Motor Horsepower Calculator

Shaft horsepower is what a motor delivers to the load, and it is always smaller than what the motor draws from the line. For a balanced three-phase supply the real input power is sqrt(3) x V x I x PF using line voltage and line current, and the sqrt(3) appears because line and phase quantities differ by that factor in wye and delta connections. Single-phase input power is simply V x I x PF. Multiplying input power by efficiency gives mechanical output, and dividing by 746 watts converts to horsepower. Power factor and efficiency describe different losses: power factor is the phase displacement caused by magnetizing current, typically 0.75 to 0.90 at full load on an induction motor, while efficiency accounts for stator and rotor I squared R losses, core losses, windage, and friction, running about 82 to 89 percent on 1 to 5 HP frames and 94 to 96 percent above 100 HP. Torque follows from horsepower and speed through T = HP x 5252 / RPM, where 5252 is 33,000 divided by 2 pi, so a 10 HP motor gives 29.2 lb-ft at 1800 RPM but only 14.6 lb-ft at 3600 RPM. Practical caveats matter more than the arithmetic. Both power factor and efficiency collapse at light load, which is why an oversized motor running at 30 percent load wastes energy even though its nameplate efficiency looks good. Nameplate values apply at rated load, rated voltage, sea level to 1000 meters, and 40 degrees C ambient; above those, derating is required. Clamp meter readings on the output of a variable frequency drive are also unreliable, because the sqrt(3) relation assumes balanced sinusoidal waveforms that a PWM inverter does not produce.

The horsepower unit itself is older than the electric motor. James Watt established it around 1782 from tests with dray horses turning a mill, settling on 33,000 foot-pounds of work per minute so that steam engines could be priced against the animals they replaced. When electrical machines arrived the value was fixed at 745.7 watts, and the electrical trades rounded it to 746 watts, the figure still embedded in motor formulas and NEC tables today. The polyphase induction motor that this calculation describes emerged in the late 1880s. Galileo Ferraris demonstrated a rotating magnetic field produced by two out of phase currents in 1885, Nikola Tesla filed his polyphase motor patents in 1887 and 1888, and Mikhail Dolivo-Dobrovolsky developed the three-phase squirrel cage rotor in 1889, the design used in the celebrated Lauffen to Frankfurt power transmission demonstration of 1891. Standardization followed the technology. The National Electrical Manufacturers Association, formed in 1926, published the MG 1 standard that fixed frame sizes, design letters, service factors, and insulation classes, while IEEE Standard 112 defined how efficiency is actually measured. Legislated minimums came later: the US Energy Policy Act of 1992 and the Energy Independence and Security Act of 2007 progressively raised required efficiencies to NEMA Premium levels, and IEC 60034-30-1 established the parallel international IE1 through IE5 classes.