How do you calculate torque from power and speed?

Torque (in N·m) can be calculated using the formula T = (P × 60) / (2 × π × N), where P is power in Watts and N is rotational speed in RPM. If power is in kW, the formula becomes T = (P × 1000 × 60) / (2 × π × N).

What is the relationship between speed and torque?

For a given constant power output, speed and torque are inversely proportional. If a gearbox reduces the speed of a shaft, the torque increases proportionally, and vice versa.

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

Input Parameters

Motor Power (P)

Mechanical power output.

Rotational Speed (N)

RPM

Operating speed of the shaft.

Allowable Torque Limit (T_max)

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

Technical Introduction

Torque in a rotating shaft represents the twisting moment that transmits mechanical power. It is a critical design parameter in drive systems, as it directly influences shaft diameter, material selection, and coupling design. The relationship between power (P), rotational speed (N), and torque (T) is fundamental in mechanical engineering and is expressed by the equation:

T = (P × 1000 × 60) / (2π × N)

Here, P is power in kilowatts, N is rotational speed in revolutions per minute, and T is torque in newton-metres. This formula is derived from the definition of mechanical power as the product of torque and angular velocity.

Derivation of the Formula

Mechanical power is defined as P = τ × ω, where ω is angular velocity in rad/s. Since ω = 2πN/60, substituting gives P = τ × (2πN/60). Rearranging for torque yields τ = (P × 60) / (2πN). Converting kilowatts to watts introduces the factor of 1000, resulting in the practical engineering formula used in this calculator.

Input Parameters Explained

Motor Power (P): The mechanical output of the motor in kilowatts. It defines the energy transfer rate. Incorrect conversion from horsepower is a common source of error.
Rotational Speed (N): The shaft speed in RPM. Higher speeds reduce torque for the same power, while lower speeds increase torque.
Torque (T): The twisting force calculated in N·m. This is the value engineers use to size shafts, couplings, and gearboxes.

Engineering Interpretation

The calculated torque represents the continuous torque transmitted by the shaft under steady-state operation. Engineers interpret this value to determine shaft diameter using torsional stress equations, verify coupling ratings, and ensure gear teeth can withstand transmitted loads. However, real systems often experience transient torques during startup, braking, or shock loading, which may exceed nominal values by factors of 2–3.

Units and Conversion

Torque is expressed in newton-metres (N·m). Power is entered in kilowatts (kW), where 1 kW = 1000 W. Rotational speed is in RPM. A simplified constant form often used in industry is:

T ≈ (9550 × P) / N

This approximation is convenient because it eliminates the need to explicitly handle π and unit conversions, but it is valid only when P is in kW and N in RPM.

Design Considerations

Shaft torque calculations are only the first step in mechanical design. Engineers must also consider:

Material strength: The shaft must resist shear stress induced by torque.
Fatigue loading: Cyclic torque can cause fatigue failure over time.
Safety factors: Service factors are applied to account for peak loads and uncertainties.
Coupling and gearbox ratings: Components must be rated for transmitted torque, not just power.

Alternative and General Cases

While this calculator assumes steady-state torque transmission, other cases exist:

Variable-speed drives: Torque varies with speed and load profile.
Transient loads: Startup and braking introduce dynamic torque peaks.
Multi-shaft systems: Torque distribution depends on gear ratios and load sharing.

These cases require more advanced dynamic analysis beyond the scope of this calculator.

Assumptions and Limitations

The formula assumes:

100% efficiency (no mechanical losses).
Steady-state operation without acceleration.
Uniform torque transmission without shock loads.

In practice, efficiency losses in gearboxes and couplings reduce transmitted torque, and shock loads can exceed nominal values significantly.

Practical Engineering Use

Shaft torque calculations are applied in:

Industrial drives: Motors driving conveyors, pumps, and compressors.
Automotive systems: Engine torque transmitted through crankshafts and drive shafts.
Wind turbines: Low-speed shafts transmitting enormous torque to gearboxes.
CNC spindles: High-speed shafts transmitting low torque for precision machining.

In all these cases, torque determines the mechanical strength requirements of shafts and couplings, not power alone.

Conclusion

The shaft torque calculator provides engineers with a reliable method to estimate torque from power and speed. While simple, the calculation highlights the inverse relationship between torque and speed and emphasizes that torque governs mechanical design. Engineers must complement these results with safety factors, material checks, and efficiency considerations to ensure safe and durable transmission systems.

Continue Calculating

calculators

Calculators

Quickly calculate and analyze parameters for your calculators requirements.

Open

calculators

Civil

Quickly calculate and analyze parameters for your civil requirements.

Open

calculators

Beam Bending Moment

Quickly calculate and analyze parameters for your beam bending moment requirements.

Open

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).