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

The relationship between power, torque, and rotational speed (RPM) is fundamental to mechanical engineering. In any rotating machine — from electric motors to internal combustion engines — these three quantities are inseparably linked by the equation:

P = τ × ω

where ω (angular velocity in rad/s) = 2π × RPM / 60.

Why This Relationship Matters

Engineers constantly need to determine how much power a motor produces given its torque and speed, or how much torque is needed to achieve a desired power output at a specific RPM.

Electric Motor Sizing: When selecting a motor, you often know the required power and operating speed — this calculator helps you find the necessary torque rating.
Engine Performance: Internal combustion engines are rated by both horsepower (power) and torque. Understanding how they relate helps in evaluating performance curves.
Drivetrain Design: Gears and transmissions change torque and RPM. This calculator helps verify that the output meets design requirements.

Important Assumptions

100% Efficiency: This calculator assumes no mechanical losses. In real systems, you must account for efficiency (η) using: P_output = P_input × η.
Steady-State Operation: The relationship assumes constant torque and speed. During acceleration, inertial effects complicate the dynamics.
SI Units: The base units are Watts (W), Newton-meters (N·m), and RPM. The calculator also displays horsepower (hp) and pound-feet (lb·ft) for convenience.

How to Use This Calculator

Select the value to calculate: Choose Power, Torque, or RPM from the dropdown.
Enter the two known values: Input the parameters you already know. For example, if calculating Power, enter Torque and RPM.
Read the result: The calculated value appears instantly in the large result box.
View alternate units (optional): Click "Show alternate units" to see results in horsepower (hp) and pound-feet (lb·ft).

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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