EngineeringFormula

Electrical Engineering

Three-Phase Power Calculator

Calculate real, reactive and apparent power for a balanced three-phase AC circuit from line voltage, line current and power factor.

Formula P = √3 × VL × IL × PFReviewed Sep 8, 2026

Three-phase power is the standard for motors, industrial equipment and utility distribution, because it delivers power more efficiently than single-phase for the same conductor size. For a balanced three-phase load, real power is P = √3 × VL × IL × PF, where VL is the line-to-line voltage and IL is the line current - the values read directly off a nameplate or a clamp meter, regardless of whether the load is wired wye or delta internally. Enter line voltage, line current and power factor, or any three of line voltage, line current, power factor and real power, to solve for the fourth and see the full power triangle.

Calculation Bench
Solve for
01

VL · Line-to-line RMS voltage - the value read directly off a nameplate or meter.

02

IL · RMS current in each line conductor.

03

PF · cos φ - the fraction of apparent power that is real power. A plain decimal from 0 to 1, not a percentage.

Solution

Enter the required values to calculate real power.

P = √3 × VL × IL × PF

Formula Sheet

P=3 VLILcos⁡φP = \sqrt{3}\, V_L I_L \cos\varphi
VL=P3 ILcos⁡φV_L = \dfrac{P}{\sqrt{3}\, I_L \cos\varphi}
IL=P3 VLcos⁡φI_L = \dfrac{P}{\sqrt{3}\, V_L \cos\varphi}
PF=P3 VLILPF = \dfrac{P}{\sqrt{3}\, V_L I_L}
  • PReal Power
  • VLLine Voltage
  • ILLine Current
  • PFPower Factor
  • SApparent Power
  • QReactive Power

Variables & Units

SymbolVariableDescriptionCommon Units
PReal PowerPower actually converted into useful work - heat, light, motion.mW, W, kW, MW, hp
VLLine VoltageLine-to-line RMS voltage - the value read directly off a nameplate or meter.V, mV, kV
ILLine CurrentRMS current in each line conductor.A, mA
PFPower Factorcos φ - the fraction of apparent power that is real power. A plain decimal from 0 to 1, not a percentage.
SApparent Power√3 × VL × IL, ignoring phase - what a volt-amp meter reads.VA
QReactive PowerPower that oscillates between source and load without being consumed, from any inductance or capacitance.VAR

How to Use This Calculator

  • 01Select which quantity you want to solve for - Real Power, Voltage, Current, or Power Factor.
  • 02Enter the other three values, choosing the correct unit for each.
  • 03Voltage and current are line values (VL, IL) - the line-to-line voltage and line current you'd read off a nameplate or meter, not per-phase values.
  • 04Power factor is entered as a plain decimal between 0 and 1 (for example, 0.85), not a percentage or an angle.
  • 05Select Calculate to see the solved value, along with the apparent power (VA) and reactive power (VAR) that go with it.
  • 06For common systems, use the line-to-line voltage: 208 V, 240 V, 400 V, 480 V, or 600 V. Do not enter 277 V on a 277/480 V system unless you are intentionally doing a per-phase calculation somewhere else.

How the Formula Works

For a single-phase circuit, real power is P = V × I × PF. A balanced three-phase circuit carries power on three conductors, each 120° out of phase with the others, and that geometry introduces a factor of √3 (≈1.732) rather than a plain factor of 3: P = √3 × VL × IL × PF. The √3 comes from the relationship between line and phase quantities - in a wye connection VL = √3 × Vphase while IL = Iphase, and in a delta connection it's the reverse - and using line voltage and line current together already accounts for that, whichever way the load is actually wired.

As with single-phase power, apparent power S = √3 × VL × IL is what a meter reading volts × amps shows without accounting for phase, and reactive power Q = S × sin φ is the power that oscillates between source and load without being consumed. The same power triangle applies: S² = P² + Q², and this calculator reports all three quantities together for a balanced load, whichever one you solve for.

Worked Example 01

Real power from line voltage, line current and power factor

Known

  • Line Voltage (VL): 400 V
  • Line Current (IL): 50 A
  • Power Factor (PF): 0.85

Formula

P = √3 × VL × IL × PF

Substitution

P = √3 × 400 × 50 × 0.85

Result

P = 29,445 W (S = 34,641 VA, Q = 18,248 VAR)

A 400 V three-phase motor drawing 50 A at 0.85 power factor consumes about 29.4 kW of real power, while the source supplies 34.6 kVA of apparent power to do it.

Worked Example 02

Current from real power, line voltage and power factor

Known

  • Real Power (P): 20000 W
  • Line Voltage (VL): 400 V
  • Power Factor (PF): 0.9

Formula

IL = P / (√3 × VL × PF)

Substitution

IL = 20000 / (√3 × 400 × 0.9)

Result

IL = 32.075 A (S = 22,222 VA, Q = 9686.4 VAR)

A 20 kW, 400 V three-phase load at 0.9 power factor draws about 32.1 A of line current.

Worked Example 03

Power factor from real power, line voltage and line current

Known

  • Real Power (P): 15000 W
  • Line Voltage (VL): 400 V
  • Line Current (IL): 25 A

Formula

PF = P / (√3 × VL × IL)

Substitution

PF = 15000 / (√3 × 400 × 25)

Result

PF = 0.866 (S = 17,321 VA, Q = 8660.3 VAR)

A meter reading 400 V, 25 A and 15 kW on a three-phase feeder implies a power factor of about 0.866.

Worked Example 04

Voltage from real power, line current and power factor

Known

  • Real Power (P): 10000 W
  • Line Current (IL): 20 A
  • Power Factor (PF): 0.75

Formula

VL = P / (√3 × IL × PF)

Substitution

VL = 10000 / (√3 × 20 × 0.75)

Result

VL = 384.9 V (S = 13,333 VA, Q = 8819.2 VAR)

A three-phase load drawing 20 A at 0.75 power factor to deliver 10 kW must be operating at roughly 385 V line-to-line.

Applications

  • 01Sizing a three-phase generator, transformer, or UPS in kVA rather than just kW, since apparent power sets the current-carrying and heating requirements
  • 02Estimating the real power draw of a three-phase motor from its nameplate voltage, current and power factor
  • 03Checking whether a facility's measured kW, kVA and power factor are mutually consistent

Assumptions

  • 01The three-phase load is balanced - all three phases carry equal voltage, current and power factor.
  • 02The circuit is in sinusoidal steady state at a single frequency.
  • 03Power factor is treated as a plain magnitude between 0 and 1; this calculator doesn't track whether it's leading (capacitive) or lagging (inductive).
  • 04Voltage and current are line (not phase) RMS values, the standard convention for reading three-phase nameplates and meters.

Where This Model Stops

  • 01Not valid for unbalanced three-phase loads - a load with unequal phase currents or voltages needs per-phase analysis, not this single balanced-load formula.
  • 02Does not distinguish leading from lagging power factor, and doesn't separate wye from delta - line voltage and line current already account for the difference, but this tool doesn't report phase (per-conductor) voltage or current separately.
  • 03Assumes an ideal sinusoidal supply. Harmonic distortion is not modeled and would make a true power-quality meter reading differ from this result.
  • 04Does not size breakers, conductors, motor overloads, starters, transformers, or generators by code. Use the current result as one input to a separate equipment-sizing workflow.
  • 05Does not include motor efficiency. If a motor nameplate gives mechanical output horsepower, convert to electrical input power using efficiency before using the three-phase power equation.

References

  1. [1]

    Balanced three-phase AC power

    Standard electrical engineering fundamentals

    P = √3 VL IL cos φ, S = √3 VL IL, Q = √3 VL IL sin φ, with the power-triangle relationship S² = P² + Q².

Frequently Asked Questions

Why √3 and not 3, if there are three phases?

√3 accounts for the 120° phase displacement between the three conductors, and for the difference between line and phase quantities in a wye or delta connection. It is not simply 3× the single-phase formula - using line voltage and line current together with √3 already gives the correct total real power for a balanced load, regardless of the internal wye or delta wiring.

What's the difference between line voltage and phase voltage?

Line voltage is measured between any two of the three line conductors - it's what a nameplate or line-to-line meter reading shows. Phase voltage is measured from one line to neutral (in a wye connection) or across one winding (in a delta connection). This calculator uses line voltage and line current throughout, since those are the values normally available from equipment ratings and field measurements.

Does this work for an unbalanced three-phase load?

No - this formula assumes all three phases carry equal voltage, current and power factor. An unbalanced load (common with single-phase loads spread unevenly across the three phases) needs per-phase power calculations added together, not this single balanced-load formula.

Why should I enter line-to-line voltage?

The √3 formula is written for line voltage and line current. On a 277/480 V system, enter 480 V. If you enter 277 V instead, the result will be about 42% too low because you effectively applied the line-to-phase conversion twice.

How is this different from the Watts to Amps Calculator?

Watts to Amps converts a known power to current across DC, single-phase, and three-phase modes. This page is focused on balanced three-phase systems and also reports the real, apparent, and reactive power triangle together.

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