Torque Calculator

Enter any two of force, lever length and torque and the third follows, with the angle handled properly. The second mode fixes the problem a torque wrench cannot see: fit an in-line adapter and the bolt receives more torque than the dial reads, and the correction is a ratio nobody applies.

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How this torque calculator works

The first mode is the physics: force, lever length and the angle between them. The second is the one that stops bolts snapping, because a torque wrench with an adapter fitted does not measure what the bolt receives, and the correction is a simple ratio that almost nobody applies.

The formula

τ = rF sinθ
wrench setting = target × L ÷ (L + E)
1 lb-ft = 1.3558179 N·m exactly

r is the distance from the pivot to where the force acts, F is the force, and θ is the angle between the lever and the force, which is 90 degrees when you pull square. L is the length of the torque wrench and E the length an in-line adapter adds to it. The lb-ft conversion is exact rather than measured, because both the pound-force and the foot are defined quantities.

Worked example

200 N on a 0.4 m bar, pulled square: 0.4 × 200 = 80 N·m, which is about 59 lb-ft. Halve the bar to 0.2 m and you need 400 N for the same torque; double it to 0.8 m and 100 N will do. The bolt cannot tell the difference between any of those, because it only ever feels the product.

Now the adapter. A bolt specified at 100 N·m, a torque wrench 450 mm long, and a crowfoot adapter that puts the socket 75 mm further out in line with the handle. The correction factor is 450 ÷ 525 = 0.857, so you must set the wrench to 85.7 N·m to deliver 100 at the bolt.

Dial in the full 100 instead and the bolt actually receives 116.7 N·m, 16.7% over specification. The wrench still clicked, the job still felt right, and the fastener has been over-torqued. This is the single most common way a correctly used torque wrench delivers a wrong number.

The extension that matters and the one that does not

There is a distinction here that catches people in both directions, and it is worth being precise about. The correction applies only when the adapter moves the socket further from your hand along the direction of the handle, lengthening the lever. Crowfoot wrenches, offset adapters and flare-nut adapters all do this.

A plain socket extension, the long bar that makes the wrench reach deeper into a recess, does not. It runs along the axis of rotation rather than along the lever, so it adds no lever length and changes nothing: the wrench reading is already correct. Nor does a universal joint, provided the socket ends up in the same place relative to your hand. The question to ask is never "is there an adapter" but "did the adapter move the socket further out along the handle", and if the answer is no, dial in the number from the manual and get on with it.

One more case worth knowing: if you fit the adapter at 90 degrees to the handle, it adds nothing to the lever either, because the extra length is perpendicular. That is a genuinely useful trick when you cannot avoid an adapter and would rather not do arithmetic.

Angle, and where your effort goes

The sinθ term is the part people leave out, and at ordinary angles it is not small. Pulling square puts every newton to work. Pull at 45 degrees and you lose 29% of your effort; at 30 degrees you lose half of it. The component you lose is not wasted in a vague sense, it is pulling the fastener out of its hole rather than turning it, which is why a badly angled pull both under-torques and risks rounding the head.

This also explains something about bicycle cranks and door handles. A pedal delivers its greatest torque when the crank is horizontal and your foot is pushing straight down, and almost none at the top and bottom of the stroke, where the force runs along the crank. A door handle is placed as far from the hinge as the door allows, for exactly the reason the table above shows: length is free force.

Why torque and energy share a unit and are not the same thing

A newton metre of torque and a newton metre of work are dimensionally identical: both are a force multiplied by a distance. They are entirely different physical quantities. The difference is geometric. In work, the force and the distance point the same way: you push and something moves in the direction you pushed. In torque, they are perpendicular: you push, and the thing rotates around an axis at right angles to both.

That is why convention writes torque as N·m and energy as joules, even though 1 J = 1 N·m exactly, and why you will never see a torque quoted in joules by anyone who knows what they are doing. It is also why holding a heavy weight at arm's length is exhausting while doing no work at all in the physics sense: there is plenty of torque at your shoulder and no motion, so the energy is going into your muscles rather than into the weight.

Frequently asked questions

How do I calculate torque?

Multiply the force by the distance from the pivot and by the sine of the angle between them. 200 N on a 0.4 m bar pulled square gives 80 N.m, which is about 59 lb-ft. When you pull square the sine term is 1 and disappears, which is why most people meet the formula as simply force times distance.

Do I need to adjust my torque wrench when using an extension?

Only if the adapter lengthens the lever. A crowfoot or offset adapter that puts the socket further out along the handle does, and the setting must be multiplied by the wrench length divided by the wrench plus adapter length. A plain socket extension that makes the wrench reach deeper does not, because it runs along the axis of rotation and adds no lever arm. Fitting an adapter at 90 degrees to the handle also adds nothing.

What happens if I ignore the adapter correction?

You over-torque the bolt, and nothing warns you. A 450 mm wrench with a 75 mm in-line adapter set to 100 N.m actually delivers 116.7 N.m, which is 16.7% over specification. The wrench still clicks at the right point for itself, because it is measuring the twist at its own handle rather than at the bolt. On a critical fastener that margin is how threads stretch and heads snap.

How do I convert N.m to lb-ft?

Divide by 1.3558179, or multiply lb-ft by that figure to go the other way. So 100 N.m is 73.76 lb-ft and 100 lb-ft is 135.58 N.m. The conversion is exact rather than measured, because both the pound-force and the foot are defined quantities. Watch for lb-in as well, which is a twelfth of lb-ft and is used for small fasteners, where mixing the two up is a factor of twelve.

Why does pulling at an angle reduce torque?

Because only the component of your force perpendicular to the lever does any turning. Pull at 45 degrees and you lose 29% of your effort; at 30 degrees you lose half. The part you lose is not merely wasted, it is pulling the fastener out of its hole rather than turning it, which is why a badly angled pull both under-torques and increases the risk of rounding the head.

Does a longer wrench really make it easier?

Yes, and exactly in proportion. Double the lever length and you halve the force needed for the same torque. That is why a breaker bar works and why the first instinct on a seized bolt is a longer handle. It is also why a manual specifies a torque rather than a force: the bolt only ever feels the product of the two, and has no way of knowing which combination produced it.

Is torque the same as energy since both are newton metres?

No, though they are dimensionally identical, which is a genuine oddity of the SI. The difference is geometric: in work the force and the movement point the same way, while in torque they are perpendicular and the result is a rotation. Convention writes torque as N.m and energy as joules to keep them apart, even though 1 J equals 1 N.m exactly. Holding a weight at arm's length is the everyday demonstration: plenty of torque at your shoulder, no motion, and therefore no work in the physics sense despite the effort.

Where do I measure the length of a torque wrench from?

From the centre of the square drive to the middle of where your hand grips it, which is usually marked on the handle or given in the manual. It is typically between 250 and 600 mm. The measurement matters only for the adapter correction, and getting it a centimetre out changes the correction by well under a percent, so a tape measure is accurate enough.

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