RPM to kW Converter

The formula to convert RPM (rotational speed) and torque to power in kilowatts is: P (kW) = (T × n) / 9549. Where: P = Power in kilowatts (kW). T = Torque in Newton-meters (N·m). n = Rotational speed in RPM. 9549 = Conversion constant (derived from 60,000 / 2π). ALTERNATIVE FORMULA: Using angular velocity: P (W) = T × ω. Where ω = angular velocity in rad/s = (RPM × 2π) / 60. DERIVATION: Power = Work / Time = Force × Distance / Time. For rotation: P = T × ω. Converting: ω = 2πn/60, so P = T × 2πn/60. To get kW: P(kW) = T × 2πn / (60 × 1000) = T × n / 9549. EXAMPLE: Motor with 100 N·m torque at 1500 RPM: P = (100 × 1500) / 9549 = 15.7 kW.

To convert pound-feet (lb-ft) to Newton-meters (N·m), multiply by 1.3558. CONVERSION FACTORS: 1 lb-ft = 1.3558179483 N·m. 1 N·m = 0.7375621493 lb-ft. COMMON TORQUE CONVERSIONS: lb-ft to N·m: multiply by 1.3558. N·m to lb-ft: multiply by 0.7376. kg·m to N·m: multiply by 9.80665. oz-in to N·m: multiply by 0.00706155. EXAMPLE: Car engine producing 300 lb-ft: 300 × 1.3558 = 406.7 N·m. WHY DIFFERENT UNITS: N·m: SI unit, used in metric countries and scientific work. lb-ft: Imperial unit, common in US automotive industry. kg·m: Sometimes used in older European specifications. PRACTICAL TIP: Most modern specifications use N·m. When comparing vehicles or motors, ensure you are using the same unit.

HP (horsepower) and kW (kilowatts) are both units of power, but they have different origins and conversion factors. CONVERSION: 1 kW = 1.341 HP (mechanical/imperial). 1 HP = 0.7457 kW. 1 kW = 1.3596 PS (metric horsepower). TYPES OF HORSEPOWER: Mechanical HP (imperial): 1 HP = 745.7 W. Defined by James Watt based on draft horses. Used in US, UK for engines. Metric HP (PS/CV/pk): 1 PS = 735.5 W. Used in Europe, Japan. Slightly smaller than imperial HP. Electrical HP: 1 HP = 746 W. Used for electric motors. WHY BOTH EXIST: HP: Historical unit from steam engine era. kW: SI unit, used in scientific and metric contexts. PRACTICAL EXAMPLES: 100 kW engine = 134.1 HP (imperial) = 136.0 PS (metric). 200 HP engine = 149.1 kW. MODERN USAGE: Automotive often quotes both. Electric vehicles typically use kW. Industrial equipment often uses kW globally.

Torque and power are related but different characteristics of motor performance. DEFINITIONS: Torque (T): Rotational force, measured in N·m or lb-ft. Represents twisting force the motor can apply. Power (P): Rate of doing work, measured in kW or HP. Represents how fast work can be done. THE RELATIONSHIP: P = T × ω (Power = Torque × Angular velocity). At constant power: Higher RPM = Lower torque. At constant torque: Higher RPM = Higher power. MOTOR CHARACTERISTICS: High Torque, Low RPM: Good for heavy loads, starting. Examples: Diesel engines, gear motors. High RPM, Lower Torque: Good for speed applications. Examples: High-rev gasoline engines. Flat Torque Curve: Consistent performance across RPM range. Examples: Electric motors, turbocharged engines. PRACTICAL IMPLICATIONS: Torque: Determines acceleration, pulling ability, hill climbing. Power: Determines top speed, sustained performance. Both matter: Best performance needs both adequate torque and power. EXAMPLE: Truck needs high torque for pulling heavy loads. Sports car needs high power for top speed. Electric vehicles have instant torque from 0 RPM.

Motor operating RPM varies widely depending on the type and application. AC INDUCTION MOTORS (most common industrial): Synchronous speeds based on frequency (50Hz or 60Hz). 2-pole: 3000 RPM (50Hz) / 3600 RPM (60Hz). 4-pole: 1500 RPM (50Hz) / 1800 RPM (60Hz). 6-pole: 1000 RPM (50Hz) / 1200 RPM (60Hz). Actual speed slightly lower due to slip (typically 2-5%). DC MOTORS: Wide speed range, easily controlled. Typical: 1000-5000 RPM. Can be higher with special designs. AUTOMOTIVE ENGINES: Idle: 600-1000 RPM. Cruise: 2000-3000 RPM. Max power: 5000-7000 RPM (gasoline). Diesel: Lower max RPM, typically 4000-5000. ELECTRIC VEHICLE MOTORS: Wide operating range: 0-15,000+ RPM. Peak efficiency often around 3000-8000 RPM. Tesla motors: Up to 18,000 RPM. SMALL MOTORS: Power tools: 2000-30,000 RPM. Computer fans: 1000-3000 RPM. Hobby motors: 5000-20,000+ RPM. HIGH-SPEED APPLICATIONS: Turbines: 10,000-100,000 RPM. Dental drills: 300,000-400,000 RPM. Centrifuges: Up to 150,000 RPM.

Motor efficiency is the ratio of mechanical output power to electrical input power. EFFICIENCY FORMULA: η = (Output Power / Input Power) × 100%. η = (Mechanical Power / Electrical Power) × 100%. MEASURING EFFICIENCY: Output Power: Measured at shaft (torque × angular velocity). Input Power: Measured electrically (voltage × current × power factor). Losses: Heat, friction, windage, core losses. TYPICAL EFFICIENCY RATINGS: Small motors (<1 kW): 60-80%. Medium motors (1-100 kW): 80-95%. Large motors (>100 kW): 90-97%. Premium efficiency motors: 95%+. EFFICIENCY CLASSES (IEC): IE1: Standard efficiency. IE2: High efficiency. IE3: Premium efficiency. IE4: Super premium efficiency. FACTORS AFFECTING EFFICIENCY: Load: Most efficient at 75-100% rated load. Speed: Variable speed can reduce efficiency. Temperature: Higher temp = lower efficiency. Age: Efficiency decreases over time. CALCULATING INPUT POWER: If you know output (shaft) power and efficiency: Input Power = Output Power / Efficiency. Example: 10 kW output, 90% efficiency. Input = 10 / 0.90 = 11.1 kW electrical input.

The speed-torque relationship is fundamental to understanding motor performance and is shown in the motor characteristic curve. BASIC RELATIONSHIP: At constant power: T = P / ω = (P × 9549) / RPM. As speed increases, torque decreases (and vice versa). This is the hyperbolic power curve. MOTOR TYPES AND CHARACTERISTICS: DC MOTORS: Nearly linear torque-speed curve. High starting torque. Speed drops as load increases. AC INDUCTION MOTORS: Complex curve with distinct regions. Starting torque: 1.5-3× rated torque. Pull-up torque: Minimum during acceleration. Breakdown torque: Maximum before stall. Operating region: Stable area near rated speed. SYNCHRONOUS MOTORS: Constant speed regardless of load. Torque limited by maximum before losing sync. VFD-CONTROLLED MOTORS: Constant torque region: Low to base speed. Constant power region: Above base speed. Field weakening: Very high speeds, reduced torque. ELECTRIC VEHICLE MOTORS: Wide constant torque region from 0 RPM. Constant power region at higher speeds. Very flat efficiency map. PRACTICAL IMPLICATIONS: Starting: Need sufficient torque to overcome inertia. Acceleration: Torque determines how fast you accelerate. Cruising: Power determines sustainable speed. Gearing: Can trade speed for torque (or vice versa).

Gearboxes change the relationship between motor output and final drive characteristics by trading speed for torque (or vice versa). GEAR RATIO EFFECTS: Speed: Output speed = Input speed / Gear ratio. Torque: Output torque = Input torque × Gear ratio × Efficiency. Power: Remains constant (minus losses). EXAMPLE: Motor: 10 kW, 3000 RPM, 31.8 N·m. Gearbox: 10:1 ratio, 95% efficiency. Output: Speed = 3000/10 = 300 RPM. Output: Torque = 31.8 × 10 × 0.95 = 302 N·m. Output: Power = 10 × 0.95 = 9.5 kW (some loss). GEARBOX EFFICIENCY: Single stage spur: 98-99%. Helical: 97-99%. Worm gear: 50-90% (varies with ratio). Planetary: 95-97%. Belt drive: 95-98%. WHEN TO USE GEARING: Need higher torque than motor provides. Need lower speed than motor runs at. Match motor to load requirements. Optimize motor efficiency by running at best speed. MULTI-STAGE GEARING: Ratios multiply: 5:1 × 4:1 = 20:1 total. Efficiencies multiply: 0.98 × 0.97 = 0.95 (95%). PRACTICAL TIP: Select motor and gearbox together. Sometimes a larger motor without gearbox is more efficient than small motor with high-ratio gearbox.