Power Transmission Calculator
Converts torque (N·m) and rotational speed (rpm) into mechanical power in kilowatts. Use it when sizing motors, drives, or shafts, or when checking whether a drivetrain can handle a given load without overheating.
About this calculator
Mechanical power transmitted by a rotating shaft is the product of torque and angular velocity. The formula is: P = T × ω, where P is power (W), T is torque (N·m), and ω is angular velocity in radians per second. Since rotational speed is usually given in rpm, the conversion is: ω = speed × 2π / 60. Combining these gives: P (W) = T × (speed × 2π / 60). Dividing by 1,000 converts watts to kilowatts. This relationship is fundamental to motor and gearbox selection — if you know the required torque and speed of a driven machine, you can directly calculate the minimum motor power needed. Efficiency losses in bearings, gears, and couplings mean the actual motor must supply more power than the ideal calculation suggests; a typical drivetrain efficiency of 90–95% should be factored in.
How to use
Suppose a shaft transmits a torque of 200 N·m at 1,450 rpm. Step 1 — convert rpm to rad/s: ω = 1,450 × 2π / 60 ≈ 1,450 × 0.10472 ≈ 151.84 rad/s. Step 2 — multiply by torque: P = 200 × 151.84 ≈ 30,368 W. Step 3 — convert to kilowatts: 30,368 / 1,000 ≈ 30.37 kW. To select a motor, add a service factor — for moderate shock loading (1.25×), you would specify at least a 38 kW motor. This confirms that a standard 37 kW motor would be marginal, and a 45 kW motor would be the appropriate commercial choice.
Frequently asked questions
How do I calculate mechanical power from torque and RPM for motor selection?
Use the formula P (kW) = T × (N × 2π / 60) / 1,000, where T is torque in N·m and N is speed in rpm. This gives the theoretical shaft power. For motor selection, divide this figure by the expected drivetrain efficiency (typically 0.90–0.95) and multiply by a service factor that accounts for start-up loads and shock (typically 1.1–1.5). Always select the next standard motor size above the calculated requirement. Motor manufacturers publish torque-speed curves that show how torque varies across the operating speed range, which is essential for applications with variable loads.
What is the relationship between torque, speed, and power in a rotating shaft?
Power, torque, and speed are inseparably linked: increasing speed while holding torque constant increases power linearly, and vice versa. This means a gearbox that reduces output speed (and increases torque) by a factor of three does not change power — it only redirects it. In practice, power is the constant quantity supplied by the motor; the gearbox trades speed for torque or vice versa. Understanding this relationship prevents over-sizing motors when high torque is needed at low speed — a gearbox and smaller motor often delivers the same result at lower cost and weight.
Why is mechanical power calculated in kilowatts rather than horsepower in engineering?
Kilowatts (kW) are the SI unit of power and are universally used in international engineering standards, motor specifications, and design codes outside North America. One kilowatt equals 1,000 watts (J/s), which integrates cleanly with SI units of force (N), length (m), and time (s). Horsepower (hp) remains common in North American markets and automotive contexts — 1 hp ≈ 0.7457 kW. When purchasing motors or drives internationally, always confirm whether ratings are in kW or hp to avoid a 34% sizing error. Most modern engineering software and standards bodies (IEC, ISO) use kilowatts exclusively.