Mechanical Engineering Calculator

Shaft Torque Calculator

Determine the twisting force (torque) acting on a rotating transmission shaft based on the motor power (kW) and rotational speed (RPM).

Power & Torque Schematic

Relationship between motor power, rotational speed, and torque

Motor (P)55 kWN = 1450 RPMT (Torque)

Input Parameters

kW

Mechanical power output.

RPM

Operating speed of the shaft.

N·m

Maximum rated torque of coupling/shaft.

Engineering Tip

When sizing components based on nominal torque, apply a service factor (SF). For example, crushers or heavy conveyors require an SF of 2.0 or higher.

Generated Shaft Torque

362.21N·m

Power Input

55 kW

Allowable Limit

400 N·m

PASS — Torque is within design limits

Calculated torque is 362.21 N·m, and your defined limit is 400 N·m.

Governing Formula

T = (P × 1000 × 60) / (2 × π × N)
TN·m

Torque / Twisting Moment

PkW

Mechanical Power

NRPM

Rotational Speed

π3.14159...

Mathematical Constant

Engineering Code

Integrate this torque formula into your own design scripts.

Python
import math

def calculate_torque(power_kw, speed_rpm):
    """
    Calculate shaft torque from power and speed.
    
    power_kw: Motor power in Kilowatts (kW)
    speed_rpm: Rotational speed in RPM
    
    Returns:
        Torque in N.m
    """
    if power_kw <= 0 or speed_rpm <= 0:
        raise ValueError("Power and speed must be greater than zero.")

    # Convert kW to Watts
    power_w = power_kw * 1000
    
    # Calculate angular velocity (rad/s)
    omega = (2 * math.pi * speed_rpm) / 60
    
    # Torque = Power / Angular Velocity
    torque_nm = power_w / omega
    
    return torque_nm

# Example
P = 55
N = 1450

T = calculate_torque(P, N)
print(f"Generated Torque: {T:.2f} N.m")
MATLAB
function T = shaft_torque(power_kw, speed_rpm)
    % Calculate shaft torque from power and speed
    % power_kw = Motor power (kW)
    % speed_rpm = Rotational speed (RPM)

    if power_kw <= 0 || speed_rpm <= 0
        error('Power and speed must be greater than zero.');
    end

    power_w = power_kw * 1000;
    omega = (2 * pi * speed_rpm) / 60;
    
    T = power_w / omega;
end

% Example
P = 55;
N = 1450;

T = shaft_torque(P, N);
fprintf('Generated Torque: %.2f N.m\n', T);
Excel Formula (Replace P and N with cell refs)
=(P*1000*60)/(2*PI()*N)

Example Calculation

Consider a standard industrial electric motor transmitting 55 kW of power at a rotational speed of 1,450 RPM. Let's calculate the generated torque.

T = (55 × 1000 × 60) / (2 × π × 1450)
T = 362.24 N·m

Understanding Power, Speed, and Torque

In mechanical drive systems, Power (P) is the rate at which work is done, while Torque (T) is the twisting force that causes rotation. These two parameters are tied together by rotational Speed (N).

The Inverse Relationship

For a constant power output, speed and torque share an inverse relationship. If you use a gear reducer to halve the rotational speed of a shaft, the torque transmitted by that shaft will double (excluding efficiency losses). This is a foundational concept when sizing gearboxes and drive components.

How to Use This Calculator

  1. Motor Power (P): Enter the mechanical power output in Kilowatts (kW). If you have horsepower (HP), remember that 1 HP ≈ 0.746 kW.
  2. Rotational Speed (N): Input the speed of the shaft in Revolutions Per Minute (RPM).
  3. Allowable Limit (Optional): Enter the maximum torque your shaft or coupling is rated for, instantly verifying if your design is safe.

Design Considerations

The torque calculated here is the nominal (continuous) torque. When designing mechanical systems, engineers must also account for starting torque or peak loads, which can be 2 to 3 times higher than the nominal torque depending on the motor type and driven load inertia.

Real-World Engineering Cases

Wind Turbine Main Shafts

Wind turbines generate massive amounts of power (e.g., 3 MW) at extremely low speeds (e.g., 10-15 RPM). Because speed is so low, the generated torque is astronomical. This requires the main shaft to be exceptionally large in diameter before entering the gearbox.

Engineering Lesson

Low-speed, high-power applications dictate massive structural requirements due to extreme torque values.

High-Speed CNC Spindles

A CNC spindle might have the same 30 kW power rating as a heavy industrial conveyor motor. However, because the spindle runs at 24,000 RPM, the actual twisting force (torque) on the shaft is very low, allowing for a much thinner, precision shaft.

Engineering Lesson

Power alone does not dictate the physical size of mechanical drive components; torque does.

Frequently Asked Questions

What is the formula for calculating torque from kW?

The standard SI formula is T = (P × 1000 × 60) / (2 × π × N), where T is torque in N·m, P is power in kW, and N is speed in RPM. A commonly used simplified constant version is T ≈ (9550 × P) / N.

How do I convert Horsepower (HP) to kW?

To convert mechanical horsepower to kilowatts, multiply the HP value by 0.7457. (e.g., 10 HP ≈ 7.46 kW).

Does this calculation include gearbox efficiency?

No, this calculates the theoretical torque for a 100% efficient system. If calculating output torque after a gearbox, you must multiply the result by the gearbox's mechanical efficiency (e.g., 0.95).

Calculations provided by this tool are theoretical nominal values. Actual systems may experience starting torques, shock loads, or peak forces significantly higher than nominal torque. Always apply appropriate service factors when designing physical systems.