Torque Calculator

Torque is a twist. A force pushes or pulls; torque is what tries to spin something around a pivot. The same equation explains why a long wrench loosens a stuck bolt and why electric cars launch off the line so hard. This page solves it for any of its four parts: torque, lever arm, force, or angle.

What torque actually is

Torque (Greek letter τ, tau) is the rotational version of force. Force moves things in a straight line; torque spins them. Three numbers control it: how hard you push, how far from the pivot you push, and what angle you push at. That's why mechanics buy long wrenches: same effort, more turn. Torque is measured in newton-meters (N·m) or pound-feet (lb-ft). The units look identical to joules, but torque is a rotational vector, not an amount of energy transferred.

How to use this calculator

Pick the three values you know. For a wrench problem, that's usually the wrench length, the force you're pulling with, and the angle of the pull. Type them in with whatever units make sense (each field has its own unit selector, so you can mix metric and imperial), and the fourth value appears. To solve for a different unknown, lock the field you want as the output and unlock the one you want to enter.

Understanding the formula

\tau = r \times F \times \sin(\theta)

τ is the torque you're after, in newton-meters or pound-feet. r is the lever arm, the distance from the pivot to where the force lands. F is the force itself, in newtons or pounds. θ is the angle between the force vector and the lever arm, in degrees or radians.

Say you're loosening a stubborn bolt. Your wrench is 0.3 m long, and you pull straight down on the end with 100 N of force, so the angle between your pull and the handle is 90°:

\tau = 0.3\text{ m} \times 100\text{ N} \times \sin(90^\circ)

$\sin(90\degree) = 1$ , so the formula collapses to a simple multiplication:

\tau = 0.3 \times 100 \times 1 = 30\text{ N}\cdot \text{m}

That's 30 newton-meters of torque. If the bolt still won't budge, you don't need to push harder. Sliding a cheater bar over the handle to extend it to 0.6 m doubles the torque to 60 N·m on the same 100 N pull.

Why the angle matters

The sin(θ) term does a lot of work. Push perpendicular to the arm and sin(θ) = 1, so every bit of your force becomes rotation. Push at 45° and you only get about 70% of that ( $\sin(45\degree) \approx 0.707$ ). Push straight toward the pivot at 0° and you get nothing, because $\sin(0\degree) = 0$ . It's the same reason a door is hard to open if you shove it next to the hinge but easy to swing from the handle. The chart below sweeps the angle from 0° to 180° so you can see the full curve.

Where torque shows up

Car spec sheets quote torque because it tells you about pulling power. An electric motor delivers peak torque from a dead stop, which is why EVs feel so quick off the line; a combustion engine has to climb the RPM band to get there. In a factory, a torque wrench clicks or slips the moment a bolt hits its target, because over-tightening snaps threads and under-tightening lets joints leak or work themselves loose. Aircraft assembly takes this to an extreme: thousands of torqued fasteners on a single airframe, each one specced so the joint is strong without the bolt being heavier than it needs to be. Behind every gear ratio, pulley, and pry bar, the same equation is doing the bookkeeping.

Tips for accurate results

A few things worth knowing. The lever arm is the perpendicular distance from the pivot to the line of force; if your push isn't already perpendicular, that's what the angle field is for. Maximum torque always lives at 90°. Negative torque is the same magnitude, just rotating the other way (clockwise vs counterclockwise), and which one that is depends on which side you're looking from, so this page reports the magnitude only. The unit selectors handle conversions for you, but glance at the unit on each field before you read a result.

Common questions

What's the difference between torque and power?

Torque is the rotational grunt that gets heavy things moving; power is how quickly that work actually gets done. They're tied together by Power = Torque × Angular Velocity. A tractor has heaps of torque at low RPM; a dental drill has barely any torque but spins at 200,000 RPM. Both are useful, for very different reasons.

Can torque be negative?

In vector mechanics, yes; the sign just flags the opposite direction of rotation. Whether that direction reads as clockwise or counterclockwise depends on which side of the pivot you're standing on, so this calculator returns the magnitude only.

Why do we use newton-meters instead of joules for torque?

They share the same dimensions (force × distance), but they describe different things. Torque is a vector that spins something; a joule measures energy actually delivered. Keeping the unit names separate keeps the two concepts from getting mixed up on a spec sheet.

What angle should I use for maximum torque?

90°. When force is perpendicular to the lever arm, $\sin(90\degree) = 1$ and all of your push translates into rotation. Any other angle wastes some of it pointing along the arm, which does nothing useful.

How do I convert between newton-meters and pound-feet?

1 N·m is about 0.7376 lb-ft, and 1 lb-ft is about 1.356 N·m. The unit selector on each field does the conversion for you, so you can enter values in one system and read the answer in another.