Amp to kW 3 phase
Convert line current to kW on a three-phase supply and watch the three voltage and current phasors rotate 120° apart.
Inputs
Three-phase phasor diagram
How amp to kW 3 phase calculator works
The amp to kW 3 phase calculator converts line current into real power in kilowatts (kW) on a three-phase supply with 4 inputs: current, voltage, voltage type and power factor. The calculator multiplies by √3 for line-to-line voltage and by 3 for line-to-neutral voltage.
P = √3 × I × V × PF / 100032 A at 400 V line to line and PF 0.85 gives 18.84 kW, or 6.28 kW on each phase. The phasor diagram rotates the 3 voltage and 3 current phasors 120° apart.
Amp to kW 3 phase formula
The amp to kW 3 phase formula is P(kW) = √3 × VL-L × I × PF / 1,000. There are 3 three-phase power formulas: line-to-line, line-to-neutral and per-phase power.
Line-to-line voltage
P = √3 × V × I × PF / 10001.732 × 400 V × 32 A × 0.85 / 1,000 = 18.84 kW
Line-to-neutral voltage
P = 3 × V × I × PF / 10003 × 230 V × 32 A × 0.85 / 1,000 = 18.77 kW
Power per phase
Pphase = P / 318.84 kW / 3 = 6.28 kW
Nikola Tesla patented the polyphase AC system in 1888. A balanced three-phase load draws the same current in all 3 lines, and line-to-line voltage equals √3 (1.732) × line-to-neutral voltage.
Amp to kW 3 phase conversion chart
The amp to kW 3 phase conversion chart lists 14 line currents from 5 A to 200 A at 5 three-phase voltages: 208 V, 380 V, 400 V, 415 V and 480 V, plus a 400 V column at power factor 0.85.
| Amps | 208 VPF 1 | 380 VPF 1 | 400 VPF 1 | 415 VPF 1 | 480 VPF 1 | 400 VPF 0.85 |
|---|---|---|---|---|---|---|
| 5 A | 1.8 | 3.29 | 3.46 | 3.59 | 4.16 | 2.94 |
| 10 A | 3.6 | 6.58 | 6.93 | 7.19 | 8.31 | 5.89 |
| 16 A | 5.76 | 10.53 | 11.09 | 11.5 | 13.3 | 9.42 |
| 20 A | 7.21 | 13.16 | 13.86 | 14.38 | 16.63 | 11.78 |
| 25 A | 9.01 | 16.45 | 17.32 | 17.97 | 20.78 | 14.72 |
| 32 A | 11.53 | 21.06 | 22.17 | 23 | 26.6 | 18.84 |
| 40 A | 14.41 | 26.33 | 27.71 | 28.75 | 33.26 | 23.56 |
| 50 A | 18.01 | 32.91 | 34.64 | 35.94 | 41.57 | 29.44 |
| 63 A | 22.7 | 41.47 | 43.65 | 45.28 | 52.38 | 37.1 |
| 80 A | 28.82 | 52.65 | 55.43 | 57.5 | 66.51 | 47.11 |
| 100 A | 36.03 | 65.82 | 69.28 | 71.88 | 83.14 | 58.89 |
| 125 A | 45.03 | 82.27 | 86.6 | 89.85 | 103.92 | 73.61 |
| 160 A | 57.64 | 105.31 | 110.85 | 115.01 | 133.02 | 94.22 |
| 200 A | 72.05 | 131.64 | 138.56 | 143.76 | 166.28 | 117.78 |
125 A per line at 400 V delivers 86.6 kW at PF 1 and 73.61 kW at PF 0.85.
Amp to kW 3 phase Excel formula
The amp to kW 3 phase Excel formula is =SQRT(3)*A2*B2*C2/1000 with line amps in A2, line-to-line volts in B2 and power factor in C2. Use =3*A2*B2*C2/1000 with line-to-neutral volts.
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | Amps | Volts | PF | kW | Formula in D |
| 2 | 32 | 400 | 0.85 | 18.84 | =ROUND(SQRT(3)*A2*B2*C2/1000,2) |
| 3 | 63 | 415 | 0.9 | 40.76 | =ROUND(SQRT(3)*A3*B3*C3/1000,2) |
| 4 | 100 | 480 | 0.9 | 74.82 | =ROUND(SQRT(3)*A4*B4*C4/1000,2) |
Add =D2/3 in column E to get kW per phase.
Amp to kW 3 phase equation
The amp to kW 3 phase equation is P = √3 × VL-L × IL × cos φ, where VL-L is line-to-line voltage and IL is line current.
- P
- Total real power in kW
- √3
- 1.732, links line-to-line and phase voltage
- I
- Line current in amperes (A)
- V
- Line-to-line voltage (V)
- PF
- Power factor, cos φ
3 phases × 230.9 V phase voltage × I equals √3 × 400 V × I, which is where the √3 factor comes from.
Amp to kW 3 phase FAQ
How many kW is 32 amps 3 phase?
32 amps 3 phase is 22.17 kW at 400 V and 26.6 kW at 480 V at a power factor of 1, or 18.84 kW at 400 V and PF 0.85.
How many kW is 63 amps 3 phase?
63 amps 3 phase is 43.65 kW at 400 V and 45.28 kW at 415 V, at a power factor of 1.
Why multiply by √3 in 3 phase?
√3 (1.732) converts line-to-line voltage into the 3 phase voltages. A 400 V line-to-line supply has 230.9 V per phase, and 3 × 230.9 V equals √3 × 400 V.
Is 3 phase power 3 times single phase?
Yes, a balanced 3 phase supply carries 3 times the power of one phase at the same current. 32 A per line at 400 V gives 22.17 kW, and 32 A on one 230 V phase gives 7.36 kW.