Motor Torque, Power & Speed Calculator
Calculate motor shaft mechanical power, torque, RPM and angular speed from the fundamental relationship between torque and angular velocity. This tool is for motor mechanical operating points, rated shaft data and first-pass motor sizing checks.
MOT-001 intentionally does not calculate electrical input power, motor efficiency, back EMF, stall current, gearing, PWM drive, encoder frequency or thermal loss. Those are separate motor or power-design workflows.
Engineering tool
Motor Torque, Power & Speed Calculator
Calculate motor shaft mechanical power, torque, RPM, angular speed and operating-point differences using the SI relation P=τω.
Calculation mode
Parameter panel
Result console
- Mechanical Power
- 104.72W
- Mechanical Power
- 0.10472kW
- Mechanical Power
- 0.140432hp
- Angular Speed
- 104.72rad/s
- Torque
- 1N·m
- Speed
- 1000RPM
Motor Torque, Power & Speed Formula Audit
| Mechanical Power Definition | Mechanical shaft power is the product of shaft torque and angular velocity. |
|---|---|
| Torque Definition | Torque is internally represented in N·m. |
| Angular Velocity Definition | Angular velocity is internally represented in rad/s. |
| RPM Definition | RPM is revolutions per minute and must be converted before using the SI equation. |
| P=τω Formula | P = τω. |
| RPM → rad/s Formula | ω = 2πRPM/60. |
| rad/s → RPM Formula | RPM = ω×60/(2π). |
| Power → Torque Formula | τ = P/ω, requiring non-zero speed. |
| Power → RPM Formula | RPM = 60P/(2πτ), requiring non-zero torque. |
| Torque Unit Convention | All torque inputs are converted to N·m before calculation. |
| Power Unit Convention | All power inputs are converted to W before calculation. |
| Horsepower Convention | Mechanical horsepower is fixed at 1 hp = 745.6998715822702 W. |
| Magnitude Mode | MOT-001 V1 accepts non-negative physical magnitudes only. |
| Zero-Speed Boundary | Forward calculation at zero RPM gives zero mechanical shaft power. |
| Zero-Torque Boundary | Forward calculation at zero torque gives zero mechanical shaft power. |
| Stall Boundary | Stalled shaft power is zero, but electrical current and copper loss may be high. |
| Electrical Power Boundary | This calculator does not use VI as mechanical shaft power. |
| Gearmotor Boundary | Use gearbox output shaft torque and speed for gearmotor datasheets. |
| Efficiency Boundary | Electrical-to-mechanical efficiency belongs in MOT-005. |
Formula
Formula reference
Motor shaft power formulas
P = τωω = 2πn / 60τ = P / ωn = 60P / (2πτ)Variable definitions
- P
- mechanical shaft power in watts
- τ
- shaft torque in newton meters
- ω
- angular velocity in radians per second
- n
- rotational speed in RPM
Motor Torque, Power & Speed Formula Audit
| Mechanical Power Definition | Mechanical shaft power is the product of torque and angular velocity. |
|---|---|
| Torque Definition | Torque is the twisting moment at the shaft and is internally handled in N·m. |
| Angular Velocity Definition | Angular velocity is rotational speed in rad/s. |
| RPM Definition | RPM is revolutions per minute and must be converted before using the SI equation. |
| P=τω Formula | P = τω. |
| RPM to rad/s | ω = 2πRPM/60. |
| rad/s to RPM | RPM = ω×60/(2π). |
| Power to Torque | τ = P/ω, requiring non-zero speed. |
| Power to RPM | RPM = 60P/(2πτ), requiring non-zero torque. |
| Horsepower Convention | 1 mechanical hp = 745.6998715822702 W. |
| Magnitude Mode | V1 accepts non-negative torque, speed and power magnitudes. |
| Zero-Speed Boundary | Forward calculation at zero RPM gives zero shaft mechanical power. |
| Stall Boundary | Zero shaft power at stall does not imply zero electrical input power or zero heating. |
| Electrical Boundary | This calculator does not calculate VI, current, back EMF, efficiency or loss. |
| Gearmotor Boundary | Use torque and speed from the same shaft, especially when gearbox output ratings are listed. |
Worked Examples
| Example | Calculation | Result |
|---|---|---|
| 1 N·m at 1000 RPM | ω≈104.719755 rad/s | P≈104.719755 W. |
| 2 N·m at 3000 RPM | ω≈314.159265 rad/s | P≈628.318531 W. |
| 500 W at 3000 RPM | τ=60P/(2πRPM) | τ≈1.59155 N·m. |
| 1 kW at 1500 RPM | τ=60×1000/(2π×1500) | τ≈6.36620 N·m. |
| 100 W and 1 N·m | RPM=60P/(2πτ) | RPM≈954.929659. |
| 60 RPM | ω=2π×60/60 | ω=2π rad/s. |
| 1 RPM | ω=2π/60 | ω≈0.104719755 rad/s. |
| 100 rad/s | RPM=100×60/(2π) | RPM≈954.929659. |
| 1 kW | Power unit conversion | 1 kW = 1000 W. |
| 1 hp | Mechanical horsepower convention | 1 hp≈745.699872 W. |
| 1 kgf·cm | 1 kgf=9.80665 N | 1 kgf·cm=0.0980665 N·m. |
| 10 kgf·cm | Multiply by 0.0980665 | 10 kgf·cm≈0.980665 N·m. |
| 10 N·m at 0 RPM | ω=0 | P=0 W shaft output. |
| 0 N·m at 3000 RPM | τ=0 | P=0 W shaft output. |
| Round-trip torque | Power + RPM -> torque -> power | Original power is recovered. |
| Round-trip RPM | Power + torque -> RPM -> power | Original power is recovered. |
| Constant torque | Torque doubles at same RPM | Power doubles. |
| Constant speed | RPM doubles at same torque | Power doubles. |
| Constant power | RPM doubles at same power | Torque halves. |
| Operating point comparison | A=1 N·m @1000 RPM, B=1 N·m @2000 RPM | Power B is approximately 2× Power A. |
Engineering Notes
Motor Torque
Torque describes the shaft twisting effort. Datasheets may list continuous torque, peak torque, stall torque or rated torque.
Mechanical Power
Mechanical power is shaft output power, not electrical input power.
Shaft Power
Use torque and speed measured or specified at the same shaft.
RPM
RPM is convenient for datasheets but must be converted to rad/s for SI power calculations.
Angular Velocity
Angular velocity in rad/s is the SI speed term used in P=τω.
N·m
N·m is the internal torque unit used before applying the formula.
Horsepower
Mechanical horsepower is fixed in this calculator to avoid metric horsepower ambiguity.
Rated Torque
Rated torque is usually a continuous or nominal operating point, not necessarily peak torque.
Rated Speed
Rated speed should be paired with the same operating point as rated torque.
Rated Power
Rated power should approximately match P=τω when using rated torque and speed from the same shaft.
Stall
At stall, mechanical shaft speed is zero, so shaft output power is zero.
Constant Torque
At fixed torque, shaft power rises linearly with speed.
Constant Power
At fixed power, required torque decreases as speed rises.
Gearmotor
For a gearmotor, use gearbox output torque and output speed when evaluating output shaft power.
Efficiency Boundary
Electrical input power and motor efficiency are outside MOT-001 and belong in MOT-005.
Common Mistakes
- Putting RPM directly into P=τω without converting to rad/s.
- Forgetting the 2π/60 conversion factor.
- Treating electrical VI as mechanical shaft power.
- Assuming stall shaft power is large because stall torque may be high.
- Thinking zero shaft power at stall means there is no heating.
- Using kgf·cm as if it were N·m.
- Mixing lb·in and lb·ft.
- Using horsepower without stating the conversion convention.
- Solving torque from power and zero RPM.
- Solving RPM from power and zero torque.
- Mixing internal motor shaft speed with gearbox output speed.
- Treating peak torque as continuous torque.
- Ignoring that datasheet rated values can be rounded.
- Assuming the equation proves a motor can thermally sustain the point.
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FAQ
Support reference
FAQ
How do I calculate motor power from torque and RPM?
Convert RPM to angular speed with omega = 2 pi RPM / 60, then calculate shaft mechanical power with P = torque times omega.
How do I calculate motor torque from power and RPM?
Use torque = P / omega, where omega is 2 pi RPM / 60. RPM must be greater than zero for a finite torque result.
How do I calculate RPM from torque and power?
Use RPM = 60P / (2 pi torque). Torque must be greater than zero for a finite speed result.
How do I convert RPM to radians per second?
Use omega = 2 pi RPM / 60. For example, 60 RPM equals 2 pi rad/s.
What is the formula for motor mechanical power?
The mechanical shaft power formula is P = torque times angular velocity, or P = torque times 2 pi RPM / 60.
How many watts are produced by 1 N·m at 1000 RPM?
1 N·m at 1000 RPM produces about 104.72 W of shaft mechanical power.
What is shaft power?
Shaft power is the mechanical output power available at the rotating shaft, calculated from shaft torque and shaft speed.
What is the difference between mechanical power and electrical power?
Mechanical power is shaft output power. Electrical power is input power such as voltage times current. Motor efficiency is needed to relate the two.
Why is mechanical power zero at stall?
At stall, shaft speed is zero. Since P = torque times angular velocity, mechanical shaft output power is zero even if torque is present.
Can a stalled motor still draw electrical power?
Yes. A stalled motor can draw high current and generate large copper loss even though shaft mechanical output power is zero.
How do I convert kgf·cm to N·m?
Use 1 kgf·cm = 0.0980665 N·m because 1 kgf is defined from standard gravity as 9.80665 N.
How do I convert horsepower to watts?
This calculator uses mechanical horsepower: 1 hp = 745.6998715822702 W.
How are rated torque, rated speed and rated power related?
For the same shaft operating point, rated power should approximately equal rated torque times rated angular speed. Datasheet rounding and test conditions can create small differences.
What happens to torque when speed increases at constant power?
At constant mechanical power, torque decreases inversely with speed.
Does this calculator include motor efficiency?
No. MOT-001 calculates shaft mechanical relationships only. Electrical input power and efficiency are reserved for the Motor Efficiency Calculator.
How should I use the calculator for a gearmotor?
Use the torque and speed from the same shaft. For a gearmotor datasheet, use gearbox output torque with gearbox output speed.
Engineering Disclaimer
This calculator gives ideal shaft-mechanics estimates. Final motor selection should consider torque-speed curves, continuous and peak ratings, drive capability, supply limits, thermal behavior, gearbox losses and measured application loads.