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Electrical Power Calculations Guide

Master the fundamental relationships between watts, amps, volts, and power factor.

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Quick Reference: Electrical Formulas

To FindSingle-Phase FormulaThree-Phase FormulaCalculator
Watts (P)I × V × PFI × V × √3 × PFCalculator
Amps (I)P ÷ (V × PF)P ÷ (V × √3 × PF)Calculator
VA (Apparent)I × VI × V × √3Calculator
VAR (Reactive)√(VA² - P²)√(VA² - P²)In main calculators

Understanding the Power Triangle

Interactive Power Triangle

Real Power (P) - WattsReactive Power (Q) - VARApparent Power (S) - VAφcos φ = PF
Real Power (P) - Actual work performed (Watts)
Reactive Power (Q) - Magnetic field energy (VAR)
Apparent Power (S) - Total power drawn (VA)

Power Factor Impact

Pure Resistive LoadPF = 1
Real: 100 W
Reactive: 0 VAR
Apparent: 100 VA
PF = 0.866
Real: 86.6 W
Reactive: 50 VAR
Apparent: 100 VA
PF = 0.707
Real: 70.7 W
Reactive: 70.7 VAR
Apparent: 100 VA
PF = 0.5
Real: 50 W
Reactive: 86.6 VAR
Apparent: 100 VA

Common Voltage Systems

120 V
Single Phase

Single-Phase 120 V

Applications:
  • Residential outlets
  • Small appliances
  • Lighting
240 V
Single Phase

Single-Phase 240 V

Applications:
  • Water heaters
  • Dryers
  • AC units
208 V
Three Phase

Three-Phase 208 V

Applications:
  • Commercial lighting
  • Small motors
  • Office equipment
480 V
Three Phase

Three-Phase 480 V

Applications:
  • Industrial motors
  • Large HVAC
  • Manufacturing

Real-World Calculation Examples

Residential Water Heater

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A 4500 W electric water heater on a 240 V circuit

Given:

  • Power: 4500 W
  • Voltage: 240 V
  • Load Type: Resistive

Solution:

I = P ÷ V = 4500 W ÷ 240 V = 18.75 A

Result:

18.75 Amps
PF: 1

Commercial LED Lighting

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50 A LED lighting circuit at 277 V with 0.95 power factor

Given:

  • Current: 50 A
  • Voltage: 277 V
  • Power Factor: 0.95

Solution:

P = I × V × PF = 50 A × 277 V × 0.95 = 13,158 W

Result:

13.16 kW
PF: 0.95

Key Concepts to Remember

Three-Phase Benefits

  • Balanced Loading
    Even distribution reduces neutral current
  • Motor Efficiency
    Better starting torque and efficiency

Practice with Our Calculators

Amps to Watts

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Watts to Amps

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Ohm's Law

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Three Phase

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kVA to Amps

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Continue Your Learning Journey

Now that you understand power calculations, explore these related topics to build your electrical engineering expertise.

Single vs Three Phase SystemsPower Factor Deep DiveWire Size Calculator

Worked Examples — Power Calculations With Real Numbers

Every formula below is applied to a concrete circuit. Memorize the pattern, plug in your numbers.

Example — Capacitor bank for PF correction

Scenario: A small machine shop draws 80 kW at PF 0.78 lagging on 480 V three-phase. Compute the kVAR of capacitors needed to correct PF to 0.95 and the resulting current reduction.

Existing reactive power: Q1 = P × tan(arccos 0.78) = 80 × 0.802 = 64.2 kVAR
Target reactive power: Q2 = P × tan(arccos 0.95) = 80 × 0.329 = 26.3 kVAR
Capacitor bank size: Q1 − Q2 = 64.2 − 26.3 = 37.9 kVAR
Pre-correction current: I = 80,000 / (1.732 × 480 × 0.78) = 123.4 A
Post-correction current: I = 80,000 / (1.732 × 480 × 0.95) = 101.3 A
Conductor relief: 22.1 A reduction