Motor Torque Calculator

What Is Motor Shaft Torque

Motor shaft torque is the turning force delivered at the motor output shaft to drive connected mechanical equipment. It is the physical quantity that loads couplings, gearboxes, belt drives, and driven machinery. While motor power describes the rate of energy delivery, torque is the direct mechanical variable that determines shaft sizing, coupling selection, and gearbox loading. For any given motor power, torque depends entirely on operating speed — higher speed produces lower torque, and lower speed produces higher torque for the same power output.

Shaft torque is derived from the fundamental relationship between rotational power, torque, and angular velocity: power equals torque multiplied by angular velocity. This relationship is fixed by physics and applies to all rotating machines regardless of technology. For a motor delivering constant output power at a given speed, the shaft torque is uniquely determined. The standard engineering formulas — T = (9550 × kW) / rpm in Metric and T = (5252 × hp) / rpm in Imperial — are direct applications of this relationship with appropriate unit conversions built into the constants.

Why Shaft Torque Matters in Engineering

Torque is the load variable for mechanical drivetrain components. Coupling manufacturers specify rated torques and peak torques, not rated power. Gearbox catalogs list input and output torque ratings as the primary selection criterion. Shaft strength calculations require the applied torque to determine stress. Bearing load analysis depends on shaft torque and geometry. In each of these cases, the motor nameplate power alone is not sufficient — the actual shaft torque at the operating speed must be calculated before any mechanical component can be properly selected or checked.

For geared drives, the torque multiplication effect of the gearbox is critical. A motor producing 90 lb-ft at 1750 rpm connected to a 10:1 gearbox delivers approximately 900 lb-ft at 175 rpm to the output shaft (before gearbox efficiency losses). This large torque amplification is why gearbox input torque ratings must be verified against motor shaft torque, and gearbox output shaft components must be sized for the amplified torque. This calculator provides the motor shaft torque — the input to gearbox and drivetrain calculations.

Using Motor Torque for Coupling and Shaft Screening

Coupling selection begins with the calculated motor shaft torque. Most coupling catalogs list a rated torque (continuous), a peak torque (intermittent), and a service factor recommendation based on drive type and load characteristics. The steady-state shaft torque from this calculator is compared against the coupling rated torque after applying the appropriate service factor. For smooth, uniform loads with no shock, a service factor of 1.0 to 1.25 is typical. For moderate shock loads — conveyor applications, reciprocating equipment, or drives with infrequent starts — service factors of 1.5 to 2.0 or higher are applied.

Shaft sizing uses the calculated torque to determine the minimum shaft diameter from torsional stress criteria. The standard torsional shear stress formula relates shaft diameter to applied torque and the material’s allowable shear stress. A larger shaft is needed to carry higher torque for the same material, or higher-strength material can be used to reduce diameter. In practice, shaft sizing also considers bending loads from overhung weights and radial forces, so the torque calculated here is an input to the shaft analysis rather than the only load to consider. For final shaft design, combined torsion and bending must both be evaluated.

Torque and Speed in Variable-Speed Applications

For variable-speed drives controlled by variable frequency drives (VFDs), the motor torque at different operating points is a common analysis requirement. At constant power (above base speed in VFD operation), torque decreases as speed increases in direct proportion to this calculator’s formula. At constant torque (below base speed in VFD operation), torque remains approximately constant while power decreases linearly with speed. Understanding which operating region applies is important for drivetrain screening at speeds other than rated speed.

For induction motors on VFDs, motor torque capability must be verified against the motor manufacturer’s torque derating curves at speeds outside the rated range. Some motors lose significant torque capability at very low speeds due to reduced cooling, and at speeds above rated due to voltage limiting. This calculator provides the torque required by the load at a given speed and power — comparing this against the motor’s available torque at that speed requires motor-specific torque-speed curves.

Practical Notes

Always use the actual operating speed rather than synchronous speed for induction motors under load. A 4-pole, 60 Hz synchronous speed is 1800 rpm, but a typical full-load speed is 1740–1760 rpm. At 30 hp and 1750 rpm the shaft torque is approximately 90 lb-ft — at 1800 rpm it would be approximately 87.5 lb-ft. The 2.9% difference is significant when comparing against coupling or shaft ratings with narrow margins.

For motor replacement comparisons, use this calculator to check whether the replacement motor produces the same shaft torque at the same speed. A motor with higher rated power at the same speed produces higher torque, which may overload mechanical drivetrain components. A motor with lower rated power produces lower torque, which may be insufficient for the driven load. Torque matching — not just power matching — is the correct criterion for motor replacement in mechanical drivetrain applications.