Torque Calculator
Compute the rotational force (torque) produced when a force is applied at a distance from a pivot point. Use it when tightening bolts, designing levers, or sizing motors.
About this calculator
Torque is the rotational equivalent of linear force. It measures how effectively a force causes an object to rotate about a pivot or axis. The formula is: τ = F × d, where τ is torque in Newton-metres (N·m), F is the applied force in Newtons, and d is the perpendicular distance from the pivot to the point where the force is applied, in metres. A larger force or a longer lever arm both increase torque proportionally. This principle is why a longer wrench handle makes it easier to loosen a tight bolt — the same hand force produces greater torque. Engineers use this relationship when designing engines, fastening systems, and any mechanism involving rotation.
How to use
Suppose you apply a force of 50 N at the end of a wrench that is 0.3 m long. Using the formula τ = F × d: τ = 50 N × 0.3 m = 15 N·m. This means you are applying 15 Newton-metres of torque to the bolt. If you need more torque — say 30 N·m — you could either double the force to 100 N or double the wrench length to 0.6 m while keeping the same 50 N force.
Frequently asked questions
What is the difference between torque and force in mechanical systems?
Force is a linear push or pull measured in Newtons, while torque is a rotational force measured in Newton-metres (N·m). Torque depends on both the magnitude of the applied force and the distance from the pivot point. Two identical forces can produce very different torques depending on where they are applied relative to the axis of rotation. Understanding this distinction is essential in mechanical design, from automotive engines to simple hand tools.
How does distance from the pivot affect the torque I can generate?
Torque increases linearly with the distance from the pivot, so doubling the lever arm doubles the torque for the same applied force. This is the fundamental reason longer wrenches, spanners, and crowbars are more effective at loosening stuck fasteners. In practice, mechanics often use extension bars to increase their effective lever arm when extra torque is needed. Always ensure the fastener's torque specification is not exceeded, as over-tightening can strip threads or cause fatigue failure.
What units should I use when calculating torque with this calculator?
This calculator uses Newtons (N) for force and metres (m) for distance, producing a result in Newton-metres (N·m), the SI unit for torque. If your measurements are in other units — such as pounds-force and inches (yielding lbf·in) or foot-pounds (lbf·ft) — convert them to Newtons and metres first for consistent results. One lbf·ft is approximately 1.356 N·m. Always check the torque specification of your application (e.g., vehicle workshop manuals) and confirm which unit system it uses before applying the result.