Torque Calculator
Torque (τ = r × F × sin θ), also called moment of force, represents the rotational tendency of a force applied at a distance from an axis or pivot point. Essential in automotive engine tuning, mechanical gearbox design, robotics actuator sizing, and structural bolt tightening, this tool calculates twisting torque alongside rotational power output at a specified angular speed (RPM).
Force applied to the lever or wrench in Newtons (N)
Distance from the pivot or rotation center to where force is applied in metres (m)
Angle between lever arm and applied force vector (90° yields maximum torque)
Shaft rotational speed in revolutions per minute (for power output calculation)
SI unit of torque in Newton-metres
How to Use This Calculator
- Enter the applied force in Newtons.
- Enter the lever arm radius or wrench length in metres (e.g. 0.3 m for a 30 cm wrench).
- Adjust the angle if pulling at an oblique angle (keep 90° for standard perpendicular pulling).
- Enter rotational speed in RPM to compute shaft horsepower and watt rating.
Formula & Calculation Methodology
Torque is the vector cross product of position vector r and force vector F. At 90° (perpendicular), sin(90°) = 1 resulting in maximum leverage. Rotational power equals torque multiplied by angular velocity (ω in rad/s).
Worked Example
Torque wrench applying 120 N force perpendicularly to a 0.40 m handle at 1,500 RPM
Frequently Asked Questions
What is the difference between a Newton-metre of torque and a Joule of work?↓
Even though both share base units of kg·m²/s², work is a scalar product (force parallel to motion) measuring energy transfer. Torque is a vector product (force perpendicular to lever arm) measuring rotational twisting tendency.
Why do longer wrenches make loosening stubborn lug nuts easier?↓
Because torque scales directly with lever length (τ = r × F). Doubling wrench handle length (2r) doubles the applied torque onto the nut using the exact same muscular effort (F).
How does engine torque relate to vehicle horsepower?↓
Horsepower is a direct mathematical derivative of torque and engine speed: Horsepower = (Torque in lbf·ft × RPM) / 5252. Thus, torque and horsepower curves always intersect at exactly 5,252 RPM on a dynamometer.
What limitation applies to flexible lever arms?↓
This formula assumes a rigid, non-deformable lever arm. In high-torque structural scenarios where the lever bends significantly, deflection reduces the effective perpendicular moment arm radius.
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Source Citation & Disclaimer
Informational tool only; not licensed tax, legal, or financial advice.