Calculation
M = F · r
Only the force component perpendicular to the axis produces torque.
M = F·r
Torque Calculator: Force and Lever Arm
Only the force component perpendicular to the axis produces torque.
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Result
Select a target and calculate.
Technical principle schematic
Understand the inputs
- Torque M — Moment about the axis.
- Tangential force F — Force perpendicular to the arm; resolve angled forces first.
- Effective lever arm r — Perpendicular distance from line of action to axis.
Example
500 N on a 0.2 m lever produces 100 N·m.
Assumptions and limits
Force is tangential; friction and dynamics are excluded.
Understand Torque Calculator: Force and Lever Arm
This calculator finds the missing quantity among torque M, force F and lever arm r from the other two. It shows why only the force component perpendicular to the lever direction produces the full torque, and explains why newton-metres (N·m) are never equated with joules (J) despite sharing the same SI base units.
What does this quantity describe?
Torque describes the turning effect of a force about a pivot point or axis. For a force F acting perpendicular at a distance r from the axis, M = F·r. If the force acts at an angle to the lever arm, only the perpendicular component is effective, giving the general form M = F·r·sin(θ), where θ is the angle between the force and the lever arm.
A door opens easily with little force at the door handle, because the handle sits far from the hinges (the pivot axis) — a large lever arm. Pushing instead close to the hinges produces a much smaller turning effect for the same force, because the effective lever arm is small.
Formula and variables
M = F · r
M = F · rF = M / rr = M / FM = F · r · sin(θ) for an angled force
| Symbol / input | Meaning |
|---|---|
| Torque M | Moment about the axis. |
| Tangential force F | Force perpendicular to the arm; resolve angled forces first. |
| Effective lever arm r | Perpendicular distance from line of action to axis. |
Choose the inputs correctly
Enter two of the three quantities. Torque requires force and lever arm, force requires torque and lever arm, lever arm requires torque and force. The lever arm r is always the perpendicular distance between the axis and the force's line of action, not necessarily the physical part length.
How to use the calculator
Select the target quantity and enter the two known values with units. If the force does not act perpendicular to the lever arm, first determine the effective component using F·sin(θ) before entering it into the calculator.
Worked example
Given F = 500 N and r = 0.2 m, with the force perpendicular to the lever arm, substitution gives M = 500 N · 0.2 m = 100 N·m. For a 100 N·m tightening torque with a 0.2 m long wrench, a force of 500 N must therefore be applied at the end of the wrench.
Understand the result and units
A torque of 100 N·m means the combination of force and lever arm produces a turning effect equivalent to a 100 N force on a 1 m lever. Whether this is enough depends on the application, such as a bolted joint's specified tightening torque or the breakaway torque required.
The SI unit is the newton-metre (N·m). Larger torques are given in kN·m; lb-ft or lb-in are common in the US. For bolted joints N·mm is also common: 1 N·m = 1,000 N·mm.
Why aren't newton-metres and joules the same thing?
Torque and work share the SI base unit kg·m²/s² but are deliberately named differently. A joule is the energy transferred when a 1 N force moves an object 1 m in the direction of the force — a scalar quantity. A newton-metre of torque instead describes the turning effect of a force at a perpendicular distance of 1 m from the axis — a directed quantity in which the force and lever-arm directions are perpendicular to each other. Formally, 1 N·m of torque equals 1 J per radian; since the radian is dimensionless, N·m is kept as the dedicated torque unit to avoid confusion with energy.
Typical applications
Torque calculations are used to design bolted joints, electric motors, gearboxes, tools such as torque wrenches, and lever mechanisms.
Assumptions, limits and common mistakes
The formula M = F·r applies to a perpendicular force on a rigid lever. For angled forces only the sine component is effective; at θ = 0° (force parallel to the lever arm) no torque is produced at all, while at θ = 90° the turning effect is maximal for given F and r. Friction, lever elasticity and dynamic effects are not included in the basic formula.
Common mistake: Do not equate newton-metres (torque) with joules (energy): both share the SI base unit kg·m²/s², but describe different physical quantities — torque is a directed (vector) quantity perpendicular to the plane of action, energy is a scalar. This is why torque is always expressed in N·m, never J. Also, do not confuse the lever arm with the full part length when the force does not act at its outermost point.
Frequently asked questions
What is the difference between force and torque?
Force is a directed quantity in newtons that accelerates or deforms a body. Torque is the turning effect of a force about an axis and additionally depends on the lever arm; the same force produces a larger torque on a longer lever.
Are newton-metres and joules the same?
No, even though both share the same SI base unit. Torque (N·m) and energy (J) are different physical quantities and are therefore never expressed with the same unit label.
When is torque maximal for a given force and lever arm?
When the force acts perpendicular to the lever arm, i.e. θ = 90°. At θ = 0°, where the force pulls or pushes along the lever arm, no torque is produced.
How do I convert N·mm to N·m?
Divide the value in N·mm by 1,000 to get N·m.