Newton-Meter Converter — N·m, ft-lb and in-lb

Background.

The service manual says 80 lb-ft and the click wrench in your hand is marked in newton-metres. Multiply by 1.3558 and you have 108.4654 N·m. Going the other way, one newton-metre is about 0.7376 pound-force foot, so a European spec of 120 N·m becomes 88.5075 lbf·ft on an American wrench.

The costly mistakes are rarely between metric and imperial, though. They happen inside the imperial system, where pound-force inches and pound-force feet differ by exactly twelve and are both casually written as "lb" and "in" or "ft" in some order. A bicycle stem bolt specified in inch-pounds and tightened in foot-pounds is overtightened twelvefold. That is why every result is listed in all five units at once: when two of the lines both look reasonable for your fastener, one of them is the wrong unit.

Beyond the three everyday units, kilogram-force metres turn up on older Japanese and European engine specifications, often written "kgm", and dyne-centimetres belong to the CGS system still used by some laboratory instruments that measure very small torques. All five are tied to the newton-metre by exact definitions, so no conversion here involves a measured or rounded constant.

A negative value converts to a negative value, which keeps a direction convention intact. What a conversion cannot tell you is the right torque for a joint, or how a gearbox or an extension on the wrench changes the torque delivered.

What is newton-meter converter?

Torque is the turning effect of a force about an axis: the force multiplied by its perpendicular distance from that axis. Every torque unit is therefore a force unit times a length unit. One newton-metre is the torque of one newton pushing at the end of a one-metre lever at right angles. A pound-force foot is one pound-force at one foot, a kilogram-force metre is one kilogram-force at one metre, and a dyne-centimetre is one dyne at one centimetre.

How to use this calculator.

1. 01Enter the torque exactly as the specification gives it. A minus sign is kept if your convention uses it for direction, such as counter-clockwise or loosening.
2. 02In From, match the abbreviation carefully: in-lb, lb-in and in·lbf are all pound-force inches; ft-lb, lb-ft and lbf·ft are pound-force feet; kgm, kg·m or kp·m on an older document means kilogram-force metre.
3. 03In To, choose the unit printed on your torque wrench or required by the document you are filling in.
4. 04Scan the full list of results. If a value looks plausible in both pound-force inches and pound-force feet, recheck the source unit before tightening anything.
5. 05Set the wrench to the nearest graduation it can actually hold; a reading to four decimals is far finer than any hand tool.

The formula.

Each unit is assigned the number of newton-metres in one of it. The input is multiplied by its source factor to reach newton-metres, then divided by the target factor: target = value × k(from) ÷ k(to).

The factors follow from definitions. The international pound is exactly 0.45359237 kg and standard gravity is exactly 9.80665 m/s², so one pound-force is 0.45359237 × 9.80665 = 4.4482216152605 N. Multiplying by the international foot, 0.3048 m, gives 1 lbf·ft = 1.3558179483314004 N·m, and by the inch, 0.0254 m, gives 1 lbf·in = 0.1129848290276167 N·m; both are exact by definition. One kilogram-force is 9.80665 N, so 1 kgf·m = 9.80665 N·m exactly. One dyne is 10⁻⁵ N and one centimetre is 10⁻² m, so 1 dyn·cm = 10⁻⁷ N·m.

Because every unit is a straight multiple of the newton-metre with no offset, zero stays zero, signs carry through, and the ratio between any two units never changes: a pound-force foot is always twelve pound-force inches, and a kilogram-force metre is always about 7.233 pound-force feet.

A worked example.

Frequently asked questions.

References& sources.

1. [1]NIST SP 811 Appendix B supplies force, length and torque conversion factors used to derive each unit.
2. [2]BIPM SI Brochure defines the newton and the SI derived-unit framework.
3. [3]NIST SP 330 documents SI units and the exact standard-gravity convention used for kilogram-force and pound-force.
4. [4]NIST Handbook 44 Appendix C documents customary/SI unit relationships used in legal metrology.