Electrical Fundamentals & Power Triangle Calculator

Calculate Ohm’s Law (V, I, R, P), 3-phase AC power triangle (kW, kVA, kVAR, PF), horsepower to kW/Amps, and kVA↔Amps conversions.

NEC edition

Inputs

kVA
PF
Ω
HP
%

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⚡ Test your knowledge
NEC Article 220 was renumbered in the 2026 code cycle. What is the new article number?
  • A. Art. 100
  • B. Art. 120
  • C. Art. 200
  • D. Art. 230
💡 NEC 2026 renumbered Article 220 (Branch-Circuit, Feeder, and Service Calculations) to Article 120.
Energy Management Systems were moved from Article 750 to which article in NEC 2026?
  • A. Art. 100
  • B. Art. 125
  • C. Art. 130
  • D. Art. 150
💡 NEC 2026 moved Energy Management Systems from Article 750 to Article 130.
Which NEC standard size overcurrent device comes after 90A?
  • A. 95A
  • B. 100A
  • C. 110A
  • D. 105A
💡 Per NEC §240.6(A), the standard sizes are …90, 100, 110, 125… There is no 95A standard size.

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How it works & the NEC rules behind it

AC electrical power consists of three vector components forming the Power Triangle:

  • Real / Active Power (P, Watts / kW): The actual working energy performing mechanical work, heat, or light: P = V × I × PF (1-phase) or P = √3 × V_LL × I × PF (3-phase).
  • Apparent Power (S, Volt-Amps / kVA): The total capacity supplied by utility transformers and conductors: S = V × I or S = √3 × V_LL × I.
  • Reactive Power (Q, Volt-Amps Reactive / kVAR): Magnetic field energy sustaining induction motors and transformers: Q = √(S² − P²).
  • Power Factor (PF): The ratio of working power to total power: PF = P ÷ S = cos(θ).
  • Horsepower to Electrical Watts: 1 HP = 746 Watts. Input electrical power accounts for motor efficiency: P_in = (HP × 746) ÷ Efficiency.

Formulas & equations

Ohm’s Law: V = I × R | P = V × I = I² × R = V² ÷ R Single-Phase Power: P (kW) = (V × I × PF) ÷ 1000 | S (kVA) = (V × I) ÷ 1000 Three-Phase Power: P (kW) = (√3 × V_LL × I × PF) ÷ 1000 | S (kVA) = (√3 × V_LL × I) ÷ 1000 Reactive Power: Q (kVAR) = √(S² − P²) | Power Factor (PF) = kW ÷ kVA

NEC reference table

Calculation Goal Single-Phase (120V / 240V) Three-Phase (208V / 480V)
Find Amps from kVAI = (kVA × 1000) ÷ VI = (kVA × 1000) ÷ (1.732 × V)
Find Amps from kWI = (kW × 1000) ÷ (V × PF)I = (kW × 1000) ÷ (1.732 × V × PF)
Find kVA from AmpskVA = (V × I) ÷ 1000kVA = (1.732 × V × I) ÷ 1000
Find kW from AmpskW = (V × I × PF) ÷ 1000kW = (1.732 × V × I × PF) ÷ 1000

Worked example, step by step

Example: 75 kVA 3-Phase 480V Transformer at 0.85 Power Factor

Given: 75 kVA load, 480V 3-Phase, Power Factor = 0.85.

  • 1. Full Load Amps: (75 × 1000) ÷ (480 × 1.732) = 90.21 Amps.
  • 2. Real Working Power (kW): 75 kVA × 0.85 PF = 63.75 kW.
  • 3. Reactive Power (kVAR): √(75² − 63.75²) = 39.51 kVAR.
  • 4. Phase Angle: arccos(0.85) = 31.79°.

Frequently asked questions

Low power factor means a higher total current (kVA) must flow through utility lines to deliver the same real working energy (kW). This causes higher line losses (I²R) and voltage drop in utility distribution equipment.

The constant 1.732 is the square root of 3 (√3). In a balanced three-phase system, the line-to-line voltage is √3 times the line-to-neutral voltage because the three phase voltages are 120 electrical degrees out of phase with each other.

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