π§ Torque Calculator
Calculate torque Ο = F Γ r Γ sin(ΞΈ) for rotational systems.
Result
How to Use This Calculator
This calculator finds torque from an applied force. Enter the force, the length of the lever arm, and the angle between them.
Enter the force in newtons.
Enter the moment arm in meters: the distance from the pivot to where the force is applied.
Enter the angle in degrees between the force direction and the lever arm. Use 90 for a perpendicular push, which gives maximum torque.
Click Calculate. The torque appears in newton-meters.
The Torque Formula
Torque is the rotational equivalent of force: it measures how effectively a push causes rotation. Three things matter, and the formula multiplies all of them. More force helps, a longer lever helps, and the angle decides how much of the force actually twists versus just shoves. Only the perpendicular component, F sin(theta), contributes; the rest pushes uselessly along the arm.
Direction matters too, though this calculator reports magnitude. By convention, counterclockwise torque is positive and clockwise is negative, or use the right-hand rule: fingers along r, curl toward F, thumb points along the torque axis. Seesaws, doors, and wrenches all balance torques, not forces, which is why a child can balance an adult on a seesaw by sitting farther out.
Worked Example
Where This Comes Up
Torque specs are everywhere in the physical world: lug nuts tightened to 110 N m, engine output quoted in N m or lb-ft, and door closers tuned by torque. Mechanics live by torque wrenches because under-tightened bolts vibrate loose and over-tightened ones snap. In biomechanics, every joint is a lever: your jaw, elbow, and knee all trade force for torque.
The sin(theta) factor is the forgotten piece. Beginners compute r x F and call it done, which overstates any angled push. A door pushed at 45 degrees to its face delivers only 71 percent of the naive answer. When in doubt, resolve the force perpendicular to the arm first, then multiply.
Frequently Asked Questions
Why does a longer wrench make bolts easier?
Torque equals force times lever arm, so doubling the wrench length doubles the torque for the same push. Your muscles supply the same force, but the bolt feels twice the twist.
What are the units of torque?
Newton-meters (N m). Dimensionally that matches the joule, but torque gets its own name because it measures twist, not energy.
At what angle is torque zero?
0 degrees or 180 degrees: pushing straight along the lever arm, toward or away from the pivot, produces no rotation. Maximum torque needs 90 degrees, pushing perpendicular to the arm.
What is the difference between torque and force?
Force causes linear acceleration (F = ma); torque causes angular acceleration (torque = I x alpha). A force through the pivot point gives zero torque no matter how large it is.
Why do car specs list torque?
Torque at the wheels determines pulling power and launch feel. High torque at low rpm means strong acceleration without downshifting, which is why diesel trucks brag about it.