What is the difference between active, reactive, and apparent power?

Active power (P, in watts) does real work; reactive power (Q, in vars) sustains electromagnetic fields; apparent power (S, in volt-amperes) is the total power flowing in the circuit.

Does this calculator work for unbalanced three-phase systems?

No, this calculator assumes a balanced three-phase system where voltages and currents are equal across all three phases.

How is the power-factor angle φ calculated?

The angle φ is calculated as the arccosine of the power factor (cosφ), representing the phase shift between voltage and current.

Why is the power triangle verification included?

It mathematically confirms that the calculated active and reactive powers satisfy the Pythagorean relationship with the apparent power.

What unit should I use for the line voltage?

You must enter the line-to-line RMS voltage in Volts (V), not the phase-to-neutral voltage.

Three-Phase Power Calculator | Online Free Tool

Execution

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2 examples

U=400 V, I=15 A, cosφ=0.85 → P≈8.33 kW, Q≈5.47 kvar, S≈10.39 kVA

S = √3·400·15 ≈ 10392.30 VA. P = S·0.85 ≈ 8833.46 W. Q = S·sinφ, sinφ=√(1−0.85²)≈0.5268, Q ≈ 5474.49 var. φ = arccos 0.85 ≈ 31.79°.

{"result":"Three-phase power, U=400 V, I=15 A, cosφ=0.85. Apparent S = √3·U·I = 10392.3048 VA. Active P = S·cosφ = 8833.4591 W. Reactive Q = S·sinφ = 5474.4863 var. φ = arccos(cosφ) = 31.7883°. Check: √(P²+Q²) = 10392.3048 VA ✓.","metadata":{"input":{"U":400,"I":15,"cosphi":0.85},"result":{"apparentPower":10392.3048,"apparentPowerUnit":"VA","activePower":8833.4591,"activePowerUnit":"W","reactivePower":5474.4863,"reactivePowerUnit":"var","powerFactor":0.85,"powerAngle":31.7883,"powerAngleUnit":"°"}}}

U=690 V, I=50 A, cosφ=1.0 → purely active, P=S≈59.76 kW, Q=0

S = √3·690·50 ≈ 59755.75 VA. cosφ=1 → sinφ=0, P=S=59755.75 W, Q=0 var, φ=0°.

{"result":"Three-phase power, U=690 V, I=50 A, cosφ=1. Apparent S = √3·U·I = 59755.7516 VA. Active P = S·cosφ = 59755.7516 W. Reactive Q = S·sinφ = 0 var. φ = arccos(cosφ) = 0°. Check: √(P²+Q²) = 59755.7516 VA ✓.","metadata":{"input":{"U":690,"I":50,"cosphi":1},"result":{"apparentPower":59755.7516,"apparentPowerUnit":"VA","activePower":59755.7516,"activePowerUnit":"W","reactivePower":0,"reactivePowerUnit":"var","powerFactor":1,"powerAngle":0,"powerAngleUnit":"°"}}}

Inputs

Set the required fields, then run the tool.

4 options

SettingsAdjust formats, ranges, numbers, and modes.4

Line Voltage U (V)numberRequiredLine-to-line RMS voltage.Line Current I (A)numberRequiredLine RMS current per phase.Power Factor cosφnumberRequiredPower factor (0 < cosφ ≤ 1). Lagging by convention.Decimal PlacesnumberOptional

Result

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Examples

1. Calculating Power for a Standard 400V Industrial Motor

Electrical Maintenance Engineer

Background

An engineer needs to document the power metrics of a balanced 400V three-phase motor drawing 15A with a power factor of 0.85.

Problem

Manually calculating active, reactive, and apparent power is prone to rounding errors and takes time.

How to use

Input 400 for Line Voltage (U), 15 for Line Current (I), and 0.85 for Power Factor (cosphi). Set decimal places to 4.

U = 400, I = 15, cosphi = 0.85, decimalPlaces = 4

Outcome

The tool outputs an apparent power of 10392.3048 VA, active power of 8833.4591 W, reactive power of 5474.4863 var, and a phase angle of 31.7883°.

2. Analyzing a Purely Resistive 690V Load

Power Grid Operator

Background

A grid operator is testing a high-voltage resistive heating system operating at 690V and drawing 50A.

Problem

The operator needs to verify that the reactive power is zero and confirm the total active power output.

How to use

Enter 690 for Line Voltage (U), 50 for Line Current (I), and 1.0 for Power Factor (cosphi).

U = 690, I = 50, cosphi = 1.0, decimalPlaces = 4

Three-Phase Power Calculator | Online Free Tool | Elysia Tools

Three-Phase Power Calculator

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Use cases

Examples

1. Calculating Power for a Standard 400V Industrial Motor

2. Analyzing a Purely Resistive 690V Load

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