Torque Calculator
Compute the effective torque produced by a force applied at a given distance and angle from a pivot, accounting for system efficiency. Use it for wrench sizing, lever design, and mechanical system analysis.
About this calculator
Torque is the rotational equivalent of linear force and measures a force's tendency to cause rotation about a point. The general formula is: Torque = force × distance × sin(angle) × (efficiency / 100), where angle is measured between the force vector and the lever arm. When the force is perfectly perpendicular to the lever arm (angle = 90°), sin(90°) = 1 and torque is maximized as simply force × distance. At any other angle, the effective torque is reduced because only the perpendicular component of the force contributes to rotation. Efficiency captures mechanical losses in the system, such as friction in bearings or joints. Units are typically lb·in in Imperial systems or N·m in SI systems.
How to use
Scenario: A technician applies 50 lbs of force at the end of a 12-inch wrench handle, at an angle of 75° from the bolt axis. System efficiency is 98%. Step 1 — Enter force = 50 lbs. Step 2 — Enter distance = 12 inches. Step 3 — Enter angle = 75°. Step 4 — Enter efficiency = 98. Calculation: Torque = 50 × 12 × sin(75°) × (98/100) = 50 × 12 × 0.9659 × 0.98 = 567.8 lb·in. For comparison, at 90° the torque would be 50 × 12 × 0.98 = 588 lb·in.
Frequently asked questions
Why does the angle of applied force affect torque output?
Only the component of force that is perpendicular to the lever arm contributes to rotation; the parallel component simply pushes or pulls along the arm without creating rotation. The perpendicular component equals force × sin(angle), which is why 90° gives maximum torque and 0° or 180° gives zero torque. In practice, tools like wrenches are most effective when pulled perpendicular to the handle. Even small deviations from 90° can reduce torque noticeably, especially at shallow angles.
What is the difference between torque and moment of force?
Torque and moment of force are closely related but used in different contexts. Torque typically refers to a twisting force that causes rotation in a mechanical system, such as an engine output shaft or a bolt. Moment of force is a broader term used in structural engineering to describe any force causing rotation about a point, including bending moments in beams. Mathematically, both are calculated as force × perpendicular distance. The distinction is mostly conventional — engineers tend to use 'torque' for rotating machinery and 'moment' for static structures.
How do I convert torque from lb·in to N·m?
To convert pound-inches (lb·in) to newton-meters (N·m), multiply by 0.11298. For example, 500 lb·in × 0.11298 = 56.49 N·m. Conversely, to go from N·m to lb·in, multiply by 8.8507. This conversion is needed when working across Imperial and SI specifications, which is common when sourcing international components. Always double-check units when combining torque values from different data sheets to avoid errors in your design.