What torque is, and why its units look like energy
Torque is a force applied at a distance from an axis: T = F × r, where r is the perpendicular distance from the axis to the line along which the force acts. Push with 100 newtons on a spanner 0.3 m long and you apply 30 N·m, provided you push square to the handle. Push at an angle and only the perpendicular component counts.
That product of force and length is why a newton-metre looks dimensionally identical to a joule — but they are different physical quantities and the SI Brochure is explicit that torque should be expressed in newton-metres and never in joules. Energy is force times distance moved along the force; torque is force times distance at right angles to it. The same distinction lies behind the English-language convention of writing torque as pound-feet and energy as foot-pounds, though in practice a great many service manuals write “ft-lb” for torque and everyone understands them.
The unit you are handed depends entirely on where the document was written. European and Japanese manufacturers publish newton-metres. American manufacturers publish pound-feet for anything substantial and pound-inches for small fasteners and electrical terminations, where a pound-foot would be an awkwardly coarse unit. Older Japanese and continental literature uses kilogram-force metres. Electronics assembly and instrument work use ounce-inches. All of them describe the same physical quantity.
Where each factor comes from
Every factor here is derived from three exact definitions: the pound is 0.45359237 kg, the foot is 0.3048 m, and standard gravity is 9.80665 m/s².
- Pound-force. The force standard gravity exerts on one pound of mass: 0.45359237 × 9.80665 = 4.4482216152605 N.
- Pound-foot. That force at one foot: 4.4482216152605 × 0.3048 = 1.3558179483314 N·m.
- Pound-inch. One twelfth of a pound-foot: 0.1129848290276 N·m. The twelve is the only number you need to move between the two imperial torque units.
- Ounce-inch. One sixteenth of a pound-inch: 0.0070615518142 N·m.
- Kilogram-force metre. The force standard gravity exerts on one kilogram, at one metre: 9.80665 N·m exactly.
Two of these are worth memorising as reciprocals. One newton-metre is 0.7375621 pound-feet, and one newton-metre is 8.8507458 pound-inches. So a 100 N·m spec is about 74 lbf·ft, and a 10 N·m spec is about 89 lbf·in — the second is the conversion that saves you when a manual gives newton-metres and your only calibrated wrench is a small inch-pound click type.
Note that the kilogram-force and pound-force units both bake in a value for gravity. That is a convention, not a physical claim about where you are standing: the factor 9.80665 m/s² is a defined constant, so a kgf·m is a fixed amount of torque anywhere in the universe. It is still not SI, and new documents should quote newton-metres.
Worked example: a wheel spec of 120 N·m on an imperial wrench
A European service manual specifies 120 N·m for the wheel bolts. Your torque wrench is graduated in pound-feet.
- Convert to pound-feet. 120 ÷ 1.3558179483 = 88.51 lbf·ft. Equivalently 120 × 0.7375621 = 88.51.
- Set the wrench. Most click wrenches are graduated in 1 or 2 lbf·ft steps, so set 88 or 89 and note which way you rounded. Rounding to 88 is 119.3 N·m, or 0.6% low — comfortably inside the few-per-cent tolerance ISO 6789 permits for hand torque tools within their calibrated range.
- Cross-check in pound-inches. 88.51 × 12 = 1,062.1 lbf·in. That confirms this is a job for a half-inch drive wrench, not an inch-pound one.
- In old Japanese units. 120 ÷ 9.80665 = 12.24 kgf·m, which is what a 1980s service chart for the same job would print.
- What the force at the handle is. On a 450 mm (17.7 in) wrench, 120 N·m needs 120 ÷ 0.45 = 267 N of push, about 60 lbf. That is a useful sanity check: if a spec implies you should be standing on the bar, re-read the units.
Reading a converted torque figure sensibly
Convert once, then set the wrench from the scale it actually has. The error people make is not arithmetic, it is graduation: converting 10 N·m to 7.376 lbf·ft and then setting “about 7” on a coarse wrench is a 5% shortfall before the tool's own tolerance is counted. If the converted figure falls between graduations, use the other unit — 10 N·m is 88.5 lbf·in, which an inch-pound wrench sets precisely.
Respect the tool's calibrated range. ISO 6789 specifies requirements and test methods for hand torque tools, and a wrench's accuracy class applies only within its stated range, typically from 20% of full scale upwards. A 150 lbf·ft wrench set to 15 lbf·ft is being used outside the range its accuracy statement covers, no matter how carefully you converted.
Finally, remember that a torque specification is a proxy for what the engineer actually wants, which is a bolt tension. The relationship between the two depends on thread friction, under-head friction, thread condition and lubrication, and it is far more variable than any unit conversion. A dry, a lubricated and a plated fastener at the same torque reach materially different preloads, which is why manufacturers specify the condition alongside the number. The bolt torque calculator works through that relationship.
Newton-metres to pound-feet, pound-inches and kgf-metres
| Newton-meters | Pound-feet | Pound-inches | kgf-meters |
|---|---|---|---|
| 5 | 3.688 | 44.254 | 0.5099 |
| 10 | 7.376 | 88.507 | 1.0197 |
| 20 | 14.751 | 177.015 | 2.0394 |
| 25 | 18.439 | 221.269 | 2.5493 |
| 40 | 29.502 | 354.030 | 4.0789 |
| 50 | 36.878 | 442.537 | 5.0986 |
| 75 | 55.317 | 663.806 | 7.6479 |
| 100 | 73.756 | 885.075 | 10.1972 |
| 150 | 110.634 | 1,327.612 | 15.2958 |
| 200 | 147.512 | 1,770.149 | 20.3944 |
To go the other way, multiply pound-feet by 1.3558 or pound-inches by 0.11298.
Torque conversion and application errors
- Reading pound-inches as pound-feet. A twelve-fold error, and the most damaging one in this family. A 89 lbf·in terminal screw taken as 89 lbf·ft will be destroyed. Check the magnitude against the fastener: three-figure inch-pound values are common on small screws; three-figure pound-foot values belong on wheel and crankshaft fasteners.
- Using a wrench below its calibrated range. Accuracy classes under ISO 6789 apply within the tool's stated range, commonly 20% of full scale and above. Convert to whichever unit lets you use a correctly sized wrench.
- Adding an extension without correcting. A crowfoot or adapter that lengthens the effective lever arm changes the torque delivered at the fastener. The correction depends on the added length relative to the wrench's own length, and only applies when the extension is in line with the handle.
- Assuming torque equals clamp load. Most of the applied torque is consumed by friction under the head and in the threads. Lubrication can change the preload achieved at a given torque substantially, which is why specifications state the fastener condition.
- Quoting kilogram-force units in new documents. They are not SI and assume standard gravity. Convert to newton-metres for anything published today, and keep the original figure alongside for traceability.
- Mixing up torque and energy. Both come out in newton-metres dimensionally, but the SI Brochure reserves the joule for energy and the newton-metre for torque. A “foot-pound” of energy and a “pound-foot” of torque are numerically related but physically distinct.
Related torque, force and fastener tools
Torque rarely stands alone. If you are choosing a value rather than converting one, the bolt torque calculator derives it from the fastener's size, grade and friction condition, which is the calculation the specification you are reading came out of. For rotating machinery, torque and speed together give power, and the horsepower from torque calculator handles that relationship in both unit systems.
The force half of the conversion has its own page: the newtons to pounds-force calculator covers pound-force, kilogram-force and newtons without the lever arm. For the length half, the mm to inches calculator is the usual companion when a drawing gives a lever arm in millimetres.
One practical note on notation: the SI style is a space or a middle dot between the unit symbols, as in N·m, and the symbol for a newton is capital N while metre is lower-case m. “NM” is a nautical mile and “nm” is a nanometre, so writing torque as “nm” in a document is an error that a reader outside your trade may take literally.