Moment of Force Converter
Convert moment of force, the turning effect of a force about a point or axis, between newton meters, kilonewton meters, kilogram-force meters, pound-force feet and other units. Pick two units, enter a value and read the result instantly.
Select two units to see the conversion factor.
This tool converts moment of force (force × perpendicular distance) only. It is not force itself (newtons) and not energy, even though N·m and joule have the same dimensions.
Moment of Force Formula
Moment of force is force multiplied by the perpendicular distance from the pivot: M = F × d. Every unit is a fixed multiple of the newton meter. Result = value × (source factor ÷ target factor). The building blocks are exact: 1 kgf = 9.80665 N, 1 lbf = 0.45359237 kg × 9.80665 m/s² = 4.4482216152605 N, 1 ft = 0.3048 m, 1 in = 0.0254 m, 1 poundal = 1 lb·ft/s² = 0.138254954376 N, 1 short ton-force = 2,000 lbf, 1 long ton-force = 2,240 lbf and 1 metric ton-force = 1,000 kgf.
What Is Moment of Force?
Moment of force is the tendency of a force to make a body rotate about a point or axis. It equals the force times the perpendicular distance from that point to the line of action of the force, M = F × d, or F × r × sin θ when the force is at an angle θ to the lever arm. A 150 N push applied 0.4 m from a hinge, at right angles to the door, produces a moment of 60 N·m. The SI unit is the newton meter (N·m).
Moments are the basis of statics. A body in equilibrium has no net force and no net moment, which is how support reactions, lever balances and beam loads are found. Structural engineers work in kN·m for bending moments, workshop practice uses kgf·m and lbf·ft, and small instrument work uses mN·m, µN·m or gf·cm. Older or specialised units in this list are the poundal foot and poundal inch (from the absolute foot-pound-second system) and the short, long and metric ton-force meter.
Do not confuse moment of force with force. Force is measured in newtons (N); a moment is force times distance, in N·m. The same force produces a larger moment at a longer lever arm. Moment of force is also not energy: a joule has the same dimension as a newton meter, but a moment is a turning effect about an axis, not an amount of energy. For the twisting action of a shaft or fastener see the Torque Converter.
Supported Units
This converter supports the following 12 moment of force units. The last column gives the value of each unit in the base unit, the newton meter. Units with “force” in the name (kilogram-force, pound-force, ton-force) are based on standard gravity, 9.80665 m/s².
| Unit | Symbol | Value in N·m |
|---|---|---|
| Newton meter | N·m | 1 |
| Kilonewton meter | kN·m | 1,000 |
| Millinewton meter | mN·m | 0.001 |
| Micronewton meter | µN·m | 1e-6 |
| Kilogram-force meter | kgf·m | 9.80665 |
| Gram-force centimeter | gf·cm | 9.80665e-5 |
| Pound-force foot | lbf·ft | 1.355817948 |
| Poundal foot | pdl·ft | 0.04214011009 |
| Poundal inch | pdl·in | 0.003511675841 |
| Ton-force (short) meter | tonf (short)·m | 8,896.443231 |
| Ton-force (long) meter | tonf (long)·m | 9,964.016418 |
| Ton-force (metric) meter | tonf (metric)·m | 9,806.65 |
How to Use the Moment of Force Converter
- Type the moment of force in the value box. Decimals and scientific notation such as 0.0025 or 2.5e-3 are accepted.
- Choose the From unit and the To unit.
- The result appears instantly, or press Convert Now. Very large or very small results are shown in scientific notation.
- Use Swap Units to reverse the conversion, Copy Result to copy the answer, open Show this value in all units for a full list, and Clear to start again.
Step-by-step by hand
- Find the size of each unit in the common base unit (N·m): 1 lbf·ft = 1.355817948 N·m and 1 N·m = 1 N·m.
- Divide the source size by the target size to get the conversion factor: 1.355817948 ÷ 1 = 1.355817948, so 1 lbf·ft = 1.355817948 N·m.
- Multiply by your value: 100 lbf·ft × 1.355817948 = 135.5817948 N·m.
A moment has a rotational direction (clockwise or counter-clockwise), so a minus sign is accepted. Zero is also valid.
Common Moment of Force Conversions
- Pound-force feet to SI: 100 lbf·ft equals 135.5817948 N·m.
- Door example: 150 N at 0.4 m gives 60 N·m, which equals 44.25372896 lbf·ft and 6.118297278 kgf·m.
- Beam bending moment: 12 kN·m equals 12,000 N·m and 8,850.745791 lbf·ft.
- Workshop figure: 8.5 kgf·m equals 83.356525 N·m.
- Instrument range: 250 gf·cm equals 0.024516625 N·m and 24.516625 mN·m.
- Ton-force units: 1 tonf (metric)·m equals 9,806.65 N·m, 1 tonf (short)·m equals 8,896.443231 N·m, and 1 tonf (long)·m equals 9,964.016418 N·m.
- Poundal foot: 1 pdl·ft equals 0.04214011009 N·m.
Pound-Force Foot to Other Moment of Force Units
Quick reference for frequently used values
| lbf·ft | N·m | kgf·m | gf·cm |
|---|---|---|---|
| 1 | 1.355817948 | 0.1382549544 | 13,825.49544 |
| 5 | 6.779089742 | 0.6912747719 | 69,127.47719 |
| 10 | 13.55817948 | 1.382549544 | 138,254.9544 |
| 25 | 33.89544871 | 3.456373859 | 345,637.3859 |
| 50 | 67.79089742 | 6.912747719 | 691,274.7719 |
| 100 | 135.5817948 | 13.82549544 | 1,382,549.544 |
| 250 | 338.9544871 | 34.56373859 | 3,456,373.859 |
| 500 | 677.9089742 | 69.12747719 | 6,912,747.719 |
Where and Why This Conversion Is Used
- Statics and structural engineering: support reactions, bending moments in beams, retaining walls and frames, in kN·m or kip-ft.
- Mechanical design: levers, cranks, brackets and hinges where a force acts at a distance.
- Machine and vehicle design: loads on axles, suspension arms and mounting points.
- Crane and lifting calculations: overturning moments from a load on a boom (heavy loads are often in ton-force meters).
- Instrumentation: small moments measured by balances and torque sensors in mN·m and gf·cm.
Limitations
- The converter changes units only. It does not compute a moment from a force and a distance; multiply the force by the perpendicular distance yourself.
- The value of a moment depends on the point or axis it is taken about, so always state the reference point.
Important Differences Between Related Measurements
- Force vs moment of force: force (N) pushes or pulls. A moment of force (N·m) turns. 100 N at a 0.5 m arm makes 50 N·m, while the same 100 N applied through the pivot makes no moment at all.
- Moment of force vs torque: they have the same dimension and units. “Moment” is the general statics term for the turning effect of a force about any point, such as a bending moment in a beam. “Torque” usually means the twisting moment on a shaft, bolt or motor. The units convert in the same way, and this site lists both converters because the reference unit lists differ.
- Moment of force vs energy: a newton meter and a joule have the same dimension, but a moment is a vector-like turning effect about an axis, while energy is a scalar. A moment of 1 N·m acting through 1 radian does 1 J of work, but the two are not interchangeable and no joule unit appears here.
- Moment of force vs moment of inertia: moment of inertia (kg·m²) is a body’s resistance to rotational acceleration. A moment of force is the push that produces it.
Each converter on this site changes units within one quantity only, and none of them mixes quantities. The related tools are: Velocity - Angular, Acceleration, Acceleration - Angular, Density, Specific Volume, Moment of Inertia, Moment of Force and Torque.