbalanced systems may require vector or wattmeter methods and should not be forced into a balanced formula.

The power triangle is a geometric representation of apparent power S, real power P, and reactive power Q for sinusoidal conditions. P is the horizontal component, Q is the vertical component, and S is the hypotenuse, so S² = P² + Q². Power factor magnitude equals P/S and corresponds to cos φ.

Real power P is measured in kW, apparent power S in kVA, and reactive power Q in kvar. For the simplified sinusoidal power triangle, S² = P² + Q² and PF = P/S. Knowing any two consistent power quantities often allows the third to be derived. Sign conventions for Q should be stated for leading and lagging conditions.

Yes, real or reactive power can be assigned negative signs depending on the adopted power-flow and metering convention, such as generation versus load or leading versus lagging reactive flow. This calculator focuses on positive real-power magnitudes for ordinary load calculations and uses an explicit sign convention for reactive power. Protection and metering studies may require different quadrant conventions.

Electrical input power is real electrical power entering the motor. Mechanical output power is shaft power delivered after motor losses. Efficiency relates them through Pout = η Pin. A direct kW-to-horsepower unit conversion does not account for motor losses, so electrical-input horsepower should not be mislabeled as mechanical shaft horsepower without an efficiency calculation.

Differences often result from line-to-line versus line-to-neutral voltage, V versus kV, A versus kA, PF entered as 0.85 versus 85, using single-phase formulas, or confusing motor shaft output with electrical input. Check whether both calculators assume a balanced system and whether their leading/lagging and horsepower conventions match. Use measured or manufacturer values whenever the calculation supports equipment selection, loading, protection, or compliance decisions.

For fixed voltage and current, apparent power does not change when PF changes, but real power is P = S PF. Raising PF therefore raises calculated real power at the same V and I, while lowering PF reduces it. Conversely, if real power is fixed, a lower PF requires more current or apparent power.

With current and power factor fixed, balanced three-phase real power is directly proportional to the selected voltage magnitude. Doubling the properly defined RMS voltage doubles P in the simplified equation. However, real equipment current, efficiency, PF, impedance, and operating point may also change with voltage, so the calculator describes the specified electrical operating point.

With voltage and power factor fixed, balanced three-phase real power is directly proportional to line current. Doubling current doubles real power in the simplified relationship. In real motors and other loads, PF and efficiency can vary with loading, so a field current change does not necessarily imply exactly proportional mechanical output.

Yes, for preliminary balanced three-phase electrical calculations when the correct voltage definition, current, power factor, and motor efficiency are known. Industrial motor selection and protection still require nameplate data, service factor, starting current, overload characteristics, voltage tolerance, frequency, duty cycle, code requirements, and manufacturer documentation. Use measured or manufacturer values whenever the calculation supports equipment selection, loading, protection, or compliance decisions.

Yes, the real, apparent, and reactive power relationships can be used for balanced three-phase generator terminals when sign convention and operating direction are defined. Generator studies may also require voltage regulation, excitation, reactive capability, losses, efficiency, harmonics, and protection analysis that are outside this simplified calculator. Use measured or manufacturer values whenever the calculation supports equipment selection, loading, protection, or compliance decisions.

Yes for balanced terminal power relationships using the correct voltage, current, and power factor. Transformer design and loading also involve efficiency, impedance, voltage drop, temperature rise, harmonics, winding connection, kVA rating, and protection. The calculator should be treated as an electrical power cross-check rather than a transformer sizing or thermal model.

Yes for preliminary balanced three-phase load calculations at an electrical panel when the measured or specified voltage, current, and PF are appropriate. Panel design also requires conductor ampacity, demand factors, breaker ratings, short-circuit current, grounding, neutral loading, harmonics, code requirements, and coordination studies that are not modeled here. Use measured or manufacturer values whenever the calculation supports equipment selection, loading, protection, or compliance decisions.

Yes, for balanced three-phase equipment when the voltage definition, current, and power factor are known. Drives, welders, rectifiers, UPS systems, furnaces, and other nonlinear equipment may have harmonics or nonsinusoidal waveforms where displacement PF alone is insufficient. Use equipment-specific data and appropriate power-quality methods for detailed analysis. Use measured or manufacturer values whenever the calculation supports equipment selection, loading, protection, or compliance decisions.