69 Torque Units, Every Row an Input

Torque is a force acting at a distance, so it has no single unit. Metric work uses newton-metres, American work uses pound-feet and pound-inches, small motors use ounce-inches, and older data uses kilogram-force metres. This page lists 69 of them in one table. Every row is an input: type a number into any row and all the others fill in at once.

The units run from everyday to extremely obscure. The first tiers are the ones you will actually meet. Further down are the strange ones, like a joule per revolution, the poundal-foot and a newton-furlong. The last tier has a newton at the Sun’s distance and the torque of an electronvolt per radian. Every unit is an exact multiple of the newton-metre, so the conversions are exact to the digits shown.

Torque Converter
Torque Unit Conversion: Type in Any Row
Start From
Either way the table below fills every unit. You can also type straight into any row of the table.
Type a Number in Any Row
You can type here, or directly in any row of the table below. Scientific notation works: 2.5e-3, 1e12.
All Units, Least to Most Obscure
The highlighted row is the one you typed in. Every other row updates as you type. The right-hand column is the size of one unit in N·m.
Show detailed calculation steps
How Every Unit Relates
\[ T = F\,r,\qquad T_{\text{unit}} = \frac{T_{\text{N}\cdot \text{m}}}{k_{\text{unit}}} \] \[ 1\ \text{lbf}\cdot \text{ft} = 1.355818\ \text{N}\cdot \text{m} \] \[ 1\ \text{kgf}\cdot \text{m} = 9.80665\ \text{N}\cdot \text{m} \]

Torque is a force times a length. So each unit is a force unit times a length unit. Its size in N·m, in the right-hand column, is the force factor times the length factor. A pound-force is 4.448222 N and a foot is 0.3048 m, so a pound-foot is 4.448222 × 0.3048 = 1.355818 N·m. The converter turns your number into N·m, then divides by each unit’s size.

Energy per angle

\[ T = \frac{dE}{d\theta}\qquad\Rightarrow\qquad 1\ \text{N}\cdot \text{m} = 1\ \text{J/rad} \] \[ 1\ \text{J/rev} = \frac{1}{2\pi}\ \text{N}\cdot \text{m} \]

Torque is also the energy a rotation transfers per unit of angle. A radian is dimensionless, so a joule per radian is the same as a newton-metre. A joule per degree is 57.3 times larger, because a degree is a smaller angle. This is how torque reaches the atomic scale. The atomic unit of torque is a hartree of energy per radian, and an electronvolt per radian is 1.6×10−19 N·m. A molecular motor turning a flagellum is in the tens of piconewton-nanometres.

Watch the pound. The pound in lbf·ft is the pound-force. The poundal-foot, by contrast, uses the poundal, the force that accelerates one pound of mass at one foot per second squared, which is about 0.138 N. The page also treats kgf·m as kilogram-force metres, the way older torque tables and some wrenches use it.
Factor Reference Guide
Reference
Tiers

What the Tiers Mean

  1. Everyday. N·m, lbf·ft, lbf·in, kgf·m, N·cm, N·mm, kN·m and ozf·in.
  2. Engineering and metric. Other kgf and gf units, decanewton-metres and the prefixed newton-metres from nano to mega. Also kip units, ounce-force feet and the three ton-force feet.
  3. Obscure. Energy per angle, such as J/rad, J/rev and BTU/rad. Dyne units and poundals. A force times an old length, from barleycorns and cubits to furlongs and leagues.
  4. Extremely obscure. A newton at astronomical distances, from the Earth’s radius to the megaparsec. A newton at atomic scales, from the ångström down to the Planck length. Also piconewton-nanometres, hartrees, rydbergs, electronvolts and the reduced Planck constant per unit time.
Constants used
  • Pound-force 4.4482216152605 N, standard gravity 9.80665 m/s², poundal from the pound mass 0.45359237 kg.
  • AU 149,597,870,700 m (exact), light-year from the Julian year, parsec 648,000/π AU.
  • Electronvolt 1.602176634×10−19 J (exact), hartree 4.3597447×10−18 J, rydberg 2.1798724×10−18 J, ħ 1.054571817×10−34 J·s (CODATA 2018).
  • Bohr radius 5.29177×10−11 m, classical electron radius 2.81794×10−15 m, Planck length 1.616255×10−35 m, Planck energy 1.956082×109 J.
Worked Example

The default is 1,200 lbf·in (100 lbf·ft). In the table it reads:

  • 135.58 N·m and 100 lbf·ft, the everyday units
  • 13.83 kgf·m and 0.1356 kN·m
  • 2.366 J/° and 851.9 J/rev: the same torque as energy per degree and per revolution
  • 9.06×10−10 N·AU and 8.46×1020 eV/rad, the extreme ends

Try typing 1 into the newton-light-year row. Every other unit jumps by fifteen orders of magnitude. Or type 40 into the piconewton-nanometre row for a molecular motor. From the lever panel: 50 lbf on a 12 in wrench is 600 lbf·in, which is 50 lbf·ft or 67.79 N·m.

Notes
  • Conversions use exact definitions where they exist. Those cover the international inch and foot, the standard pound-force and gravity, the astronomical unit and the electronvolt. The rest use CODATA 2018 or IAU values.
  • Old length units such as the cubit, fathom and league have several historical sizes. The page uses a common one and states it in the unit name.
  • Torque and energy share the unit N·m, but torque is not energy. The energy-per-angle units are torque in disguise, and are not an amount of energy.
  • Results are shown to the digits you choose. Very small and very large values use e-notation, such as 1.6e-19.

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