Torque Calculator

Calculate torque — the turning effect of a force — from the force, lever-arm length, and angle, using τ = r·F·sin θ, in newton-metres and pound-feet.

Torque Calculatorمباشر

كيفية استخدام هذه الحاسبة

1Enter the force applied.
2Enter the lever-arm length — the distance from the pivot to where the force acts.
3Enter the angle between the force and the arm (90° for maximum torque).
4Read the torque in newton-metres and pound-feet.

طريقة الحساب

Torque

τ = r × F × sin θ
τ = torque, r = lever-arm length, F = force
θ = angle between the force and the lever arm
maximum torque when θ = 90° (force perpendicular to arm)

Torque is the measure of a force's tendency to rotate an object about a pivot or axis — the rotational counterpart of force in straight-line motion. It depends not just on how hard you push but on where and in what direction. The formula multiplies the force by the length of the lever arm (the distance from the pivot to where the force is applied) and by the sine of the angle between the force and the arm. The sine term captures the fact that only the component of the force perpendicular to the arm does any turning: a force applied at right angles to the arm is fully effective, giving maximum torque, while a force directed along the arm, straight toward or away from the pivot, has no turning effect and produces zero torque. This is why leverage works — increasing the arm length multiplies the torque a given force can produce.

مثال محلول

Pushing with 50 newtons at the end of a 0.3-metre wrench, perpendicular to it, produces a torque of 50 × 0.3 × sin 90° = 15 N·m (about 11 lb·ft). Double the wrench length to 0.6 m and the same push gives 30 N·m — the reason a longer handle loosens a tight bolt.

Torque Calculator: الدليل الكامل

Torque is force with leverage

Torque answers a question that plain force cannot: not just how hard you push, but how effectively that push turns something. The same force produces wildly different turning effects depending on where it is applied. Push on a door right at the hinge and it barely moves; push at the far edge, where door handles are placed, and it swings easily. The force is identical, but the lever arm — the distance from the pivot — is far greater at the edge, and torque is force multiplied by that distance. Leverage is torque made intuitive.

This is why tools that turn things are shaped the way they are. A wrench has a long handle so a modest hand force becomes a large torque at the bolt. A door handle sits opposite the hinges to maximise the lever arm. A steering wheel is wide, and a bottle opener long, for the same reason. Whenever you need to increase turning power without increasing force, the answer is to increase the lever arm, because torque scales directly with it. Halving the distance halves the torque; doubling it doubles the torque.

Why the angle matters

The direction in which a force is applied to a lever is as important as its size and position, and this is where the sine term in the formula comes in. Only the part of the force that acts perpendicular to the lever arm contributes to turning it. A force applied at a right angle to the arm is entirely effective — the sine of 90° is one, giving maximum torque. As the angle shifts away from perpendicular, the effective portion shrinks, and a force pointing straight along the arm, directly toward or away from the pivot, produces no torque at all, because the sine of zero is zero.

This has practical consequences anyone who has used a wrench in a tight space knows. If you cannot pull the wrench handle perpendicular to itself and end up pulling at an awkward angle, you get less turning effect from the same effort, and the bolt is harder to move. The most efficient way to apply force to any lever, from a crowbar to a pedal, is at right angles to it. Understanding the angle term explains why pushing a door at a slant is harder than pushing it straight, and why mechanics position themselves to pull a wrench squarely.

Torque in engines, bodies, and everyday life

Torque is one of the most useful concepts in engineering and everyday physics because rotation is everywhere. In a car, the engine's torque determines how forcefully it can accelerate and pull, which is why torque figures matter as much as horsepower — torque is the twisting force delivered to the wheels, while power is the rate at which that work is done. High torque at low engine speeds is what lets a truck haul a heavy load or a car pull away briskly from a stop.

The same physics governs the human body, where muscles produce torque about joints to move limbs, and the placement of muscle attachments relative to the joint sets the leverage. It appears in the tightening specifications for bolts, given in newton-metres or pound-feet, where too little torque leaves a joint loose and too much strips or snaps it, which is why torque wrenches exist. Gears, pulleys, and levers all trade force for distance or vice versa while conserving the underlying work, and torque is the language for describing those trade-offs. From opening a jar to designing a wind turbine, the balance of force, lever arm, and angle captured by this one formula is at work.

الأسئلة الشائعة

How do I calculate torque?

Multiply the force by the lever-arm length and by the sine of the angle between them: τ = r·F·sin θ. Pushing 50 N at the end of a 0.3 m wrench perpendicular to it gives 50 × 0.3 × sin 90° = 15 N·m. At 90° the sine is 1, giving maximum torque.

Why does a longer wrench make a bolt easier to turn?

Because torque is force times lever-arm length. A longer handle increases the lever arm, so the same hand force produces more torque at the bolt. Double the wrench length and you double the turning effect — which is why cheater bars are used on stubborn fasteners.

Why does the angle affect torque?

Only the component of force perpendicular to the lever arm turns it, and the sine term captures that. A force at 90° to the arm is fully effective (maximum torque); a force directed straight along the arm produces zero torque. Applying force perpendicular to the lever is most efficient.

What's the difference between torque and horsepower?

Torque is the twisting force an engine produces; power (horsepower) is the rate at which it does work, combining torque and rotational speed. Torque determines pulling and accelerating force; power determines how quickly that work happens. Both matter, which is why cars quote each.