Free Engineering Tool
Torque — Power — Speed Calculator
Convert between torque, power, and rotational speed. Given any two, calculate the third. Supports kW, Nm, RPM with imperial conversions.
Results
Fundamental Relationship
The relationship between power, torque, and rotational speed is:
Where ω = 2πn/60 is the angular velocity in rad/s, and n is speed in RPM.
Practical Formulas (with constant 9549)
Substituting and rearranging for each unknown, using the constant 9549 ≈ 60000/(2π):
Unit Conversions
| From | To | Factor |
|---|---|---|
| kW | hp (mechanical) | × 1.341 |
| hp | kW | × 0.7457 |
| Nm | ft·lbf | × 0.7376 |
| ft·lbf | Nm | × 1.3558 |
| RPM | rad/s | × 2π/60 |
Practical Example
Given: P = 15 kW, n = 1500 RPM
T = 9549 × 15 / 1500 = 95.49 Nm
ω = 2π × 1500 / 60 = 157.08 rad/s
Power in hp: 15 × 1.341 = 20.12 hp
Torque in ft·lbf: 95.49 × 0.7376 = 70.44 ft·lbf
💡 The 9549 constant: This convenient number equals 60000/(2π) ≈ 9549.2966. It eliminates the need to convert RPM to rad/s explicitly. It works when power is in kW, torque in Nm, and speed in RPM.
Use the formula: T = 9549 × P / n
- T = torque in Nm
- P = power in kW
- n = speed in RPM
This is derived from the fundamental relationship P = T × ω, where ω = 2πn/60 is the angular velocity in rad/s.
Power (kW) and torque (Nm) are related through rotational speed:
P = T × n / 9549
Key insights:
- At constant speed, power is directly proportional to torque
- At constant power, torque is inversely proportional to speed
- Doubling the speed at constant power halves the torque
The constant 9549 (more precisely 9549.2966...) is a convenient conversion factor:
9549 = 60000 / (2π)
It arises from converting RPM to rad/s and watts to kilowatts simultaneously. Using it avoids the need to manually calculate ω = 2πn/60 and convert kW to W.
Multiply kW by 1.341 to get mechanical (imperial) horsepower:
- 1 kW = 1.341 hp
- 1 hp = 0.7457 kW
Note: Metric horsepower (PS/CV) is slightly different: 1 PS = 0.7355 kW. The calculator uses mechanical (imperial) horsepower.
For a given power output, yes — torque and speed are inversely proportional: T = 9549 × P / n.
However, actual machine behavior varies:
- AC induction motors have nearly constant torque up to rated speed, then torque drops at higher speeds (constant power region)
- DC motors can deliver constant torque over a wide speed range with proper control
- Combustion engines have peak torque at a specific RPM, with the torque curve varying by design
The procedures described on this page were developed and field-tested by the Vibromera team using the Balanset-1A, a portable dual-channel balancer and vibration analyzer for on-site rotor balancing.
Professional field balancing instruments and software. Achieve ISO compliance on-site. Used in 50+ countries.
Nikolai Shelkovenko
Nikolai Shelkovenko is a vibration analysis engineer and the founder and CEO of Vibromera. For more than 15 years he has balanced rotating equipment in the field rather than on a test bench: mulchers, industrial fans, crushers, centrifuges, shafts and spindles. That work is what the Balanset instruments grew out of — they were designed as a tool a specialist can carry to the machine and use alone, on site, not as laboratory equipment. Vibromera was founded in 2017 and has been based in Porto, Portugal, since 2023. Development, assembly and support of the Balanset line all happen here. The flagship instrument is the Balanset-1A, a portable analyser for single- and two-plane balancing and for vibration diagnostics. Nikolai is personally involved in customer support, in working through difficult balancing cases and in the development of the software. He works with customers worldwide, in any language.
