Mechanics

Torque Calculator (τ = r·F·sin θ)

Calculate torque from force, lever arm length and angle. Understand wrenches, door handles and engine torque with instant results in newton-metres.

τ = r × F × sin(θ)
Torque
30N·m

How it works

Torque is rotational force — the ability of a push to twist something around an axis. It grows with the force applied, the distance from the pivot, and how perpendicular the push is. That's the whole physics of levers, wrenches and door handles.

Doubling the lever arm doubles the torque for the same effort. This is why door handles sit far from the hinge, why breaker bars exist, and why Archimedes claimed he could move the Earth with a long enough lever.

Pushing at 90° to the lever is maximally effective (sin 90° = 1). Push along the lever and you produce zero rotation no matter how strong you are — angle matters as much as strength.

Use it in real life

DIY and mechanics: a wheel-nut spec of 110 N·m means about 37 kg of push at the end of a 30 cm wrench — or an easy 11 kg at 1 m. Extending the handle is cheaper than a gym membership.

Cars: engine torque is what you feel as pull when overtaking; gearing multiplies it exactly like a longer lever.

Body mechanics: carrying a load close to your body shortens the lever arm on your spine, slashing the torque your back muscles must counter — the physics behind every safe-lifting guideline.

Frequently asked questions

What's the difference between torque and force?

Force pushes in a straight line; torque twists around a pivot. The same force produces different torque depending on where and at what angle it's applied.

Why do mechanics use torque wrenches?

Bolts clamp correctly only within a torque range: too little and they loosen, too much and threads strip or bolts snap. A torque wrench measures the twist directly instead of guessing from effort.

Is engine torque the same physical quantity?

Yes — an engine quoted at 400 N·m can exert the same twist as 400 N applied at the end of a 1 m lever. Gearboxes then trade rotational speed for torque, like choosing a longer lever.