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Converters & physics calculator

Three-phase power calculator: kW ↔ amps, star and delta

Calculates three-phase real, reactive and apparent power from current (or current from power), with line and phase voltages and currents for star (Y) and delta (Δ) connections, motor efficiency and a table of standard voltages.

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Results

400 V three-phase, 32 A per line at PF 0.9 → 19.95 kW real, 22.17 kVA apparent. Each star winding sees 231 V and 32 A.
Real power
19.95kW
32 A at 400 V, PF 0.9
Line current
32A
Apparent power
22.17kVA
Reactive power
9.66kVAr
Phase voltage
230.9V
V_ph = V_L ÷ √3
Phase (winding) current
32A
I_ph = I_L
Impedance per phase
7.22Ω
Motor shaft output
18.36kW
24.6 hp at 92% efficiency
Suggested breaker (≥125%)
40 A
continuous-load rule of thumb; check local code
Single-phase equivalent
96A at 230 V
why big loads use three phases
Instantaneous phase voltages over one cycle
Current for the same 20 kW at standard voltages

Standard three-phase voltages

Line-to-line (V)Phase, star (V)Typical useAmps for 20 kWkW per 100 A
208120US commercial61.532.4
230133old IEC / Japan55.735.9
400231Europe, IEC3262.4
415240UK, Australia30.864.7
480277US industrial26.774.8
600346Canada21.393.5
690398industrial / wind18.6107.6
3,3001,905MV motors3.9514.4
6,6003,811MV1.91,028.8
11,0006,351MV distribution1.21,714.7
20,00011,547MV distribution0.63,117.7
33,00019,053MV / wind farm collector0.45,144.2
  • Balanced load assumed (equal current in all three lines). For unbalanced loads compute each phase separately: P = Σ V_ph · I_ph · cos φ.
  • Star: line voltage = √3 × phase voltage, line current = phase current. Delta: line voltage = phase voltage, line current = √3 × phase current. Total power is the same formula either way.
  • Breaker size is a rough guide (125% of continuous current). Cable size, length, installation method and local regulations decide the real protection.

How this three-phase power calculator works

Three-phase power supplies almost all industrial loads, large buildings, EV fast and wallbox chargers, heat pumps above a few kilowatts and every power plant. Its arithmetic is simple once you keep two pairs of quantities apart: line voltage and current (what you measure between the wires and in each wire) and phase voltage and current (what each winding or element of the load experiences).

Choose whether you want power from current or current from power, enter the line-to-line voltage and power factor, and pick a star (wye) or delta load. For motors you can enter the shaft output and an efficiency, and the calculator works back to the electrical input. Results include real, apparent and reactive power, line and phase values, impedance per phase, a suggested breaker size, the single-phase current that the same power would need and a table of currents at all standard voltages from 208 V to 33 kV.

The formulas

P = √3 × V_L × I_L × cos φ S = √3 × V_L × I_L Q = √(S² − P²) Star (Y): V_ph = V_L ÷ √3 I_ph = I_L Delta (Δ): V_ph = V_L I_ph = I_L ÷ √3 Motor: P_electrical = P_shaft ÷ η I_L = P ÷ (√3 × V_L × cos φ)

Worked example: a 32 A outlet at 400 V

The default is a European 400 V supply carrying 32 A per line at a power factor of 0.9, star-connected load:

  • Real power: 1.732 × 400 × 32 × 0.9 = 19.95 kW
  • Apparent power: 22.17 kVA; reactive power 9.66 kVAr
  • Each winding sees 400 ÷ 1.732 = 231 V and carries 32 A (impedance 7.2 Ω per phase)
  • A motor at 92% efficiency would deliver 18.4 kW (24.6 hp) at the shaft
  • The same 20 kW on a single 230 V phase would need about 96 A, three times the current

How to read the results

  • Line current sizes the cables, breakers and contactors.
  • Phase values matter for the load itself: winding insulation, heater elements, motor nameplates (e.g. “230 V Δ / 400 V Y”).
  • The waveform chart shows the three phase voltages 120° apart; their sum is zero at every instant, which is why a balanced load needs no neutral current.
  • The bar chart compares current for your power at standard voltages: higher voltage, lower current, thinner cables.

Standard three-phase voltages

Line-to-line Phase (star) Where
208 V 120 V US commercial buildings
400 V 230 V Europe and most IEC countries
415 V 240 V UK, Australia (nominal 400 V ±)
480 V 277 V US industry
600 V 347 V Canada
690 V 400 V Large motors, wind turbines
11–33 kV 6.4–19 kV Medium-voltage distribution, wind and solar parks

Current for common loads at 400 V

Load Power PF Line current
11 kW EV wallbox 11 kW 0.99 16 A
22 kW EV wallbox 22 kW 0.99 32 A
15 kW heat pump 5 kW electrical 0.95 7.6 A
7.5 kW motor (IE3, η 90%) 8.3 kW input 0.82 14.7 A
55 kW motor (η 94%) 58.5 kW input 0.86 98 A

Tips

  1. Balance the phases. Single-phase loads spread unevenly cause neutral current and voltage imbalance; distribute them across L1–L3.
  2. Check the motor nameplate connection: a “230/400 V” motor must be star-connected on a 400 V network, delta-connected on 230 V.
  3. Star–delta starting reduces starting current to about one third by starting in star and switching to delta.
  4. Account for power factor with the kVA to kW calculator, and use Ohm’s law for single elements.
  5. Breaker sizing shown here is only a rule of thumb; cable size, length, grouping and local code take precedence.

Limitations

The model assumes a balanced, sinusoidal three-phase system. Unbalanced loads, harmonics from drives and rectifiers, voltage drop along long cables and motor starting currents require further analysis. Efficiency and power factor of motors vary with load, so use part-load values for oversized motors.

Method & assumptions

Balanced three-phase power: P = √3 · VL · IL · cos φ (equivalently 3 · Vph · Iph · cos φ). Apparent power S = √3 · VL · IL; reactive Q = √(S² − P²). For a motor, electrical input = shaft power ÷ efficiency.

Frequently asked questions

What is the formula for three-phase power?
For a balanced load, P (W) = √3 × V_L × I_L × PF, where V_L is the line-to-line voltage, I_L the line current and PF the power factor. Apparent power is S = √3 × V_L × I_L in VA.
How many kW is 32 A three-phase?
At 400 V and a power factor of 0.9: √3 × 400 × 32 × 0.9 = 19.95 kW (22.2 kVA). At unity power factor it is 22.2 kW, which is why a 32 A three-phase outlet supports a 22 kW EV charger.
How many amps is 22 kW three-phase?
I = P ÷ (√3 × V × PF). At 400 V and PF 0.99 a 22 kW charger draws 32 A per phase. At 480 V and PF 0.9 a 22 kW load draws 29 A.
What is the difference between star (wye) and delta?
In star, each winding is connected between a line and the neutral point, so it sees the phase voltage (V_L ÷ √3, e.g. 230 V on a 400 V system) and carries the line current. In delta, each winding sits between two lines, sees the full line voltage and carries I_L ÷ √3. Total power is the same.
Why is the line voltage 400 V when the phase voltage is 230 V?
The three phase voltages are 120° apart, so the difference between any two of them is √3 ≈ 1.732 times the phase voltage: 230 × 1.732 = 398 V, rounded to 400 V. In North America 120 V phases give 208 V line-to-line, and 277 V phases give 480 V.
Why use three-phase power at all?
For the same power and conductor size, three-phase delivers √3 times the power of a single-phase circuit with only 1.5 times the conductors, produces constant (not pulsating) power and lets motors start and run without capacitors.

Sources & references

  1. IEC 60038 — IEC standard voltages
  2. Schneider Electric — Electrical Installation Guide (three-phase systems, power and current)
  3. IEC 60034-30-1 — Efficiency classes of line-operated AC motors (IE code)

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