How to Convert Amps to Kilowatts: Single-Phase and Three-Phase Formulas
Convert amps to kilowatts using the correct formula for single-phase or three-phase circuits. Covers power factor, worked examples, and a quick reference table.
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Why Amps and Kilowatts Need a Formula
Amps (A) measure current — the flow of electric charge. Kilowatts (kW) measure real power — the rate of energy consumption. They are related by voltage and power factor, not directly interchangeable.
You cannot convert amps to kilowatts without knowing the voltage and power factor of the circuit.
Single-Phase AC: Amps to Kilowatts
Formula: kW = (A × V × PF) ÷ 1,000
Where: - A = Amps (current) - V = Voltage (volts) - PF = Power Factor (0 to 1; 1.0 for resistive loads, 0.8–0.95 for motors)
Example: 20-amp circuit at 120V, PF = 0.95: kW = (20 × 120 × 0.95) ÷ 1,000 = 2,280 ÷ 1,000 = 2.28 kW
Example (240V): 30-amp dryer circuit at 240V, PF = 1.0: kW = (30 × 240 × 1.0) ÷ 1,000 = 7.2 kW
Three-Phase AC: Amps to Kilowatts
Formula: kW = (A × V × 1.732 × PF) ÷ 1,000
The 1.732 is √3, the mathematical relationship between line and phase voltage in three-phase systems.
Example: 3-phase motor, 15 amps at 480V, PF = 0.85: kW = (15 × 480 × 1.732 × 0.85) ÷ 1,000 = (10,559) ÷ 1,000 = 10.56 kW
Example: 3-phase commercial panel, 100A at 208V, PF = 0.90: kW = (100 × 208 × 1.732 × 0.90) ÷ 1,000 = 32.4 kW
Power Factor Explained
Power factor (PF) accounts for the phase difference between voltage and current waveforms in AC circuits:
- PF = 1.0: Purely resistive loads — incandescent lights, electric heaters, hot water heaters
- PF = 0.85–0.95: Inductive loads — motors, compressors, HVAC
- PF = 0.7–0.85: Heavily inductive loads — older motors, fluorescent lighting without correction
If PF is unknown, common estimates: - Residential general: PF ≈ 0.95 - Motors: PF ≈ 0.85 - Mixed commercial: PF ≈ 0.90
Quick Reference Table (Single Phase, PF = 0.90)
kW vs. kVA vs. kVAR
- kW (kilowatts): Real power — actual energy consumed, what you pay for
- kVA (kilovolt-amps): Apparent power = A × V ÷ 1,000 (without PF)
- kVAR: Reactive power — "wasted" power in inductive circuits
Relationship: kW = kVA × PF
Transformers and generators are rated in kVA (they must handle full apparent power), while energy bills are in kWh (real power over time).
Related Guides
- How Three-Phase Power Is Calculated: Watts, Amps, and Power FactorUnderstand three-phase power calculations — how to find real power (kW), apparent power (kVA), reactive power (kVAR), and current from three-phase motor and generator specifications.
- How to Convert Watts to Amps: Single-Phase and DC FormulasLearn how to convert watts to amps using Ohm's Law and power formulas for DC circuits, single-phase AC, and three-phase AC with practical worked examples.
- Air Changes Per Hour: What ACH Means and How to Calculate ItUnderstand air changes per hour (ACH): what it measures, ASHRAE targets for different room types, how to calculate the airflow needed, and why it matters for indoor air quality.
- How Three-Phase Motor Amperage Is Calculated from HP and VoltageLearn the three-phase motor current formula — how to calculate full-load amps from horsepower, voltage, motor efficiency, and power factor, with NEC table values for quick reference.
Frequently Asked Questions
- How do I convert amps to kilowatts?
- kW = (Amps × Volts × Power Factor) ÷ 1,000 for single-phase. For three-phase: kW = (Amps × Volts × 1.732 × Power Factor) ÷ 1,000. You need voltage and power factor — amps alone cannot convert to kW. For resistive loads (heaters), PF = 1.0; for motors, use PF = 0.85.
- What is power factor and does it matter for amps-to-kW conversion?
- Power factor (PF) accounts for the phase difference between voltage and current in AC circuits. At PF = 0.85 vs. PF = 1.0, the same 20 amps at 240V produces 4.08 kW vs. 4.80 kW — a 15% difference. For resistive loads (heaters, incandescent lights), PF = 1.0 is correct. For motors and compressors, use the nameplate PF or assume 0.85.
- What is the formula for three-phase amps to kilowatts?
- kW = (A × V × 1.732 × PF) ÷ 1,000, where 1.732 = √3. For a 3-phase 20-amp circuit at 480V with PF = 0.90: kW = (20 × 480 × 1.732 × 0.90) ÷ 1,000 = 14.93 kW. Voltage here is line-to-line voltage.
- How many kilowatts is a 200-amp service?
- For residential 200A service (single-phase, 240V, PF = 0.95): kW = (200 × 240 × 0.95) ÷ 1,000 = 45.6 kW maximum. In practice, 200A service is never loaded to 100% simultaneously. Typical average home loads are 5–15 kW of active consumption at any given time.
Last updated 7/28/2026