Motor Power & Torque Calculator

Calculate motor torque, power, efficiency, and current draw from nameplate data.

η=0.85 typical, PF=0.87 typical
Please check your inputs and try again.

Motor Torque, Speed, and Power Are Directly Linked

Mechanical shaft power equals torque multiplied by angular speed, so a motor cannot change torque independently of speed and power. Pmech=τω, with ω=2πn/60 when n is rpm. The practical relation τ(N·m)=9550P(kW)/n(rpm) is the same equation with unit conversions built in. At fixed mechanical power, lower shaft speed means higher torque.

Electrical input power is larger than shaft output because real motors have copper, iron, mechanical, and stray losses. Efficiency η=Pout/Pin. Current draw also depends on supply type, voltage, power factor, and motor loading, so a power estimate alone does not replace nameplate or drive data.

Pmech=τω,   ω=2πn/60,   η=Pout/Pin
SymbolMeaningWhy it appears / units
τShaft torqueN·m; turning moment delivered at the shaft.
nRotational speedrpm; convert to rad/s for SI power.
PPowerW or kW; rate of mechanical energy transfer.
ηEfficiencyDimensionless or percent; output divided by input.

A gearbox can raise output torque while lowering speed, but it does not create power. For motor selection, distinguish continuous rated torque from short-duration starting or peak torque and check thermal limits as well as mechanical power.

At fixed mechanical power, torque and angular speed are inversely related. Doubling rpm should halve torque if losses and power remain unchanged. This is why gear reduction can provide higher shaft torque at lower rotational speed without creating extra power.

Worked Examples

Example 1: 5kW motor at 1450 RPM
T=5000×60/(2π×1450)
Result: 32.9 N·m rated torque
Shaft torque from nameplate
Example 2: Motor current: 5kW, 400V 3-phase, PF=0.87, η=0.90
I=5000/(1.732×400×0.87×0.90)
Result: 9.24 A
Size cables and circuit breaker
Example 3: 5 kW motor at 1500 rpm
τ=9550×5/1500
Result: 31.8N·m
The compact 9550 relation is useful when power is in kW and speed is in rpm.
Example 4: Electrical input from efficiency
Pout=5kW, η=0.90
Result: Pin=5.56kW
Losses require more electrical input than useful shaft output.

Common Mistakes

⚠️
Using rpm directly as angular speed

The equation P=τω requires ω in rad/s, not rpm. Convert with 2πn/60.

⚠️
Treating efficiency as power factor

Efficiency measures real energy conversion. Power factor describes AC current and voltage phase or distortion and is a different quantity.

⚠️
Assuming rated power is available at every speed

Motor torque-speed capability depends on motor type, supply, cooling, and drive control. Constant-power and constant-torque regions differ.

Frequently Asked Questions

Synchronous vs actual speed?
4-pole 50Hz motor: synchronous speed=1500 RPM. Actual (slip): 1450-1480 RPM. Slip increases with load. VFDs can vary speed by changing frequency.
Torque-speed curve?
Induction motors: max torque (breakdown torque) at ~80% synchronous speed. Starting torque at zero speed. Rated operating point well below breakdown. Starting current 5-8× rated — important for switchgear sizing.
Why does torque rise when speed falls at constant power?
Because P=τω. If the same power is transmitted at a lower angular speed, torque must be larger. Real machines also have efficiency and torque-limit constraints.
What is the difference between starting torque and rated torque?
Starting torque is available near zero speed during acceleration, while rated torque is the continuous torque associated with rated power and speed under specified thermal conditions.
Can motor current be found from mechanical power alone?
Not uniquely. Electrical current also depends on voltage, phase count, efficiency, power factor, and operating condition. Nameplate and drive information are needed for reliable current estimates.
Why is 9550 used in motor torque formulas?
It comes from converting kW to watts and rpm to rad/s in P=τω. The constant is approximately 60,000/(2π).
Why must rpm be converted before using P=τω?
The angular speed in P=τω is in radians per second. Convert rotational speed n in rpm with ω=2πn/60. Using rpm directly as if it were rad/s overstates power by a factor of 60/(2π), or produces the reciprocal error when solving for torque.

Formula Explorer connections

Interpretation: This formula is the rotational counterpart of linear mechanics, relating angle, angular motion, torque, inertia or rotational energy. Assumption: Define the rotation axis and sign convention. Rigid-body behavior, no slipping, steady rotation or negligible bearing losses may be assumed.

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