A technician clamps one phase of a 480V three-phase compressor. Reads 62 amps. Calculates: 480 × 62 × 3 = 89.4 kW. Actual power: 38.2 kW. Where did 51 kW come from?
The two mistakes
Mistake 1: ×3 instead of ×√3
Three-phase power uses √3 (1.732), not 3.
The phases are 120° apart — they don't simply add.
Mistake 2: No power factor
V × I = apparent power (kVA), not real power (kW).
A motor at 74% PF draws 26% more current than its kW suggests.
The correct formula
Three-phase real power:
P (kW) = √3 × V_line × I_line × PF / 1,000
= 1.732 × 480 × 62 × 0.74 / 1,000
= 38.2 kW
Compare to the wrong method:
P = V × I × 3 / 1,000
= 480 × 62 × 3 / 1,000
= 89.4 kW ← 134% too high
Three common errors ranked
Method Result Error
──────────────────────────────────────────────
V × I × 3 89.4 kW +134% ← worst
V × I × √3 (no PF) 51.6 kVA +35% (kVA, not kW)
√3 × V × I × PF 38.2 kW 0% ← correct
Three correct measurement methods
1. True 3-phase power meter
Clamp all three phases simultaneously.
Meter calculates kW directly.
Best accuracy. No PF needed.
2. Single clamp + PF
P = √3 × V × I × PF
Works if: phases balanced (±5%), PF known.
Use clamp meter with PF function.
3. kWh meter reading
Read utility meter. Wait 15-60 min. Read again.
kW = ΔkWh / hours
Most accurate field method — meter is calibrated.
Why it matters
Energy audit:
Baseline at 89 kW → "VFD saves 30 kW" → approved
Actual baseline 38 kW → VFD saves 11 kW → never pays back
Generator sizing:
89 kW measurement → buy 100 kW generator
Actual load 38 kW → 50 kW generator is plenty
Wasted: $15,000+ on oversized equipment
Billing check:
Your measurement: 89 kW
Utility bill: 38 kW
"The meter must be wrong" ← No, your formula is wrong
The rule
For three-phase equipment, always:
P = √3 × V × I × PF
Never V × I × 3. Never V × I × √3 without PF. The √3 accounts for the phase angle. The PF converts apparent power to real power. Skip either one and the number is fiction.
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