Torque Converter: N·m, lbf·ft and kgf·m

Torque Unit Converter

Torque is a twisting force. A torque unit converter rewrites a torque figure from one unit into another, such as newton metres into pound-force feet. This page converts between newton metres, pound-force feet and kilogram-force metres, and shows all three values at the same time.

A torque is a force multiplied by the distance from the turning point to the place where the force acts. The same push on a long spanner produces more torque than on a short one.

What the converter does

A visitor types one number and picks the unit that number is written in. The page returns the same torque in all three units.

Results are shown to eight significant figures. Only the display is rounded. The conversion runs on the number as typed.
A result below 0.0001 in size, or of a billion or more, is shown in scientific notation. Zero is shown as a plain 0.
Negative values are accepted. Torque has a direction of rotation, so a value below zero describes a twist the other way.
An empty box produces a prompt rather than a number. A link carrying a unit the page does not offer produces a message rather than a conversion.

The three units

Unit	Symbol	Newton metres in one unit	Exact by definition
Newton metre	N·m	1	Yes, the SI unit of torque
Pound-force foot	lbf·ft	1.3558179483314004	Yes
Kilogram-force metre	kgf·m	9.80665	Yes

The newton metre is the SI unit: one newton of force acting one metre from the turning point. The other two units are each a fixed number of newton metres. Neither of those numbers is a measurement, so neither changes over time.

A torque written "lb-ft" or "ft-lb" on a spanner or in a service manual is the pound-force foot. The two spellings name one unit, and only the word order differs.

Torque conversion formula

Every unit here is a fixed multiple of the newton metre, so a conversion is one multiplication followed by one division. The value is carried into newton metres, then back out into the unit wanted:

$\tau_2 = \frac{\tau_1 \times k_1}{k_2}$

where $\tau_1$ is the torque typed in, $k_1$ is the number of newton metres in one unit of the chosen unit, $k_2$ is the number of newton metres in one unit of the wanted unit, and $\tau_2$ is the answer.

Nothing is added or subtracted along the way, because all three scales read zero at the same torque. Only the size of the step changes. Temperature is the case where that is untrue: Celsius and Fahrenheit start counting from different points, so a converter that only multiplied would report 0 °C as 0 °F instead of 32 °F.

Where the two non-SI units come from

Both rest on standard gravity, which the 3rd General Conference on Weights and Measures fixed at exactly 9.80665 m/s² in 1901. That is an agreed value rather than a local measurement, and it is what lets a unit of mass stand in for a unit of force.

A pound-force is the 1959 international pound, exactly 0.45359237 kg, pulled by that gravity, which comes to 4.4482216152605 N. A pound-force foot is that force acting one foot from the turning point, and the same 1959 agreement fixes the foot at exactly 0.3048 m.

$1\ \mathrm{lbf}\cdot\mathrm{ft} = 4.4482216152605\ \mathrm{N} \times 0.3048\ \mathrm{m} = 1.3558179483314004\ \mathrm{N}\cdot\mathrm{m}$

A kilogram-force is one kilogram pulled by the same gravity, so a kilogram-force metre is standard gravity written as a torque:

$1\ \mathrm{kgf}\cdot\mathrm{m} = 1\ \mathrm{kg} \times 9.80665\ \mathrm{m/s^2} \times 1\ \mathrm{m} = 9.80665\ \mathrm{N}\cdot\mathrm{m}$

Gravity drops out when those two units are compared with each other, because each carries it once. What is left is the pound times the foot:

$\frac{1\ \mathrm{lbf}\cdot\mathrm{ft}}{1\ \mathrm{kgf}\cdot\mathrm{m}} = 0.45359237 \times 0.3048 = 0.138254954376$

NIST Special Publication 811, Appendix B, lists the pound-force foot rounded to 1.355818 N·m.

Example: a wheel nut tightened to 100 N·m

Dividing by the newton metres in one pound-force foot gives the figure used in the United States and the United Kingdom:

$\tau = \frac{100}{1.3558179483314004} \approx 73.756215\ \mathrm{lbf}\cdot\mathrm{ft}$

Dividing the same 100 by 9.80665 gives the kilogram-force metre figure, which still appears in older service manuals and on some torque wrenches:

$\tau = \frac{100}{9.80665} \approx 10.197162\ \mathrm{kgf}\cdot\mathrm{m}$

For this input the page shows 100 N·m, 73.756215 lbf·ft and 10.197162 kgf·m side by side. All three describe one setting on one wrench. The numbers differ because the units differ, not because the nut is being tightened any harder.

Common torque conversions

Each row shows what one unit produces in the other two, at eight significant figures.

Input	N·m	lbf·ft	kgf·m
1 N·m	1	0.73756215	0.10197162
1 lbf·ft	1.3558179	1	0.13825495
1 kgf·m	9.80665	7.2330139	1

Which values are exact and which are rounded

All three units rest on definitions, but only some of those definitions can be written out in full as decimals.

1 lbf·ft is exactly 1.3558179483314004 N·m. The decimal stops there, because the foot and the pound-force are themselves exact decimals.
1 kgf·m is exactly 9.80665 N·m, the value of standard gravity.
1 lbf·ft is exactly 0.138254954376 kgf·m. Gravity cancels, and the pound times the foot is again an exact decimal.
1 N·m is 0.73756214927726536… lbf·ft, with digits that never end, so any decimal written for it has been cut short.
1 kgf·m is 7.2330138512098943… lbf·ft, also unending.

The converter builds each factor from the defining constants rather than storing a shortened decimal, so the rounding a reader sees comes from the display and not from the numbers behind it. Eight significant figures is wide enough to show a defining value clearly and narrow enough to hide the last digits of the computer's arithmetic, which carry rounding noise rather than information.

Frequently asked questions

How many newton metres is one ft-lb? One pound-force foot is exactly 1.3558179483314004 N·m, which the page shows as 1.3558179 N·m. Going the other way, one newton metre is 0.73756215 lbf·ft.

Is ft-lb the same as lb-ft? Yes. Both name a force of one pound-force acting one foot from the turning point. Manuals use either word order for the same unit.

Is a newton metre the same as a joule? Both are built from a newton and a metre, but they measure different things. A joule measures energy, and a torque does work only while the shaft actually turns. The names are kept apart on purpose: energy is written in joules, torque in newton metres.

What is a kilogram-force metre used for? It is an older metric torque unit, still found in service manuals and on some torque wrenches. One kilogram-force metre is 9.80665 N·m, or 7.2330139 lbf·ft.

Can a negative torque be converted? Yes. Torque is signed, because it has a direction of rotation, so a value below zero describes a twist the other way. The page converts it rather than refusing it.

Why does the page show so many digits? Eight significant figures keeps a defining value legible without showing the last digits of the arithmetic, which carry rounding noise. The stored constants are never shortened, so a short display never feeds back into the next conversion.

Torque Converter: N·m, lbf·ft and kgf·m