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
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.