Convert apparent power (kVA) to horsepower for motor sizing and selection. Calculate mechanical power output with efficiency and power factor considerations.
Motor Engineering | Version 2.1
Select configuration type
Enter the apparent power rating
Typical range: 80-95%
Typical range: 0.8-0.9 for inductive load (0.85 is common)
Mechanical Power: 0 HP
Mechanical Power (kW): 0 kW
Electrical Power: 0 kW
System Type: Three-Phase
Overall Efficiency: 0%
Enter values above to see detailed calculations
HP = (kVA × 1000 × Efficiency × Power Factor) ÷ 746
Where:
• kVA = Apparent Power (kilovolt-amperes)
• Efficiency = Motor efficiency (decimal, e.g., 0.90 for 90%)
• Power Factor = Motor power factor (decimal, e.g., 0.85)
• 746 = Conversion factor (1 HP = 746 watts)
Problem: Calculate HP for a three-phase motor with 25 kVA, 88% efficiency, and 0.85 power factor
HP = (kVA × 1000 × Efficiency × Power Factor) ÷ 746
HP = (25 × 1000 × 0.88 × 0.85) ÷ 746
Converting kVA to HP is essential for motor sizing, selection, and performance analysis. kVA represents the total electrical power supplied to the motor, while HP represents the useful mechanical power output available for work. This conversion helps determine: actual shaft power for load matching, motor efficiency and performance, energy consumption costs, proper motor sizing for applications, and compliance with mechanical power requirements. Engineers use this conversion to ensure motors can handle the required mechanical load while operating efficiently.
While the kVA to HP conversion formula is identical for both single-phase and three-phase motors, the initial kVA calculation differs. Single-phase: kVA = (V × I) ÷ 1000, while three-phase: kVA = (√3 × V × I) ÷ 1000. However, once you have the kVA value, the conversion to HP uses the same formula regardless of phase configuration. Three-phase motors typically have higher efficiency, better power factor, and more consistent power delivery compared to single-phase motors of the same HP rating.
Motor efficiency and power factor are typically found on the motor nameplate or specification sheet. If unavailable, use these typical values: High-efficiency motors (92-96% efficiency, 0.85-0.9 PF), Standard industrial motors (85-92% efficiency, 0.8-0.85 PF), Small motors under 1 HP (75-85% efficiency, 0.7-0.8 PF). For precise calculations, measure actual values using power analyzers. Motor efficiency decreases with age and poor maintenance, while power factor can vary significantly with load conditions. Always use nameplate values when available for accurate motor sizing and energy calculations.
The conversion factor 746 represents the exact number of watts in one horsepower. This relationship was established by James Watt, who defined horsepower as the power needed to lift 550 pounds one foot in one second. When converted to the metric system: 1 HP = 550 ft-lb/s = 745.7 watts ≈ 746 watts. This conversion factor allows us to convert mechanical power from watts (derived from electrical calculations) to horsepower, which is the standard unit for expressing motor shaft power output in many industries, particularly in the United States.
Motor loading significantly affects efficiency and power factor, which directly impact the kVA to HP conversion. At full load (100%), motors operate at rated efficiency and power factor. At partial loads (25-75%), efficiency decreases slightly while power factor drops significantly. Overloading (>100%) reduces efficiency and may damage the motor. For accurate conversions, use efficiency and power factor values corresponding to the actual operating load. Lightly loaded motors (< 50%) have poor power factor (0.6-0.7) and reduced efficiency, resulting in lower HP output per kVA input. This is why proper motor sizing is crucial for optimal performance and energy efficiency.