To select the right cables, fuses and protective devices, the power of a device or system
must be converted to amps. For a 400V three-phase network, the square root of 3 is used.
What does 1.732 mean?
This is the rounded square root of 3 (more precisely ≈ 1.73205). It is used in three-phase
calculations because a three-phase system has three phases, each shifted by 120°.
1. Formula without power factor (purely resistive load)
I = P / (U × 1.732)
- I = current in amps (A)
- P = power in watts (W) or kW (1 kW = 1000 W)
- U = three-phase voltage, usually 400 volts (V)
- 1.732 = rounded square root of 3
Worked example:
P = 5 kW = 5000 W, U = 400 V
I = 5000 / (400 × 1.732)
I = 5000 / 692.8
I ≈ 7.22 A
The current is approximately 7.22 A.
2. Formula with power factor (cos φ)
I = P / (U × 1.732 × cos φ)
Many devices, especially motors and transformers, have a power factor (cos φ) below 1.
This factor is typically between 0.7 and 1.0.
Worked example with cos φ = 0.8:
P = 5 kW = 5000 W, U = 400 V, cos φ = 0.8
I = 5000 / (400 × 1.732 × 0.8)
I = 5000 / 554.24
I ≈ 9.02 A
The current is approximately 9.02 A.
Why is the current higher with cos φ?
When cos φ is less than 1, not all of the electrical power is converted into useful power.
Part of it flows back and forth as reactive power.
Quick Overview as a Table
Without cos φ (assuming cos φ = 1)
| P (kW) |
Prąd (A) with I = P / (400 × 1.732) |
| 5 kW | 5000 / 692.8 ≈ 7.22 A |
| 10 kW | 10000 / 692.8 ≈ 14.45 A |
| 15 kW | 15000 / 692.8 ≈ 21.67 A |
With cos φ = 0.8
| P (kW) |
Prąd (A) with I = P / (400 × 1.732 × 0.8) |
| 5 kW | 5000 / 554.24 ≈ 9.02 A |
| 10 kW | 10000 / 554.24 ≈ 18.05 A |
| 15 kW | 15000 / 554.24 ≈ 27.07 A |
Converting kilowatts (kW) to amps (A) is essential for planning electrical systems on a
400V three-phase network. For complex calculations or high power values, a qualified
electrician should be consulted.