Torque (Moment of Force) Calculator — τ = rFsin(θ)
Enter any 3 of force, lever arm length, and angle to instantly solve for the 4th (torque, force, lever arm, or angle) — with automatic N·m to ft·lb unit conversion.
Typical tightening torque reference values
| Application | Typical torque |
|---|---|
| Car wheel lug nuts | 100 - 140 N·m（74 - 103 ft·lb） |
| Spark plugs | 20 - 30 N·m（15 - 22 ft·lb） |
| Bicycle stem bolts | 5 - 6 N·m（3.7 - 4.4 ft·lb） |
| Laptop case screws | 0.2 - 0.3 N·m（0.15 - 0.22 ft·lb） |
Usage Tips
- Choose which variable you want to solve for (τ, F, r, or θ) first — the other three input fields will appear automatically.
- Torque is maximized when the angle is 90°, and drops to zero at 0° or 180°, since the force becomes parallel to the lever arm and can no longer produce rotation.
- When solving for the angle, two mathematical solutions exist because sinθ = sin(180° − θ); this tool always shows the primary value between 0° and 90°.
- Automotive torque wrenches are often calibrated in ft·lb (foot-pounds), so results are always shown in both N·m and ft·lb for convenience.
- The lever arm length is the perpendicular distance from the pivot to the line of the applied force — if the force is parallel to the arm (θ = 0°), it produces no rotational effect at all.
Frequently Asked Questions
Side Note — Why a Longer Wrench Makes Loosening Bolts Easier
The common piece of workshop wisdom — 'the longer the wrench handle, the less force it takes to loosen a stubborn bolt' — is a direct, practical expression of the torque formula τ = rFsinθ. To produce the same torque τ, the required force F is inversely proportional to the lever arm length r. That's exactly why the trick of slipping a length of pipe over a wrench handle (a so-called 'cheater bar') works so well — though exceeding a tool's design limits this way risks breakage or injury, so staying within recommended torque specifications matters for safety.
Torque wrenches are considered essential tools in auto mechanics because under-tightening a bolt risks loosening or falling out, while over-tightening risks yielding the bolt or stripping the threads. Manufacturers specify precise target torque values (usually in N·m or ft·lb) for components like wheel lug nuts and cylinder head bolts, and hitting that number accurately is central to repair quality.
The concept of torque extends far beyond engineering and construction — it shows up in everyday design too. A doorknob is placed near the edge of a door rather than at its center specifically so the force is applied as far as possible from the hinge (the pivot), maximizing torque for a given amount of push and making the door easy to open with minimal effort.