Convert torque to kW: enter torque in Nm (or lbf·ft) and speed in rpm to get power in kW or hp, or convert kW and rpm back to torque in Nm.
| Torque to kW | kW to Torque |
|---|---|
| 5 Nm @ 1500 RPM = 0.7854 kW | 0.75 kW @ 1500 RPM = 4.7746 Nm |
| 10 Nm @ 1500 RPM = 1.5708 kW | 1 kW @ 1500 RPM = 6.3662 Nm |
| 15 Nm @ 1500 RPM = 2.3562 kW | 1.5 kW @ 1500 RPM = 9.5493 Nm |
| 20 Nm @ 1500 RPM = 3.1416 kW | 2 kW @ 1500 RPM = 12.7324 Nm |
| 25 Nm @ 1500 RPM = 3.9270 kW | 3 kW @ 1500 RPM = 19.0986 Nm |
| 30 Nm @ 1500 RPM = 4.7124 kW | 5 kW @ 1500 RPM = 31.8310 Nm |
| 40 Nm @ 1500 RPM = 6.2832 kW | 7.5 kW @ 1500 RPM = 47.7465 Nm |
| 50 Nm @ 1500 RPM = 7.8540 kW | 10 kW @ 1500 RPM = 63.6620 Nm |
| 75 Nm @ 1500 RPM = 11.7810 kW | 15 kW @ 1500 RPM = 95.4930 Nm |
| 100 Nm @ 1500 RPM = 15.7080 kW | 20 kW @ 1500 RPM = 127.3240 Nm |
| Rounded formulas: kW ≈ (Nm x RPM) / 9549.2966 and Nm ≈ (kW x 9549.2966) / RPM. | |
| Torque to kW | kW to Torque |
|---|---|
| 10 Nm @ 3000 RPM = 3.1416 kW | 1 kW @ 3000 RPM = 3.1831 Nm |
| 20 Nm @ 3000 RPM = 6.2832 kW | 2.5 kW @ 3000 RPM = 7.9577 Nm |
| 30 Nm @ 3000 RPM = 9.4248 kW | 5 kW @ 3000 RPM = 15.9155 Nm |
| 40 Nm @ 3000 RPM = 12.5664 kW | 7.5 kW @ 3000 RPM = 23.8732 Nm |
| 50 Nm @ 3000 RPM = 15.7080 kW | 10 kW @ 3000 RPM = 31.8310 Nm |
| 60 Nm @ 3000 RPM = 18.8496 kW | 15 kW @ 3000 RPM = 47.7465 Nm |
| 80 Nm @ 3000 RPM = 25.1327 kW | 20 kW @ 3000 RPM = 63.6620 Nm |
| 100 Nm @ 3000 RPM = 31.4159 kW | 30 kW @ 3000 RPM = 95.4930 Nm |
| 150 Nm @ 3000 RPM = 47.1239 kW | 40 kW @ 3000 RPM = 127.3240 Nm |
| 200 Nm @ 3000 RPM = 62.8319 kW | 50 kW @ 3000 RPM = 159.1549 Nm |
| Rounded formulas: kW ≈ (Nm x RPM) / 9549.2966 and Nm ≈ (kW x 9549.2966) / RPM. | |
- All Unit Converters
- Torque to Weight Ratio Calculator
- Torque to Pressure Calculator
- Torque to Power Calculator
Torque to kW Formula
The standard formula for converting torque and rotational speed to power in kilowatts is:
Variables:
- P is the mechanical shaft power in kilowatts (kW)
- T is the torque in newton-meters (Nm)
- N is the rotational speed in revolutions per minute (RPM)
The inverse forms are T(N·m) = P(kW) × 60,000 / (2π × N(rpm)) and N(rpm) = P(kW) × 60,000 / (2π × T(N·m)). A zero denominator with nonzero power is impossible in this model; zero power divided by zero does not identify a unique torque or speed.
Where the 9549 Constant Comes From
The fundamental relationship between power, torque, and rotation is P = T x w, where w (omega) is angular velocity in radians per second. Since most real-world equipment measures speed in RPM rather than rad/s, a unit conversion is needed. One revolution equals 2pi radians, and one minute equals 60 seconds, so w = (2pi x N) / 60. Substituting this into P = T x w gives P(W) = T(Nm) x 2pi x N(RPM) / 60. Dividing both sides by 1000 to convert watts to kilowatts produces the constant: 60,000 / (2pi) ≈ 9549.2966. The symbolic expression is an exact unit conversion factor; the displayed decimal is rounded. The calculator uses the available numerical precision of pi.
Torque and Power in Electric Motors
In an electric motor, shaft torque is the turning moment delivered at the output shaft. The relationship between torque and kilowatts is not a fixed ratio because it depends entirely on operating speed. A 10 kW motor running at 1500 RPM produces 63.66 Nm, but the same 10 kW motor running at 3000 RPM produces only 31.83 Nm. Rated power and speed together allow the rated shaft torque to be calculated.
Standard induction motors operate at synchronous speeds determined by their pole count and supply frequency. On a 50 Hz supply, a 2-pole motor runs near 3000 RPM, a 4-pole motor near 1500 RPM, a 6-pole near 1000 RPM, and an 8-pole near 750 RPM. On a 60 Hz supply (common in North America), these shift to approximately 3600, 1800, 1200, and 900 RPM respectively. Actual shaft speed is slightly lower due to slip, typically 1 to 5% below synchronous speed under load.
Torque Types in Motor Design
Motors produce different torque values during operation. Rated full-load torque is the torque at rated shaft power and speed. Starting or locked-rotor torque is available at standstill. Pull-up torque is the minimum motor torque during acceleration, and breakdown torque is the maximum sustained torque before a motor loses its operating equilibrium. Required starting and accelerating performance depends on the motor design, supply and load; use the manufacturer’s torque-speed data rather than a universal percentage.
Motor Efficiency and Actual Shaft Power
For positive steady-state shaft output during motoring, electrical input exceeds shaft output because of losses, and input kW = shaft kW / efficiency. IEC 60034-30-1 defines efficiency classes for the motor types within its scope; applicable requirements depend on the edition, rated output, poles and supply frequency. This torque-to-power conversion does not supply a motor efficiency estimate.
Use the motor’s applicable manufacturer or tested efficiency at the operating point. A generic efficiency-class label alone does not establish the electrical demand at an arbitrary load or speed. Electrical supply, starting and protection design require the motor’s complete ratings and application data.
IEC vs. NEMA Motor Standards
IEC (International Electrotechnical Commission) and NEMA (National Electrical Manufacturers Association) are the two dominant frameworks for motor specification globally. IEC motors rate shaft output in kilowatts and follow preferred sizes (0.75, 1.1, 1.5, 2.2, 3, 4, 5.5, 7.5, 11, 15, 18.5, 22, 30, 37, 45, 55, 75, 90, 110 kW and above). NEMA motors rate output in horsepower with their own preferred sizes (1, 1.5, 2, 3, 5, 7.5, 10, 15, 20, 25, 30, 40, 50, 60, 75, 100 HP and above). The conversion between them is 1 HP = 0.7457 kW. IEC frame sizes are specified in millimeters (shaft center height), while NEMA uses a proprietary numbering system. IEC Design N motors are broadly equivalent to NEMA Design B, which is the most common general-purpose type in industrial applications.
Motor Sizing by Application
The torque-to-kW conversion is essential when selecting a motor for a specific mechanical load. Different applications have distinct torque profiles that affect sizing decisions.
Centrifugal pump and fan torque often scales approximately with the square of speed under the relevant similarity assumptions. A load delivering 15 kW at 1750 rpm corresponds to about 81.9 N·m. Starting and operating requirements also depend on the system curve, drive and load; this conversion alone does not establish an appropriate motor size.
Conveyors and hoists present constant-torque loads where the required torque stays roughly the same regardless of speed. A conveyor needing 150 Nm at 1500 RPM draws 23.6 kW. These loads often demand higher starting torque because the belt or hoist must overcome static friction and full load from zero speed.
Positive-displacement compressors are often treated as constant-torque loads over an operating range, but the actual profile depends on pressure and capacity-control conditions. Multiplying a 22 kW rating by 1.15 gives 25.3 kW as arithmetic; a service factor alone does not establish actual electrical input or authorize continuous overload. Use manufacturer ratings and application-specific limits.
Common Unit Conversions
Useful conversions are 1 lbf·ft = 1.3558179483314004 N·m and 1 kgf·m = 9.80665 N·m. One mechanical hp is approximately 0.745699872 kW or 745.699872 W; 1 kW is approximately 1.34102209 mechanical hp. Mechanical horsepower differs from metric horsepower. The calculator converts torque and power quantities when their input units change, and its result selectors choose the displayed unit.
