Three-Phase Power Calculator
Convert amps to kW and kVA, or kW and motor horsepower to amps, for single-phase and three-phase circuits with line-to-line or line-to-neutral voltage and PF.
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About this toolWhat is the Three-Phase Power Calculator?
This calculator turns any one of current, real power (kW), apparent power (kVA) or motor horsepower into all the others. Pick single-phase or three-phase, enter the voltage, the power factor and, for motors, the efficiency, and the line current, kW, kVA and kVAR appear as you type.
Three-phase voltage causes more mistakes than anything else, so the tool asks which voltage you have. A 480 V system has 480 V between lines and 277 V from each line to neutral; enter either one and pick the matching option, and both voltages are shown in the results so you can check you used the one on the drawing.
A small table underneath shows how the current changes at other power factors for the same real power. It is a quick way to see why a poorly loaded motor or an uncorrected welder draws more current than its kW suggests.
- Single-phase and three-phase, line-to-line or line-to-neutral voltage
- Solve from amps, kW, kVA or horsepower
- Power factor, efficiency, kVAR and phase angle
- Comparison table of current at other power factors
- Formula panel with your numbers, copy and share
How to use the Three-Phase Power Calculator
- Pick single-phase, three-phase with line-to-line voltage, or three-phase with line-to-neutral voltage.
- Enter the voltage. The preset buttons cover common systems such as 208, 400, 480 and 600 V line to line or 120, 230 and 277 V line to neutral.
- Choose what you know: current, kW, kVA or motor horsepower, and type the value.
- Enter the power factor (1 for resistive heaters, 0.8 to 0.9 for loaded induction motors) and, for motors, the nameplate efficiency.
- Read current, kW, kVA, kVAR and shaft output, and check the formula panel to see the numbers substituted.
Worked examples
100 A on a 480 V three-phase feeder
Input
Three-phase, 480 V line to line, 100 A, PF 0.85
Output
83.14 kVA, 70.67 kW, 43.8 kVAR; 277.1 V line to neutral
√3 × 480 × 100 = 83,138 VA. Multiply by 0.85 for real power.
15 kW load on 400 V
Input
Three-phase, 400 V, 15 kW, PF 0.85
Output
25.47 A per line, 17.65 kVA
Divide kW by PF for kVA, then by √3 × 400 V for current.
5 hp single-phase motor
Input
Single-phase, 240 V, 5 hp, PF 0.85, efficiency 88%
Output
4.24 kW input, 20.77 A
5 × 745.7 W ÷ 0.88 = 4,237 W of input, and 4,237 ÷ (240 × 0.85) = 20.8 A. The NEC table value for a 5 hp, 230 V motor is 28 A, which is what you would size the circuit for.
Line-to-neutral input
Input
Three-phase, 277 V line to neutral, 100 A, PF 0.9
Output
83.1 kVA, 74.79 kW, 479.8 V line to line
3 × 277 × 100 gives the same 83.1 kVA as √3 × 480 × 100, as it should.
Background and insight
For a balanced three-phase load the apparent power is S = √3 × V(LL) × I, where V(LL) is the line-to-line voltage and I the current in each line. The √3 comes from the 120° spacing of the phases: the voltage between two lines is √3 times the voltage from a line to neutral, and three phases each carry V(LN) × I, so S = 3 × V(LN) × I = √3 × V(LL) × I. Single-phase is simply S = V × I.
Real power, the part that does work and that a kWh meter bills, is P = S × PF. Reactive power, which circulates between the supply and the magnetic fields of motors and transformers, is Q = S × sin φ, where φ = arccos PF. Cables, breakers and transformers must carry the full current, so they are rated in amps or kVA, not kW. A 100 A load at 480 V and PF 0.85 is 83.1 kVA but only 70.7 kW.
Motor nameplates give output power in horsepower or kW at the shaft. The electrical input is the output divided by efficiency, so a 10 hp motor (7.457 kW) at 90% efficiency draws 8.29 kW from the supply. One horsepower is 745.7 W (NIST SP 811). For wiring and protection the NEC uses its own full-load current tables (430.248 for single-phase, 430.250 for three-phase) rather than nameplate amps, because they are deliberately conservative.
Common use cases
Feeder and breaker checks
Convert a kW or kVA schedule into amps to choose cables, breakers and busbars.
Motor circuits
Estimate the running current of a pump, fan or compressor from its horsepower, efficiency and power factor.
Generator and UPS loading
Turn measured amps into kVA and kW to compare with a generator or UPS rating.
Reading meter data
Make sense of a power analyser reading by relating amps, kW, kVA and kVAR.
Tips and limitations
- If the drawing says 208Y/120 V, use 208 V line to line or 120 V line to neutral, not both.
- Power factor and efficiency are different. PF relates kW to kVA; efficiency relates shaft output to electrical input. A motor has both.
- Motor power factor drops sharply at light load. A motor running at half load may be at PF 0.6 to 0.7, so measured amps can look high for the kW delivered.
- For unbalanced loads, calculate each phase separately with V(LN) × I and add the powers.
- Size motor branch circuits from the NEC full-load current tables, not from this calculator or the nameplate.
Frequently asked questions
What is the formula for three-phase power?
P = √3 × V(LL) × I × PF in watts, where V(LL) is line-to-line voltage, I is line current and PF the power factor. Apparent power is the same without the PF: S = √3 × V × I in volt-amperes.
How do I convert kW to amps for three-phase?
Divide watts by √3 × voltage × power factor. 15 kW at 400 V and PF 0.85 is 15,000 ÷ (1.732 × 400 × 0.85) = 25.5 A.
Why is √3 used in three-phase calculations?
Because the line-to-line voltage of a balanced three-phase system is √3 times the line-to-neutral voltage. Three phases each delivering V(LN) × I add up to √3 × V(LL) × I.
What is the difference between kW and kVA?
kVA is apparent power, the product of voltage and current. kW is the real power that does work. kW = kVA × PF, so at PF 0.8 a 100 kVA load delivers 80 kW.
How many amps does a 10 hp motor draw at 480 volts?
With 90% efficiency and PF 0.85 the formula gives about 11.7 A at 480 V (12.2 A at 460 V). For sizing wire and protection the NEC table value of 14 A for a 460 V, 10 hp motor is used instead.
Should I use 208 or 120 volts for a 208Y/120 system?
Use 208 V with the line-to-line option or 120 V with the line-to-neutral option. Both give the same three-phase current for the same power.
Is there an in-depth guide to the Three-Phase Power Calculator?
Yes. “The Three-Phase Power Formula: Where √3 Comes From” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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