The Calculation, Explained
Where the √3 comes from
In a balanced three-phase system each phase carries Vph × Iph × cos φ of real power. Line voltage is √3 times phase voltage (the phases sit 120° apart, and the geometry of that phasor triangle is the whole story), so with line quantities:
Assumptions and applicability
- Nameplate efficiency and power factor are rated-load values. A motor at half load does not keep its 0.86 power factor — it may fall to 0.7 or lower, because magnetising current barely changes while load current halves. Load surveys that multiply measured current by nameplate PF overstate part-load power; that is the standard error this calculator cannot protect you from — measure PF where it matters.
- Balanced, sinusoidal supply is assumed. Voltage unbalance of even 2% adds disproportionate heating (NEMA derating) and a few percent of current error.
- Current → power gives the electrical picture: to judge whether the driven machine is healthy, convert to shaft power and compare with the duty the pump or fan should be absorbing (the Pump & Fan Calculator works the other side).
- Starting current (typically 6–7× full-load current) and starting torque are separate nameplate/design matters, not derivable from these steady-state relations.
Worked example (the defaults above)
A 400 V motor drawing 85 A at PF 0.86: input = 1.732 × 400 × 85 × 0.86 = 50.6 kW; at 93% efficiency the shaft delivers 47.1 kW, which at 1,480 rpm is a torque of 47.1 × 9,550 / 1,480 = 304 Nm, on 58.9 kVA of apparent power. If the driven pump's duty only accounts for 38 kW, the missing 9 kW is a finding — throttled valve, worn internals passing flow, or a motor oversized into poor efficiency — before it is a mystery.
References
IEC 60034 (rotating electrical machines — rating and performance); NEMA MG 1 (motors and generators, incl. unbalance derating).
Related calculators: Pump & Fan Calculator · Unit Converter