Force (measured in newtons, N) and torque (measured in newton-metres, N·m) are different physical quantities, so you cannot convert one into the other with a single unit-conversion factor — to turn a force into a torque you also need a perpendicular lever-arm distance, and the relationship is τ = F × d. Most searches that phrase the problem as "convert force into torque" are actually after one of two underlying tasks: either the reader wants the torque formula spelled out with a distance plugged in, or they have a force value quoted in awkward units (kilogram-force, pound-force, kip, dyne) and need it converted into newtons or another unit before they apply the formula. This article covers both. Below you'll find the exact τ = F × d relationship, a worked example, a reference table of NIST-traceable force conversion factors, and the step-by-step use of the Force Converter, which routes every conversion through the newton using factors from NIST Special Publication 811, Appendix B.8, so a value in kilogram-force or pound-force lands on the same SI base before you multiply by your lever arm.
Force vs Torque: Different Quantities, Not Different Units
Force and torque look similar in everyday speech — both involve pushing, twisting, or "effort" — but in physics they are separate quantities with different dimensions. Force is what accelerates a mass; in symbols, F = m × a, and the SI unit is the newton (N), defined as the force that accelerates a 1 kg mass at 1 metre per second squared (1 N = 1 kg·m/s²). Torque, by contrast, is the rotational equivalent of force: it is what causes an angular acceleration around an axis. The SI unit of torque is the newton-metre (N·m), which already tells you torque is force multiplied by a distance, not a stand-alone "amount of push".
Because the dimensions are different, you cannot replace a force value in newtons with a torque value in newton-metres (or pound-force with pound-foot) using a unit-conversion factor. There is no scalar that turns 100 N into 100 N·m. What you can do, and what most readers who land on this page actually need, is one of the following:
- Apply the torque formula τ = F × d once you know both the force and the perpendicular lever arm.
- Convert the force into a friendlier unit (N ↔ lbf ↔ kgf ↔ kip) before plugging it into the torque formula.
The rest of this article works through both of those tasks in order.
The Torque Formula: τ = F × d
The relationship between force and torque is one short equation:
τ = F × d
where τ is torque (in newton-metres), F is the applied force (in newtons), and d is the perpendicular distance from the axis of rotation to the line of action of the force (in metres). Two details decide whether the result is correct:
- Perpendicular distance. If the force is applied at an angle, only the component perpendicular to the lever arm contributes to torque. The general form is τ = F × d × sin(θ), where θ is the angle between the force vector and the lever arm.
- Unit consistency. Whatever units you use for F and d, the resulting torque will be in those units multiplied together. Newtons × metres gives newton-metres. Pound-force × feet gives pound-foot (ft·lbf). Pound-force × inches gives pound-inch (in·lbf), which is a real US customary torque unit used on torque wrenches alongside ft·lbf.
Note that "metre-kilogram" (m·kg) is not the same thing as newton-metre, even though both involve a mass times a distance. Energy (joules) and torque (N·m) share the same unit dimensions, but they are physically distinct quantities, and torque is never expressed in joules.
Convert the Force First — Then Multiply by Distance
Before you can plug F into τ = F × d, the force has to be in a unit that matches your lever arm. If your spec sheet quotes bolt preload in pound-force but your distance is in metres, the units won't cancel cleanly and you'll end up with a meaningless number. The fastest way to land in the right unit system is to run the force through the Force Converter, which moves any force between newtons (N), kilonewtons (kN), dynes (dyn), kilogram-force (kgf), gram-force (gf), pound-force (lbf), ounce-force (ozf), poundal (pdl), and kip. Every conversion is routed through the newton using factors from NIST Special Publication 811, Appendix B.8, so the result is exact to the published definitions rather than a rounded lookup table.
How to use it:
- Type the amount you want to convert into the force value field.
- Choose the source unit (From) and the target unit (To) — for example Newton to Pound-force, or Kilogram-force to Kip.
- Read the converted result instantly, or tick "Show all units at once" to see newtons through kip side by side.
Everything runs client-side, so the value never leaves your browser — useful if you're working with proprietary load data you don't want to upload. Once the force is in the same unit system as your lever arm, multiply by the distance and you have your torque.
Exact Force Unit Conversion Factors (NIST SP 811)
The table below lists the units the Force Converter handles, with each one defined in terms of the newton. These are the official NIST factors, so any pair you build from them will agree to the last decimal place shown.
| Force unit | Symbol | Exact value in newtons (N) |
|---|---|---|
| Newton (SI) | N | 1 N |
| Kilonewton | kN | 1,000 N |
| Dyne (CGS) | dyn | 0.00001 N (1 × 10⁻⁵ N) |
| Kilogram-force | kgf | 9.80665 N |
| Gram-force | gf | 0.00980665 N |
| Pound-force | lbf | 4.4482216152605 N |
| Ounce-force | ozf | 0.27801385095378125 N |
| Poundal | pdl | 0.138254954376 N |
| Kip (kilopound-force) | kip | 4,448.2216152605 N |
Two mental bridges cover most day-to-day work:
- 1 kip ≈ 4.448 kN, so a structural load quoted in kN can be read off in kips by dividing by 4.448.
- 1 kgf ≈ 9.81 N, so a kilogram-force reading is almost ten times a newton reading for the same physical push.
A Worked Example: 100 N at 25 cm
Suppose a wrench handle is 25 cm long and you push on the end with a force of 100 N perpendicular to the handle. The torque at the bolt is:
τ = F × d = 100 N × 0.25 m = 25 N·m
If the same load were quoted as 22.4809 lbf (because 100 N ÷ 4.4482216152605 = 22.4809 lbf), and the wrench were still 25 cm, you'd want to convert the lever arm to feet before multiplying to keep the units consistent: 0.25 m = 0.82021 ft, so 22.4809 lbf × 0.82021 ft ≈ 18.44 ft·lbf. That's the same torque expressed in US customary units — 25 N·m ≈ 18.44 ft·lbf, because 1 N·m = 0.73756 ft·lbf.
Force-Unit Errors That Skew Torque Results
Most "off by a factor of ten" mistakes in torque work trace back to one of three confusions:
- Kilogram (mass) vs kilogram-force (force). A kilogram is a unit of mass; kilogram-force is the weight of a 1 kg mass under standard gravity, equal to exactly 9.80665 N. If a load cell is rated for 50 kgf and you treat the number as 50 N, your torque will be off by almost an order of magnitude — and in structural work that's the difference between a safe design and a failed one.
- Pound (mass) vs pound-force (force). The split mirrors the metric case. A pound is a unit of mass; a pound-force is the force gravity exerts on a 1 lb mass at standard gravity, equal to exactly 4.4482216152605 N. US engineering specs quote forces in lbf and torques in ft·lbf or in·lbf, never in "lb-ft" in the mass sense.
- Newton-metre vs joule. Both have identical dimensions (kg·m²/s²), but torque is a vector with a direction along the axis of rotation, while energy is a scalar. They are not interchangeable. A torque wrench reads N·m or ft·lbf, never joules.
The Force Converter deals only in force units, which keeps the mass-vs-force distinction from leaking into your torque calculation. Convert first, then multiply by the lever arm.
When Torque Becomes Force (and Back)
The same τ = F × d relationship works in reverse. If you know the torque applied by a motor or a wrench and you know the effective lever arm, you can recover the force: F = τ ÷ d. That calculation is often needed when sizing a fixture, a clamp, or a hydraulic actuator: you start from a required torque, divide by the moment arm of the mechanism, and the result is the linear push or pull the actuator must deliver. Again, get the units consistent first — typically by converting the torque into N·m, the lever arm into metres, and the resulting force will come out in newtons ready for the next stage of the calculation.
For very small forces (surface tension measurements, spring scales, older scientific literature), work in dynes or gram-force; for large structural loads, work in kN or kip. The Force Converter keeps the factors exact, so the only thing left to manage is the lever-arm unit.