🚀 Torque & Power Calculator & Simulator
- Set Input Units: Select and activate any two reference variables among Power (kW, HP), Torque (N·m, kgf·m, kgf·cm), and Rotational Speed (RPM) to enter your values.
- Adjust Sliders or Enter Directly: Use the sliders or directly input values for the two active variables. (The remaining third variable will be calculated in real time.)
- Observe Real-Time Physics: The 2D motor shaft and drum rotate according to the entered torque and speed. Higher torque visually intensifies the tension of the rope winding around the drum and the glowing power flux of the motor housing.
- Utilize Preset Configurations: Choose from predefined presets—such as High Torque-Low Speed (Crane), Low Torque-High Speed (Spindle), or Standard Industrial Motor—to compare differences in operation.
📚 View Detailed Mechanical Engineering Explanations & Design Standards (KS/ISO) ▼
1. Relationship Between Torque and Power in Rotary Machinery Design
In mechanical design and industrial applications, Power (P) and Torque (T) are the core physical quantities that define rotary motion systems. Torque refers to the moment of force that causes an object to rotate, while power represents the rate at which work is performed by the motor per unit of time. Therefore, power is a comprehensive physical quantity defined not just by the magnitude of the force (torque) but also by how fast that force is acting (angular velocity, ω).
Understanding the organic relationship between these two is essential during shaft design and gearbox selection. When a gearbox is used to reduce the rotational speed, the power remains constant (excluding friction losses), but the torque increases proportionally to the reduction ratio. This enables the design of systems that can lift heavy loads or drive heavy machinery using relatively small motors.
2. Derivation of Key Conversion Formulas and Unit Conversions
Physically, power P is defined as the product of torque T and angular velocity ω:
P = T × ω [W]
Here, converting the angular velocity ω to the widely used practical unit of revolutions per minute, N [RPM], yields ω = (2π × N) / 60. Substituting this gives:
P = T × (2π × N) / 60 [W]
Converting the unit of Watts (W) to Kilowatts (kW) (1 kW = 1000 W) and simplifying the precision constants derives the famous 9549 engineering constant formula, which is most frequently used in the field:
P [kW] = (T [N·m] × N [RPM]) / 9,549.3 or T [N·m] = 9,549.3 × P [kW] / N [RPM]
In addition, the engineering constants primarily used when converting horsepower (HP) units are 716.2 and 726. The conversion relationship between imperial horsepower (HP) and metric torque (kgf·m) is as follows:
T [kgf·m] = 716.2 × P [HP] / N [RPM]
3. Motor Capacity Selection Guide and Safety Factors (KS B 6310 Standard)
When selecting industrial rotary electric motors, the rated motor output must be finalized by adding appropriate safety factors and environmental coefficients to the required mechanical power. Since a starting torque of 1.5 to 2.5 times the rated torque is required when the motor starts, a load review must be performed to ensure it can overcome heavy starting loads or static friction.
- Inertial Load Review (GD²): For machinery with a large moment of rotational inertia on the load side—such as large fans, blowers, and flywheels—excessive heat accumulates during the startup period before the motor reaches its rated speed. Therefore, a startup safety factor of at least 2 times the rated torque should be applied.
- Overload Capacity: For equipment subjected to frequent and sudden shock loads, such as crushers or shredders, a load safety factor of
S_f = 1.5 to 2.0relative to the torque required during normal operation must be applied to safely evaluate the shear stress on shafts and keyways (refer to KS B ISO 1940).