What Is Torque?
Torque (also called moment of force) is a measure of the turning force on an object. When you use a wrench, push a door handle, or turn a steering wheel, you’re applying torque. It depends on three things: how hard you push, how far from the pivot you push, and the angle of your push.
τ = Fr sin(θ)
Where F is the applied force, r is the distance from the axis of rotation to the point of force application (lever arm), and θ is the angle between the force vector and the lever arm. Maximum torque occurs when θ = 90°.
τ = Iα (Rotational Newton’s 2nd Law)
Just as F = ma relates force to linear acceleration, τ = Iα relates net torque to angular acceleration. I is the moment of inertia (how mass is distributed relative to the axis), and α is the angular acceleration in rad/s².
Gear Torque Conversion
In a simple gear pair, the output torque equals the input torque multiplied by the gear ratio (driven teeth / driver teeth). A larger driven gear increases torque but reduces rotational speed. This is the principle behind transmissions, bicycle gears, and industrial gearboxes.
Torque Units
| Unit | Symbol | Conversion to N·m |
|---|---|---|
| Newton-metre | N·m | 1 (base) |
| Pound-foot | lb·ft | 1.3558 |
| Pound-inch | lb·in | 0.1130 |
| Kilogram-force metre | kgf·m | 9.8067 |
Common Bolt Torque Specifications
| Application | Torque (N·m) | Torque (lb·ft) |
|---|---|---|
| Car lug nut (M12) | 80–110 | 60–80 |
| Car lug nut (M14) | 110–140 | 80–100 |
| Bicycle pedal | 35–40 | 25–30 |
| Bicycle stem bolt | 5–8 | 3.7–5.9 |
| Spark plug | 15–30 | 11–22 |
| Engine head bolt (typical) | 60–120 | 44–89 |
These are typical ranges. Always consult the manufacturer’s specifications for the exact torque value.
How to Use the Calculator
- Select what to find: torque, force, lever arm, angle, or gear torque.
- Enter known values and select units.
- Click Calculate.
- View torque in multiple units with formula breakdown.
Example Calculations
100 N at 0.3 m, 90°
τ = 100 × 0.3 × 1 = 30 N·m
Wrench: 50 N at 25 cm
τ = 50 × 0.25 = 12.5 N·m
τ = Iα: I = 2 kg·m², α = 5 rad/s²
τ = 2 × 5 = 10 N·m
Gear: 10 N·m input, 20T → 60T
T₂ = 10 × (60/20) = 30 N·m (3:1 ratio, speed reduced by 3×)
Common Mistakes
- Forgetting sin(θ) when force is not perpendicular to the lever arm.
- Confusing torque (N·m) with energy (J) even though they share dimensions.
- Using the total length instead of the perpendicular distance to the line of action.
- Mixing lb·ft with lb·in (a factor of 12 error).
- Ignoring friction losses in gear calculations.
Accuracy and Limitations
These calculations assume a rigid body, a well-defined axis of rotation, and a single point of force application. Gear calculations assume ideal (frictionless) meshing. Real-world factors like material deformation, multiple forces, and friction at the pivot affect actual torque. Use for education and estimation.
FAQ
What is torque?›
Torque is the tendency of a force to rotate an object about an axis. It depends on force magnitude, lever arm length, and the angle between them.
What is the difference between torque and force?›
Force pushes or pulls in a straight line. Torque causes rotation. Torque = force × perpendicular distance from the axis.
Why is a longer wrench easier to use?›
A longer wrench increases the lever arm (r), so less force is needed for the same torque: F = τ/r.
Is N·m the same as joules?›
Dimensionally yes (both are kg·m²/s²), but they measure different things. N·m for torque and J for energy should not be interchanged.
What is the rotational equivalent of Newton’s second law?›
τ = Iα, where I is moment of inertia (kg·m²) and α is angular acceleration (rad/s²). Just as F = ma relates force to linear acceleration, τ = Iα relates torque to angular acceleration.
How do I convert lb·ft to N·m?›
Multiply by 1.3558: 1 lb·ft = 1.3558 N·m.
What is the difference between torque and moment?›
In physics and engineering, torque and moment are often used interchangeably. Strictly, ‘moment’ is the general term for a force’s turning effect, while ‘torque’ specifically refers to twisting (rotation about the long axis). In practice, most sources treat them as synonyms.
How much torque to tighten a lug nut?›
Typical automotive lug nut torque is 80–140 N·m (60–100 lb·ft), depending on the vehicle. Always check your vehicle’s manual for the correct specification. Over-torquing can stretch or break studs.
How do gears affect torque?›
A gear pair trades torque for speed. The output torque equals input torque multiplied by the gear ratio (N₂/N₁). A larger driven gear increases torque but reduces angular velocity.
Sources
Author & technical reviewer
Manish Kumar
PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.
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