Torque Calculator - N.m and lb-ft from Force and Lever Arm

A bolt has no idea how hard you pulled

It only feels the turning effect, and that depends as much on the handle as on your arm. A wheel nut wanting 120 N·m takes 800 N from a 150 mm wrench and 120 N from a meter-long bar. Same nut, same spec, and the difference between hanging 81.6 kg on the end and hanging 12.2 kg on it.

That is why the honest answer to "is this tight enough" is never a feeling. It is a number, and the number has two halves.

What you get instead of a guess

Give the calculator any two of the three quantities and it returns the third, in metric and imperial at the same time, and then shows what that answer means with a tool in your hand.

Both unit systems, one answer

Type 25 lbf on an 18 in handle and read 50.84 N·m next to 37.5 lb-ft. No second tab, no conversion done by hand at the point where mistakes are expensive.

The pull you actually have to produce

Every answer comes with the force needed on five real handle lengths, converted to pounds and to a mass you can picture hanging off the end.

The angle, priced

Pull at 45° to the handle instead of square to it and you deliver 70.7% of the turning effect. The calculator says so rather than quietly assuming you were perfect.

Which distance to measure, and from where

The lever arm is the part people get wrong, and it is the only input with a rule worth memorising: measure from the center of rotation to the point where your hand sits, not the total length of the tool. A 300 mm ratchet gripped 40 mm from its end has a lever arm of 260 mm, and the difference is a real 13% off your torque. Work through the fields in this order and there is nothing left to get wrong.

What are you solving for - torque from a force, the force a spec demands, or the handle length that would make that force comfortable. The form then only asks for what it needs.
Force - in newtons, kilonewtons, kilograms-force or pounds-force. A firm two-handed pull from a standing adult is roughly 200 to 400 N, or 45 to 90 lb.
Lever arm - in meters, centimeters, millimeters, feet or inches. Center of the fastener to the middle of your grip.
Torque - when you already have the spec, in N·m, kN·m, lb-ft, lb-in or kgf·m. Workshop manuals print lb-in for small fasteners precisely because 37.5 lb-ft and 450 lb-in are the same thing and the second one is harder to misread by a factor of twelve.
Angle - optional. Leave it empty and the calculator assumes the textbook case, a pull square to the handle at 90°. Fill it in when you know you were pulling at a slant.
Read the answer - the headline number, the working that reproduces it, the five-handle table and the ladder that says whether your figure belongs on a jar lid or a truck.

One nut, five tools, five completely different pulls

This is the decision the number is for. A passenger-car lug nut at 120 N·m is the same job in every row below; only the handle changes. The last column is the mass whose weight equals the force needed, which is the version that settles arguments in a parking lot.

Tool	Lever arm	Force needed	In pounds	Realistic?
150 mm (6 in) combination wrench	0.150 m	800 N	179.8 lb	No. That is most of an adult standing on it
250 mm (10 in) ratchet	0.250 m	480 N	107.9 lb	Hard. Two hands and your body weight behind it
400 mm (16 in) lug wrench	0.400 m	300 N	67.4 lb	Yes. This is why the car carries one
600 mm (24 in) breaker bar	0.600 m	200 N	45.0 lb	Comfortable one-handed
1 m (3 ft) bar	1.000 m	120 N	27.0 lb	Easy, and now over-tightening is the risk

Read the table from the bottom up and you have the argument against the cheater pipe in one line. The bar that finally makes a seized nut move is the same bar that sails past the spec on the way back, because the force your arm reads as "firm" is now producing five times the turning effect it did with the short wrench.

Nine jobs and the figure each one wants

Torque spans seven orders of magnitude between a jar lid and a wind turbine, which is why a single number means nothing until you know what it is attached to. Every metric figure below is a typical value; every imperial figure is the exact conversion of it at 1 lb-ft = 1.3558179483 N·m.

Job	N·m	lb-ft	What sets the figure
Twisting open a screw-top jar	3	2.2	Grip friction, not strength
Spark plug in an aluminum head	25	18.4	The soft thread strips long before the plug does
Bicycle pedal into the crank	35	25.8	Loose here destroys the crank arm, not the pedal
Engine oil drain plug	35	25.8	A crush washer that only crushes once
Passenger-car lug nut	120	88.5	Clamp load holding a wheel against a hub
Compact gasoline engine at peak	190	140.1	Cylinder pressure on a crank throw
Semi-truck wheel nut	610	449.9	Ten times the wheel mass and no second chances
Performance EV, both motors	640	472.0	Available from zero rpm, which is the whole point
Wind turbine main shaft, 3 MW at 12.8 rpm	2,238,116	1,650,750	Power divided by a very slow rotation

That last row is worth a second look, because it is the one people write down wrong. Torque is power divided by angular speed, so a slow shaft carrying a lot of power carries an enormous torque: 3 MW at 12.8 rpm is 1.34 rad/s, and 3,000,000 divided by 1.34 is 2.24 million N·m. Put the same 3 MW through a gearbox onto a generator spinning at 1,500 rpm and the shaft only sees 19,099 N·m. Same power, same machine, a factor of 117 between the two shafts. Whenever a torque figure looks impossible, the missing information is almost always which shaft it belongs to.

The angle nobody measures, priced in percent

Every workshop figure assumes you are pulling square to the handle. In an engine bay you often are not, and the shortfall is not linear. The sine is generous near the top and brutal at the bottom, which is why a pull that feels only slightly off can be halfway wasted.

Angle to the handle	sin	Torque delivered	From 400 N on 0.25 m
90° square on	1.000000	100%	100.00 N·m
75°	0.965926	96.6%	96.59 N·m
60°	0.866025	86.6%	86.60 N·m
45°	0.707107	70.7%	70.71 N·m
30°	0.500000	50.0%	50.00 N·m
15°	0.258819	25.9%	25.88 N·m
0° straight along the arm	0.000000	0%	0 N·m

Losing 3.4% at 75° is not worth worrying about. Losing half at 30° is, and that is a much smaller misalignment than it sounds when you are lying under a car. The bottom row is not a curiosity either: a force pointing straight along the handle is pure pull on the pivot and turns nothing at all, which is why this calculator refuses to solve for a force at 0° or 180° instead of dividing by a number that is only zero-ish.

Torque, moment, and the words that mean the same thing

The quantity has collected several names and it causes real confusion, so here they are in one place. Torque and moment of force are the same thing, M = F × r × sinα. Engineers analysing a static beam tend to say moment; anyone talking about a rotating shaft says torque. Bending moment is the same arithmetic applied where nothing turns, which is why it is still measured in newton-meters.

The unit collision is worse than the naming one. A newton-meter and a joule have identical dimensions, and they are not interchangeable: a joule is a force along a distance, a newton-meter of torque is a force across one. That is exactly why torque is never written in joules, even though the algebra would allow it. And in imperial the trap is lb-ft against lb-in, a factor of twelve: 37.5 lb-ft and 450 lb-in are one figure, and reading one as the other is how small fasteners get destroyed. This calculator prints both on every result so the mistake has nowhere to hide.

The cheat sheet

You want	Formula	Worked example
Torque	M = F × r × sinα	250 N on 0.3 m at 60° = 64.95 N·m
Force	F = M ÷ (r × sinα)	120 N·m on 0.4 m square on = 300 N
Lever arm	r = M ÷ (F × sinα)	610 N·m from 400 N = 1.525 m
N·m to lb-ft	divide by 1.3558179483	120 N·m = 88.5 lb-ft
lb-ft to lb-in	multiply by 12	37.5 lb-ft = 450 lb-in
Torque from power	M = P ÷ ω, ω = rpm × 2π ÷ 60	3 MW at 1,500 rpm = 19,099 N·m

What people ask when the nut still will not move

Is a longer bar cheating, or is it just physics?

It is physics, and it is also how fasteners get ruined. Doubling the handle halves the force you need for the same torque, which is genuinely useful for undoing something seized. The problem is the return trip. Your arm has no idea what torque it is producing; it only knows how hard it is pulling. A pull that gave 120 N·m through a 250 mm (10 in) ratchet gives 480 N·m through a 1 m (3 ft) bar, which is four times the spec on a passenger-car wheel. Use the bar to loosen, use a torque wrench to tighten.

Do I measure to the end of the wrench or to my hand?

To your hand, or more precisely to the middle of your grip, because that is where the force is actually applied. On a 300 mm ratchet held with your palm centered 40 mm from the end, the lever arm is 260 mm and you are delivering 13% less than the length stamped on the tool suggests. It matters most on short handles, where a couple of centimeters is a large fraction of the whole arm.

Why does a newton-meter look like a joule but is not one?

Because the geometry differs even though the dimensions do not. Work is force multiplied by distance along the force; torque is force multiplied by distance perpendicular to it. The two are built from the same ingredients arranged at right angles, so the units come out identical while the quantities are not interchangeable. Convention keeps them apart: energy is written in joules, torque in newton-meters, and nobody writes torque in joules even though the algebra would let them.

The spec says 450 lb-in. Is that a lot?

It is 37.5 lb-ft, or 50.84 N·m, so no, it is a modest fastener. Manuals print small figures in pound-inches on purpose, because 37.5 written in the wrong unit and read as pound-feet would be twelve times over spec. If a figure looks absurdly large for the size of the bolt, check which of the two units it is in before you check anything else.

Does the calculator handle a force I am pulling at a slant?

Yes, through the optional angle field, and it prints the sine at full precision so you can check the working. Leave the field empty and it assumes 90°, the square pull every published torque figure is written for. What it will not do is solve backwards at 0° or 180°: a force along the arm produces no turning effect at all, so no force of any size delivers the torque you asked for, and returning an astronomically large number there would be worse than refusing.

Why is an electric motor's torque figure so much higher than an engine's?

Partly because it genuinely is, and mostly because of where it appears. A combustion engine reaches peak torque in a narrow band of engine speed, so its 190 N·m arrives somewhere around the middle of the rev range. An electric motor produces close to its maximum from a standstill, so a figure like 640 N·m is available the instant you ask. The number that gets quoted for an EV is usually both motors added together, too, which is fair as long as you know that is what you are reading.

Can I work out torque from a horsepower figure?

Only if you also know the rotational speed, because torque is power divided by angular speed and nothing else. Convert rpm to radians per second by multiplying by 2π and dividing by 60, then divide the power in watts by that. The same 3 MW gives 2,238,116 N·m on a shaft turning at 12.8 rpm and 19,099 N·m at 1,500 rpm. A power figure on its own tells you nothing about torque.

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