Three-Phase Power Calculator
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Calculate
Line-to-line voltage — the voltage measured between any two phase conductors
Current in any phase conductor — assumes balanced loading across all three phases
Load power factor as a decimal — typically 0.80 to 0.95 for motor and mixed industrial loads
Overview
The Three-Phase Power Calculator computes apparent power (kVA), real power (kW), and reactive power (kVAR) for a balanced three-phase electrical system from line voltage, line current, and power factor. All three outputs are reported together so apparent, real, and reactive demand can be compared against equipment ratings.
This calculator applies the fixed balanced three-phase model: kVA from line quantities using the √3 factor, kW from apparent power and power factor, and kVAR from the geometric relationship between apparent and real power. The model is appropriate for standard motor loads, transformer loading reviews, generator sizing, feeder ampacity checks, and power factor screening, where all three phase currents are assumed equal and the system is assumed to operate at a single steady-state point.
The result should be treated as a steady-state screening estimate. Final power system analysis should still verify whether the load is actually balanced, account for harmonic distortion and demand variations, and use actual measured values rather than nameplate assumptions. Unbalanced three-phase systems, high-harmonic environments, and transient conditions require a full power system study beyond this calculator. For accurate power system design, final analysis should be checked against system measurements, protection coordination requirements, demand factor assumptions, and project-specific design criteria.
How to Use This Calculator
Enter the line voltage — line-to-line voltage in V (e.g. 208, 480, or 4160).
Enter the line current — current per phase conductor in A.
Enter the power factor — as a decimal value between 0.01 and 1.0.
Click "Calculate" — get apparent power (kVA), real power (kW), and reactive power (kVAR).
Review the three results together — kVA against transformer and conductor ratings, kW against energy demand, kVAR as the basis for power factor correction.
Use the results to support transformer sizing, generator rating, feeder ampacity checks, or power factor correction screening.
Inputs & Outputs
Inputs
- •Line Voltage (V)
- •Line Current (A)
- •Power Factor
Outputs
- •Apparent Power (kVA)
- •Real Power (kW)
- •Reactive Power (kVAR)
Formula
Calculator Formula
This calculator uses the standard balanced three-phase power formula.
Step 1: Apparent power
S = (√3 × V_L × I_L) ÷ 1000
Where:
- S = Apparent power, kVA
- √3 ≈ 1.7321 (phase separation factor in balanced three-phase systems)
- V_L = Line-to-line voltage, V
- I_L = Line current per phase, A
Step 2: Real power
P = S × PF
Where:
- P = Real power, kW
- PF = Power factor (dimensionless, 0 to 1)
Step 3: Reactive power
Q = √(S² − P²)
Where:
- Q = Reactive power, kVAR
Variable Reference
| Variable | Meaning | Units |
|---|---|---|
| Line Voltage | Line-to-line voltage | V |
| Line Current | Line current per phase | A |
| Power Factor | Load power factor | dimensionless |
| kVA | Apparent power | kVA |
| kW | Real power | kW |
| kVAR | Reactive power | kVAR |
Input Conversion Notes
- Voltage and current are the same in Metric and Imperial modes — no unit conversion applies
- Power factor 0.85 stays 0.85 — it is dimensionless
- All output power quantities (kVA, kW, kVAR) are identical in both unit systems
Formula Meaning
This calculator estimates real power, apparent power, and reactive power from the three primary observable quantities in a balanced three-phase circuit: line voltage, line current, and power factor.
The √3 factor arises from the 120° phase separation between conductors. It is not an approximation — it is the exact geometric ratio between line and phase quantities in a balanced three-phase system.
Apparent power (kVA) represents the total demand on conductors and supply equipment. Real power (kW) is the energy-converting component. Reactive power (kVAR) is the non-working component associated with inductive and capacitive loads. The three are related by S² = P² + Q², which is the right-triangle (power triangle) identity used in this formula.
What is Three-Phase Power
Three-phase power is the standard method of generating and distributing electrical energy in industrial, commercial, and large-scale infrastructure applications. In a balanced three-phase system, three sinusoidal voltages of equal magnitude are displaced 120° apart in time, which allows continuous power transfer without the pulsation present in single-phase circuits. This property makes three-phase power more efficient for motors, transformers, and large electrical loads than single-phase supply.
The three fundamental power quantities in a three-phase system are apparent power (kVA), real power (kW), and reactive power (kVAR). Real power performs useful work such as driving motors, producing heat, or powering lighting. Apparent power is the total demand placed on conductors, transformers, and supply equipment. Reactive power is associated with energy stored and released by inductive and capacitive elements — it flows through the system but does not perform useful work. All three quantities are related by the power triangle: S² = P² + Q².
Why √3 Appears in the Formula
In a balanced three-phase system, the relationship between line quantities and phase quantities introduces a factor of √3 (≈ 1.7321). Line voltage is the voltage between any two phase conductors. Phase voltage is the voltage from one conductor to the neutral point. In a wye-connected system, line voltage = √3 × phase voltage. A similar geometric relationship applies to delta-connected systems.
This factor is not an approximation — it is the exact result of the 120° phase angle between conductors and applies to any balanced three-phase circuit regardless of voltage level.
Power Factor and Its Significance
Power factor is the ratio of real power to apparent power. A power factor of 1.0 means the load is purely resistive — all apparent power converts to useful work. A lower power factor indicates a mix of real and reactive demand. Motor loads, transformers, and inductive equipment typically operate at power factors between 0.80 and 0.95.
Low power factor increases conductor current for the same real power output, reduces available system capacity, and can increase utility demand charges. Power factor correction — typically using capacitor banks — is used to bring reactive demand under control in industrial installations.
Practical Tips
Always verify that the voltage you enter is line-to-line, not line-to-neutral. Common line-to-line voltages in North America include 208 V (low-voltage distribution), 480 V (industrial), and 4160 V or 13.8 kV (medium voltage). Using line-to-neutral voltage will understate kVA, kW, and kVAR by a factor of √3.
For power factor, use a realistic assumption based on the actual load type. Resistive heating loads may have a power factor near 1.0. Induction motors at full load typically operate between 0.85 and 0.95. Lightly loaded motors can have power factors well below 0.80. Using an overestimated power factor will overstate real power for the same apparent power demand.
When using this calculator for transformer or generator sizing, note that equipment is rated in kVA or MVA — apparent power — not kW. Real power (kW) alone is not sufficient to size supply equipment. Apparent power (kVA) determines the equipment rating that must be met.
Key Facts
- The √3 factor (≈ 1.7321) is a geometric consequence of 120° phase separation in balanced three-phase systems.
- Apparent power (kVA) is always ≥ real power (kW) for any load with power factor less than 1.0.
- Reactive power (kVAR) flows through conductors and must be supplied by the source, even though it performs no useful work.
- Power factor 1.0 means kVA = kW and kVAR = 0 — a purely resistive load.
- Low power factor increases line current and reduces available system capacity for the same real power.
- Conductors must be sized for line current, not directly for kW — ignoring power factor leads to undersized wiring.
- Three-phase power calculations assume equal current in all three phase conductors.
- Line voltage is measured between phase conductors — not between phase and neutral.
Applications
- Motor load estimation — calculate real power draw from measured voltage and current on motor feeders
- Transformer loading review — compare calculated apparent power against transformer kVA nameplate rating
- Generator sizing — estimate real and apparent power demand for generator selection and load bank testing
- Feeder ampacity checks — screen feeder loading against conductor ampacity limits at current line current
- Power factor correction — calculate reactive power demand as a basis for capacitor bank sizing
- Metering and billing review — verify metered demand against calculated kW and kVA values
- UPS and standby power — estimate three-phase load apparent power for UPS VA rating selection
- Switchgear and panel loading — compare calculated kVA against breaker and bus ratings
- Power quality screening
Example Calculation
Example Calculation
Given:
- Line voltage = 480 V
- Line current = 120 A
- Power factor = 0.85
Step 1: Apparent power
kVA = (√3 × 480 × 120) ÷ 1000 = (1.7321 × 480 × 120) ÷ 1000 ≈ 99.77 kVA
Step 2: Real power
kW = 99.77 × 0.85 ≈ 84.80 kW
Step 3: Reactive power
kVAR = √(99.77² − 84.80²) = √(9953 − 7191) ≈ 52.55 kVAR
Result:
- Apparent Power: 99.77 kVA
- Real Power: 84.80 kW
- Reactive Power: 52.55 kVAR
This is a typical loading for a medium-sized industrial motor group or HVAC equipment on a 480 V distribution panel — note that the transformer serving this load must be rated for the 99.77 kVA apparent power, not the 84.80 kW real power.
Standards & References
- IEEE 1459-2025 — IEEE Standard Definitions for the Measurement of Electric Power Quantities
- NFPA 70 (NEC), Article 220 — Branch-Circuit, Feeder, and Service Load Calculations — free online access: NFPA 70 2026 edition
- IEEE 141 (Red Book) — Electric Power Distribution for Industrial Plants
- IEEE 242 (Buff Book) — Protection and Coordination of Industrial and Commercial Power Systems
Units
This calculator uses:
| Unit | Purpose |
|---|---|
| V (volts) | Line-to-line voltage |
| A (amperes) | Line current per phase |
| dimensionless | Power factor |
| kVA (kilovolt-amperes) | Apparent power |
| kW (kilowatts) | Real power |
| kVAR (kilovolt-amperes reactive) | Reactive power |
All units are identical in metric and imperial display modes — electrical quantities have no unit conversion between measurement systems.
Limitations
- Assumes balanced three-phase loading — equal current in all three phases.
- Does not account for unbalanced phases.
- Does not calculate line losses or voltage drop.
- Does not account for harmonic distortion or nonlinear load effects.
- Does not calculate phase-to-neutral voltage or neutral current.
- Does not calculate motor efficiency, starting current, or demand factor.
- Does not perform power-factor correction sizing.
- Assumes sinusoidal voltage and current waveforms.
- Results are for a single operating point — does not account for load variation over time.
- Not a substitute for a full power system study or arc flash analysis.
Common Mistakes to Avoid
- Entering phase-to-neutral voltage instead of line-to-line voltage — this understates kVA, kW, and kVAR by a factor of √3.
- Using the single-phase formula (V × I ÷ 1000) and omitting the √3 factor.
- Ignoring power factor when comparing kW and kVA results.
- Treating kVAR as always harmful — some reactive demand is normal and expected for motor and transformer loads.
- Sizing conductors from kW alone — conductors must be sized to line current, which depends on kVA, not kW.
- Using nameplate voltage instead of actual measured line-to-line voltage.
- Applying this calculator to an unbalanced three-phase system — the formula assumes equal current in all three phases.
Frequently Asked Questions
What does this calculator compute?
Why does three-phase power use √3?
What is the difference between kW, kVA, and kVAR?
Do I enter line-to-line or phase-to-neutral voltage?
Does it matter if the system is wye or delta?
Can this calculator be used for unbalanced three-phase systems?
Does reactive power (kVAR) waste energy?
Is this calculator valid for all three-phase voltages?
Frequently Used Together
Engineers often use these calculators in combination for complete project workflows:
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Calculate
Line-to-line voltage — the voltage measured between any two phase conductors
Current in any phase conductor — assumes balanced loading across all three phases
Load power factor as a decimal — typically 0.80 to 0.95 for motor and mixed industrial loads