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3-Phase & 1-Phase Power / kVA Calculator

Calculate Apparent Power (kVA), Real Power (kW), Line Current (Amps), and Transformer Secondary Full-Load Amps across 208V, 240V, 480V, and 600V systems.

⚡ Electrical Code Basis & Safety Disclaimer

Based on NEC 2023 / IEEE Std 141 complex power relations. Estimates for planning only — electrical installations must comply with local code editions and be performed/verified by a licensed electrician. Not a substitute for engineered design or an AHJ ruling.

⚡ Power Triangle & AC Vector Schematic
Power Triangle DiagramDiagram showing apparent power kVA, real power kW, reactive power kVAR, and power factor angle.

Electrical Power Calculation Results

Apparent Power (S)
83.1 kVA
S = √3 × V × I / 1000
Real Working Power (P)
70.7 kW
P = S × PF (0.85 PF)
Equivalent Mechanical Output
94.8 HP
1 kW = 1.341 HP
Line Current / Transformer FLA
100.0 A
480V 3-Phase Line Current

Worked Examples: 3-Phase Power & Transformer Sizing

Review two fundamental electrical engineering calculations:

  • Example 1 (3-Phase 480V Feeder): For a 480V 3-phase system drawing 100 Amperes at 0.85 power factor:
    • $S = \frac{\sqrt{3} \times 480 \text{ V} \times 100 \text{ A}}{1000} = \frac{1.73205 \times 48000}{1000} = \mathbf{83.14 \text{ kVA}}$.
    • $P = 83.14 \text{ kVA} \times 0.85 = \mathbf{70.67 \text{ kW}}$.
  • Example 2 (75 kVA Transformer 208V Secondary): For a 75 kVA 3-phase step-down transformer with a 208V secondary:
    • $I_{\text{sec}} = \frac{75,000 \text{ VA}}{\sqrt{3} \times 208 \text{ V}} = \frac{75,000}{360.25} = \mathbf{208.18 \text{ Amperes secondary FLA}}$.

Engineering Code & Reference Citations

  • IEEE Std 141 (Red Book): Recommended Practice for Electric Power Distribution for Industrial Plants. ieee.org
  • NFPA 70 / NEC Article 450: Transformers and Transformer Vaults. nfpa.org
  • NEMA ST 20: Dry Type Transformers for General Applications. nema.org

Frequently Asked Questions (FAQ)

How do you calculate 3-phase kVA from voltage and current?

For a 3-phase system, apparent power S (kVA) = (√3 × Volts × Amps) / 1000. For example, at 480V and 100A: S = (1.73205 × 480 × 100) / 1000 = 83.14 kVA.

What is the secondary FLA for a 75 kVA 3-phase 208V transformer?

The secondary full-load current (FLA) = (75,000 VA) / (√3 × 208V) = 75,000 / 360.25 = 208.2 Amperes.

How do you convert 10 kW to kVA at a 0.9 power factor?

Apparent power kVA = Real Power (kW) / Power Factor = 10 kW / 0.9 = 11.11 kVA.

What is the difference between kVA and kW?

kVA (kilovolt-amperes) measures apparent power (the total electrical capacity required), while kW (kilowatts) measures real working power actually converted into useful work. kW = kVA × Power Factor.

What is the multiplier √3 (1.732) in 3-phase power calculations?

The square root of 3 (approximately 1.73205) accounts for the 120-degree phase separation between three AC voltage waveforms when using line-to-line voltage and line current.

How do you calculate single-phase kVA?

Single-phase apparent power kVA = (Volts × Amps) / 1000. For example, 240V at 50A equals (240 × 50) / 1000 = 12.0 kVA.

How many horsepower (HP) are in 1 kilowatt (kW)?

One kilowatt equals approximately 1.341 horsepower (1 HP = 745.7 Watts = 0.7457 kW).

What is a typical power factor for industrial electric motors?

Standard industrial AC induction motors typically operate at a power factor of 0.80 to 0.90 under full load, dropping lower during light load conditions.

What is the primary FLA for a 45 kVA 3-phase 480V transformer?

Primary FLA = (45,000 VA) / (√3 × 480V) = 45,000 / 831.38 = 54.1 Amperes.

How does power factor affect transformer and generator sizing?

Transformers and generators are rated in kVA because current creates heating regardless of power factor. A low power factor increases current draw for the same kW output, requiring a larger kVA transformer.

What is reactive power (kVAR)?

Reactive power (kVAR) is the non-working power required to establish magnetic fields in inductive equipment like motors and transformers. It forms the imaginary side of the power triangle: kVAR = √(kVA² - kW²).

Are these power formulas standard across NEC, IEEE, and IEC standards?

Yes. Fundamental AC complex power equations (kVA = √3·V·I/1000 and kW = kVA·PF) are fundamental physical laws defined by IEEE, IEC, and NEMA standards universally.