The base units are Watts (W) for power, Newton-meters (N·m) for torque, and RPM for rotational speed. You can also see alternate units like horsepower (hp) and pound-feet (lb·ft).

Does this account for efficiency?

No. The calculator assumes 100% efficiency. In real systems, you should multiply the calculated power by the efficiency factor to get the actual mechanical power output.

Mechanical Engineering Calculator

Motor Power, Torque & RPM Calculator

Calculate the missing parameter — power, torque, or RPM — for electric motors, engines, and rotating machinery using the fundamental relation P = τ × ω.

Power–Torque–RPM Relationship

The fundamental equation of rotating machinery

CONCEPTUAL

Motor Power, Torque & RPM

The relationship between mechanical power, torque, and rotational speed

Input Parameters

Select which value you want to calculate, then enter the other two.

Calculate

Power (P)

Mechanical power output.

Torque (τ)

N·m

Rotational force.

RPM (n)

rev/min

Rotational speed.

Engineering Tip

Power is proportional to both torque and RPM. Increasing either one (while keeping the other constant) increases power output.

Calculated Power

15,707.96W

Power

15,707.96 W

Torque

100.00 N·m

RPM

1,500

All values are consistent

The relationship P = τ × ω holds for the given inputs.

Governing Formula

P = τ × ω = τ × (2π·RPM / 60)

Power

τN·m

Torque

ωrad/s

Angular velocity

Assumptions

Constant torque and speed
No losses (100% efficiency)
SI units (N·m, W, RPM)
Steady-state operation

Engineering Code

Reuse the calculation in your own engineering workflow.

Python

import math

def power_from_torque_rpm(torque_Nm, rpm):
    """Calculate power (W) from torque (N·m) and RPM."""
    if torque_Nm <= 0 or rpm <= 0:
        raise ValueError("Values must be positive.")
    return torque_Nm * rpm * (2 * math.pi / 60)

def torque_from_power_rpm(power_W, rpm):
    """Calculate torque (N·m) from power (W) and RPM."""
    if power_W <= 0 or rpm <= 0:
        raise ValueError("Values must be positive.")
    return power_W / (rpm * (2 * math.pi / 60))

def rpm_from_power_torque(power_W, torque_Nm):
    """Calculate RPM from power (W) and torque (N·m)."""
    if power_W <= 0 or torque_Nm <= 0:
        raise ValueError("Values must be positive.")
    return power_W / (torque_Nm * (2 * math.pi / 60))

# Example
torque = 100
rpm = 1500
power = power_from_torque_rpm(torque, rpm)
print(f"Power: {power:.2f} W")

MATLAB

function P = power_from_torque_rpm(T, n)
    % Calculate power (W) from torque (N·m) and RPM.
    if T <= 0 || n <= 0
        error('Values must be positive.');
    end
    P = T * n * (2*pi/60);
end

function T = torque_from_power_rpm(P, n)
    % Calculate torque (N·m) from power (W) and RPM.
    if P <= 0 || n <= 0
        error('Values must be positive.');
    end
    T = P / (n * (2*pi/60));
end

function n = rpm_from_power_torque(P, T)
    % Calculate RPM from power (W) and torque (N·m).
    if P <= 0 || T <= 0
        error('Values must be positive.');
    end
    n = P / (T * (2*pi/60));
end

% Example
T = 100;
n = 1500;
P = power_from_torque_rpm(T, n);
fprintf('Power: %.2f W\n', P);

Excel Formulas

=A2*B2*2*PI()/60   // Power from Torque (A2) and RPM (B2)
=A2/(B2*2*PI()/60)   // Torque from Power (A2) and RPM (B2)
=A2/(B2*2*PI()/60)   // RPM from Power (A2) and Torque (B2)

Governing Formula

P = τ × (2π·RPM / 60)

Mechanical Power

τN·m

Torque

RPMrev/min

Rotational Speed

Governing Formula

τ = P / (2π·RPM / 60)

τN·m

Torque

Mechanical Power

RPMrev/min

Rotational Speed

Technical Explanation: Motor Power, Torque & RPM

Technical Introduction

In rotating machinery, three quantities define performance: power (P), torque (τ), and rotational speed (RPM). These parameters are not independent; they are linked by the fundamental equation of rotational mechanics. Understanding this relationship is essential for engineers working with electric motors, internal combustion engines, turbines, pumps, and industrial drives. It allows proper sizing of motors, prediction of performance, and verification of drivetrain requirements.

Power represents the rate of mechanical energy transfer, torque is the twisting force applied to a shaft, and RPM defines how fast the shaft rotates. Together, they describe how effectively a machine converts energy into useful work.

Governing Formula

The governing equation is:

P = τ × ω = τ × (2π × RPM / 60)

where P is mechanical power in watts (W), τ is torque in newton-metres (N·m), and ω is angular velocity in radians per second. The conversion factor 2π/60 translates RPM into rad/s. This equation assumes steady-state operation and ideal efficiency.

The formula originates from the definition of work and power. Work done by a torque is τ × θ (torque times angular displacement). Differentiating with respect to time gives power = τ × angular velocity.

Calculation Method

To calculate one parameter, two must be known:

Power from Torque and RPM: P = τ × (2π × RPM / 60).
Torque from Power and RPM: τ = P / (2π × RPM / 60).
RPM from Power and Torque: RPM = (60 × P) / (2π × τ).

These rearrangements allow engineers to solve for whichever variable is missing. The calculator automates this process, ensuring unit consistency and reducing manual errors.

Input Parameters Explained

Torque (τ): The twisting force applied to the shaft. Measured in N·m. Higher torque means greater ability to overcome resistance.
Rotational Speed (RPM): The number of revolutions per minute. Determines how fast the shaft spins. High RPM increases angular velocity.
Power (P): The rate of energy transfer. Measured in watts. Represents the useful mechanical output of the motor or engine.

Engineers must ensure correct units. Mixing pound-feet with N·m or horsepower with watts without conversion leads to errors.

Engineering Interpretation

The calculated values guide design decisions. For example, a motor delivering 10 N·m at 1500 RPM produces approximately 1.57 kW. If the application requires 2 kW, either torque or speed must be increased. Engineers interpret these results to size motors, select gear ratios, and evaluate performance curves.

In engines, torque curves show how twisting force varies with RPM, while power curves highlight maximum energy output. Understanding both is crucial for matching motors to loads.

Units and Conversion

The SI units are watts (W), newton-metres (N·m), and RPM. Common conversions include:

1 horsepower (hp) = 745.7 W.
1 pound-foot (lb·ft) = 1.356 N·m.

Engineers often use horsepower and lb·ft in automotive contexts, while industrial applications prefer SI units.

Alternative and General Cases

This calculator assumes constant torque and speed. In reality, motors may operate under variable load, acceleration, or transient conditions. In such cases, instantaneous power must be calculated using time-dependent torque and speed. Additionally, efficiency factors must be included for real systems, where mechanical losses reduce output power.

Assumptions and Limitations

The calculation assumes:

Steady-state operation without acceleration.
Ideal efficiency (η = 1).
Uniform torque across the rotation.

In practice, motors have efficiency between 70–95%, and torque may fluctuate with load. These factors must be considered in detailed design.

Practical Engineering Use

Applications of this calculation include:

Motor selection: Ensuring the chosen motor can deliver required torque at operating speed.
Gearbox design: Matching torque and RPM to load requirements.
Performance testing: Comparing measured torque and speed to rated power.
Energy efficiency analysis: Evaluating how much input energy is converted to useful mechanical work.

These calculations appear in industries ranging from automotive and aerospace to manufacturing and robotics.

Conclusion

The relationship between power, torque, and RPM is a fundamental principle of mechanical engineering. This calculator provides a straightforward way to compute the missing parameter, enabling engineers to size motors, evaluate performance, and design reliable systems. While simple, the formula highlights the trade-offs between torque and speed, and the importance of efficiency in real-world applications.

Real-World Engineering Cases

The Underpowered Conveyor Motor

A conveyor system was designed with a motor rated for 5 kW at 1500 RPM. The motor kept stalling under load. The engineer had calculated the torque requirement based on the conveyor's belt tension but forgot to account for the gearbox's mechanical efficiency.

Engineering Lesson

Always factor in efficiency losses. If the gearbox is 85% efficient, the actual torque delivered to the conveyor is 15% less than calculated. Use this calculator with an efficiency factor to properly size motors.

The High-Speed Spindle Meltdown

A CNC machining center was upgraded to a higher-power spindle motor. The machine operator increased the RPM to achieve higher material removal rates, but the spindle bearings failed catastrophically due to excessive heat generation.

Engineering Lesson

Power dissipation increases with both torque and RPM. Running at higher RPM without reducing torque can exceed the power rating of the motor and its cooling capacity. This calculator helps identify the safe operating envelope.

Frequently Asked Questions

What is the relationship between power, torque, and RPM?

Power is the product of torque and angular velocity. In SI units: Power (W) = Torque (N·m) × Angular Velocity (rad/s), where Angular Velocity = 2π × RPM / 60. This means increasing either torque or RPM (while keeping the other constant) increases power output.

How do I use this calculator?

Select the value you want to calculate (Power, Torque, or RPM) from the dropdown menu. Then enter the other two values. The calculator will automatically compute the missing one. You can also toggle alternate units (hp and lb·ft) for convenience.

What units are used?

The base units are Watts (W) for power, Newton-meters (N·m) for torque, and RPM for rotational speed. The calculator also displays alternate units: horsepower (hp) and pound-feet (lb·ft) when the "Show alternate units" button is clicked.

Does this account for motor efficiency?

No. This calculator assumes 100% efficiency. In real-world systems, motors and gearboxes have efficiency losses (typically 70%–95%). To get the actual mechanical power output, multiply the calculated power by the efficiency factor: P_actual = P_calculated × η.

Can I use this for internal combustion engines?

Absolutely! This calculator works for any rotating machine, including internal combustion engines, turbines, pumps, and compressors. The relationship P = τ × ω is universal for mechanical power transmission.

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