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How to Convert Between kW, kVA and Amps
Manesh Jayawardhana
CIO & Co-founder
A 15 kW three-phase motor on a 400 V supply. How much current does it draw, and what size cable does it need?
The answer isn’t 15,000 divided by 400. It’s not even close, and the two things it’s missing — the √3 factor and power factor — are the reason three-phase calculations catch people out.
Where the √3 comes from
In a three-phase system, the three windings are 120 degrees apart in phase. That geometry means the line-to-line voltage is √3 (about 1.732) times the phase voltage in a star-connected system, and the same factor appears in the power equation:
P = √3 × V_line × I_line × cos φ
Rearranged for current:
I = P ÷ (√3 × V × cos φ)
For 15 kW at 400 V with a power factor of 0.85:
15,000 ÷ (1.732 × 400 × 0.85) ≈ 25.5 A
Without the √3 you’d calculate 44 A and oversize everything. Without the power factor you’d get 21.7 A and undersize the protection.
Why power factor matters for cable sizing
Real power (kW) is what does useful work. Apparent power (kVA) is what the supply actually has to deliver — the vector sum of real power and reactive power, which flows back and forth without doing work.
apparent power = real power ÷ power factor
15 kW at 0.85 power factor is 17.6 kVA. That’s the figure that determines current, and current is what heats cables and trips protective devices.
This is why a facility with poor power factor pays for infrastructure sized larger than its useful load, and why many commercial tariffs penalise low power factor directly. Correction equipment exists precisely because the difference is expensive.
| Quantity | Unit | What It Represents |
|---|---|---|
| Real power | kW | Work actually done |
| Apparent power | kVA | What the supply must deliver |
| Power factor | cos φ | Ratio of real to apparent |
| Line current | A | What cables and breakers see |
Why people get stuck here
- Single-phase habits. The single-phase formula works and gives a wrong answer, which is the worst kind of error.
- Power factor assumed as 1. True for resistive heating, not for motors, drives or discharge lighting.
- Line versus phase voltage. A “400 V three-phase” supply is 400 V line to line and about 230 V line to neutral.
- Unbalanced loads. The standard equations assume balance; unbalanced systems need per-phase calculation, including neutral current.
Common mistakes to avoid
- Omitting √3 and oversizing cable by nearly 75%.
- Assuming unity power factor on a motor load, and undersizing protection.
- Using the phase voltage where the line voltage belongs.
- Applying the balanced equations to a distribution board with significantly unbalanced single-phase loads.
- Sizing cable on kW rather than on current — cables carry amps, not kilowatts.
How to do it with Three-Phase Power Calculator
The Three-Phase Power Calculator reports current and apparent power together.
- Enter the line-to-line voltage — the figure normally quoted for a three-phase supply.
- Add the real power in kW and the load’s power factor.
- Read the current and the kVA together, since protection is sized on current.
- For unbalanced systems, calculate per phase instead; the balanced equations don’t apply.
Anything that will be installed needs checking against your local wiring regulations — BS 7671 in the UK, or the equivalent standard where you are. Other engineering calculators are in the tools directory.
Frequently asked questions
Where does the √3 come from?
From the 120-degree phase relationship between the windings. Line voltage is √3 times phase voltage in a star connection, and the same factor carries through into the power equation.
Why does power factor matter for cable sizing?
Because cables and protective devices carry current, not kilowatts. A poor power factor means more current for the same useful power, so the installation must be sized larger.
Is this valid for an unbalanced load?
No. These equations assume a balanced three-phase load. Unbalanced systems must be calculated per phase, and the neutral current needs checking too.
Final thought
Two numbers turn a three-phase calculation from wrong to right: √3 and the power factor. Leave either out and the answer is confidently incorrect in a direction that costs money.