Convert amps to kW and kW to amps for DC, single-phase, and 3-phase AC circuits. Free calculator with formulas, power factor, 5.5kW motor sizing, and worked examples.
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In electrical engineering, current (measured in amperes or amps, symbol I) represents the rate of electric charge flow through a conductor, where 1 ampere equals 1 coulomb of charge per second. In contrast, active power (measured in kilowatts or kW, symbol P) represents the actual rate at which electrical energy is transformed into physical work, such as mechanical torque, thermal heat, or illumination.
Because current is merely the flow rate of charge, it cannot be converted into power without knowing the electrical pressure (voltage, V) pushing that current and, for alternating current systems, the synchronization between the voltage and current waveforms (power factor, cos φ). A 20-amp load on a 12-volt battery delivers only 0.24 kW, whereas that same 20-amp current on a 400-volt three-phase industrial line delivers over 11.7 kW.
Direct Current (DC): In DC circuits (such as solar photovoltaic panels, electric vehicle battery packs, and telecom power systems), voltage and current remain constant over time without sinusoidal cycles. As a result, the phase angle is zero and power factor is always 1.0. The formula is P(kW) = (V × I) / 1000.
Single-Phase Alternating Current (1Φ AC): In standard utility outlets (120V in North America, 230V across Europe, Africa, and Australasia), current and voltage oscillate sinusoidally. When powering inductive equipment (like refrigerator compressors, air conditioners, and washing machines), the magnetic fields cause current to lag behind voltage. The active power performing real work is P(kW) = (V × I × PF) / 1000.
Three-Phase Alternating Current (3Φ AC): Used in commercial facilities, data centers, and heavy manufacturing. Three separate alternating phase voltages are offset by 120 electrical degrees (2π/3 radians). Total three-phase power equals the sum of the three phases. When using Line-to-Line voltage (V_L-L, measured between two hot phases), the line current is shared across phases and must be scaled by the square root of 3 (√3 ≈ 1.73205): P(kW) = (√3 × V_L-L × I × PF) / 1000. When using Line-to-Neutral voltage (V_L-N), the formula is P(kW) = (3 × V_L-N × I × PF) / 1000. Because V_L-L = √3 × V_L-N, both formulas produce identical, mathematically consistent power values.
When sizing electrical feeders, circuit breakers, and variable frequency drives (VFDs), engineers frequently need to perform the reverse calculation: determine the full-load amperage drawn by a machine with a known kilowatt rating.
For example, a common industrial inquiry is 5.5 kW to amps. For a standard 5.5 kW three-phase induction motor operating on a 400V line-to-line supply with a 0.84 power factor, rearranging the 3-phase equation yields I = (P × 1000) / (√3 × V_L-L × PF) = 5500 / (1.73205 × 400 × 0.84) = 9.45 amperes. If factoring in typical motor mechanical efficiency (η ≈ 88%), the electrical input power increases to 5.5 / 0.88 = 6.25 kW, resulting in approximately 10.74 amperes drawn from the grid.
Under electrical codes like NEC Article 430 and IEC 60364, continuous motor branch conductors and overcurrent protective devices must be rated for at least 125% of the motor full-load running current, meaning a 5.5 kW motor circuit requires cable and protection sized for at least 11.8 A to 13.5 A.
The reference table below compares real active power (in kW) across standard operating voltages for common commercial and residential currents. AC calculations assume standard commercial power factors (0.95 for single-phase general loads; 0.85 for three-phase motor/industrial loads).
| Current (Amperes) | 120V 1Φ (PF 1.0) | 230V 1Φ (PF 0.95) | 400V 3Φ (PF 0.85) | 480V 3Φ (PF 0.85) |
|---|---|---|---|---|
| 10 A | 1.20 kW | 2.19 kW | 5.89 kW | 7.07 kW |
| 16 A | 1.92 kW | 3.50 kW | 9.42 kW | 11.31 kW |
| 24 A (Continuous) | 2.88 kW | 5.24 kW | 14.13 kW | 16.96 kW |
| 32 A | 3.84 kW | 6.99 kW | 18.84 kW | 22.61 kW |
| 50 A | 6.00 kW | 10.93 kW | 29.45 kW | 35.33 kW |
| 100 A | 12.00 kW | 21.85 kW | 58.89 kW | 70.67 kW |
| 500 A | 60.00 kW | 109.25 kW | 294.45 kW | 353.34 kW |
| 1,000 A | 120.00 kW | 218.50 kW | 588.89 kW | 706.68 kW |
| 3,000 A (Substation) | 360.00 kW | 655.50 kW | 1,766.69 kW | 2,119.95 kW |
For complete electrical engineering projects, conductor sizing requires analyzing circuit resistance, voltage drop over extended cable runs, and fundamental circuit parameters. Use our suite of dedicated engineering calculators for seamless workflow execution.
Need to compute circuit resistance, conductor voltage drop, or solve for unknown electrical variables? Check our Ohm’s Law Calculator to solve V, I, R, and P relationships, or launch our Electrical Power Calculator for comprehensive VI, I²R, and V²/R wattage analysis.
Launch Ohm's Law Calculator →A plant technician is sizing the thermal overload relay and supply branch circuit for a 5.5 kW three-phase motor operating on a 400V line-to-line 50Hz supply with a rated power factor of 0.84.
At 400V 3-phase, 5.5 kW converts to 9.45 amps of continuous running current. Overload relays should be calibrated to 9.45 A with standard 16A branch protection.
An electrician is evaluating an electric vehicle (EV) charging station or continuous heating load drawing 24 amperes on a standard single-phase residential supply.
A 24-ampere load on a 230V single-phase circuit delivers 5.24 kW of active power (5.52 kVA apparent). On a 120V single-phase resistive line, 24 amperes equals 2.88 kW.
A chief electrical engineer reviews the maximum load capacity for an industrial facility main switchboard busbar rated for 3,000 amperes at 480V three-phase with an average factory power factor of 0.85.
A 3,000-amp load on a 480V 3-phase system delivers 2,119.95 kW (2.12 Megawatts) of active real power while requiring 2.49 MVA of distribution transformer capacity. At 400V 3-phase, 3,000 amps delivers 1,766.69 kW (1.77 MW).
A renewable energy installer calculates the power flow through a 48V DC lithium iron phosphate (LiFePO4) solar battery bank discharging at 100 amperes.
In Direct Current (DC) systems, power factor does not apply. A 100A draw at 48V produces exactly 4.80 kW of continuous DC electrical power.
To convert 5.5 kW to amps for a three-phase motor, use the formula: Current (I) = (Power in Watts) / (√3 × Line-to-Line Voltage × Power Factor). For a standard 400V 3-phase supply with a motor power factor of 0.84: I = 5,500 / (1.73205 × 400 × 0.84) = 5,500 / 581.97 = 9.45 amperes of full-load running current (FLA). On a 480V 3-phase supply, that same 5.5 kW motor draws approximately 7.87 amperes. Switch to the "kW to Amps" mode in this calculator to compute exact current for any voltage or power factor rating.
The power produced by 24 amperes depends entirely on voltage and circuit phase: On a 230V single-phase circuit with a typical power factor of 0.95 (such as an EV wall charger or heat pump), 24A produces 5.24 kW (or 5.52 kW with a pure resistive heater where PF = 1.0). On a North American 120V single-phase resistive line, 24A produces 2.88 kW. On a 240V split-phase circuit, 24A equals 5.76 kW. On a 400V 3-phase circuit (PF 0.85), 24A produces 14.13 kW.
A 3,000-ampere current indicates major industrial distribution switchgear or an electrical substation busbar. On a 480V 3-phase line-to-line system with a standard industrial plant power factor of 0.85, 3000A equals 2,119.95 kW (2.12 Megawatts) of active real power, requiring 2,494.15 kVA (2.49 MVA) of apparent transformer capacity. On a 400V 3-phase system at 0.85 power factor, 3,000A equals 1,766.69 kW (1.77 MW).
For three-phase AC circuits, the formula depends on whether you measure Line-to-Line voltage (V_L-L, between two phases) or Line-to-Neutral voltage (V_L-N, between one phase and neutral). Using Line-to-Line voltage: P(kW) = (√3 × V_L-L × I × PF) / 1000, where √3 ≈ 1.73205. Using Line-to-Neutral voltage: P(kW) = (3 × V_L-N × I × PF) / 1000. Both formulas yield identical power because V_L-L = √3 × V_L-N.
Amperes measure electric current (the rate of charge flow), whereas kilowatts measure active real power (the rate of energy consumption or work performed). Because electrical power equals the product of current and potential difference (P = V × I), current alone has no fixed energy value without knowing the circuit voltage pushing it. Furthermore, in AC circuits with inductive or capacitive equipment, voltage and current waveforms do not peak simultaneously; the power factor (cos φ) accounts for this phase displacement to determine real power (kW) rather than total apparent power (kVA).
Line-to-Line voltage (V_L-L) is measured between any two hot phase conductors (typically 400V in 50Hz IEC countries or 480V in 60Hz North American systems). Line-to-Neutral voltage (V_L-N) is measured between any individual phase conductor and the grounded neutral point (typically 230V in 400V systems, or 277V in 480V systems). In balanced systems, Line-to-Line voltage is always √3 times Line-to-Neutral voltage (V_L-L = 1.73205 × V_L-N).
Pure resistive loads (such as electric water heaters, space heaters, and incandescent bulbs) have a power factor of 1.0 (unity). Standard three-phase induction electric motors and compressors typically have a full-load power factor between 0.80 and 0.88 (dropping to 0.40–0.60 when running unloaded). Modern switch-mode computer power supplies with active PFC achieve 0.95–0.98. LED lighting drivers generally range between 0.90 and 0.95.
UtilityBase provides a full suite of precision electrical engineering tools: visit our Ohm’s Law Calculator (/engineering-physics/ohms-law-calculator/) to calculate voltage, current, resistance, and wattage using V = I × R and P = V × I; or explore the Electrical Power Calculator (/engineering-physics/electrical-power-calculator/) for complete Joule heating, daily kilowatt-hour consumption, and multi-unit conversions.