Torque Calculator
Calculate torque τ = F × d in Nm and ft-lb from force and lever arm, or solve for any missing variable.
Returns examples for wrenches, engines, and beams.
Torque is the rotational equivalent of linear force — it measures the tendency of a force to rotate an object around an axis. Understanding torque is essential in mechanical engineering, automotive maintenance, construction, and physics education.
Torque formula: τ = F × r × sin(θ)
Where:
- τ (tau) = torque in Newton-meters (N·m) or foot-pounds (ft·lb)
- F = applied force in Newtons (N) or pounds-force (lbf)
- r = moment arm — distance from the pivot point to where force is applied (meters or feet)
- θ = angle between the force vector and the moment arm (lever)
When force is applied perpendicular to the lever (θ = 90°, sin 90° = 1), torque is maximized: τ = F × r
Unit conversions:
- 1 N·m = 0.7376 ft·lb
- 1 ft·lb = 1.3558 N·m
Torque and rotational work: Work (J) = τ × θ (radians) Power (W) = τ × ω where ω = angular velocity (radians/second)
Mechanical advantage of a lever: Effort × Effort Arm = Load × Load Arm (Law of the Lever, Archimedes) Mechanical Advantage = Load Arm / Effort Arm
Common torque values:
| Application | Typical Torque |
|---|---|
| Removing a bolt (1/2" drive) | 50–150 N·m |
| Tightening lug nuts (car wheel) | 90–120 N·m (120–160 ft·lb) |
| Bicycle pedal installation | 35–40 N·m |
| Car engine output (mid-size sedan) | 200–350 N·m |
| Semi-truck engine | 1,800–2,500 N·m |
Worked example: A mechanic applies 40 N of force to a 0.25 m wrench at 90° to tighten a bolt: τ = 40 × 0.25 × sin(90°) = 40 × 0.25 × 1 = 10 N·m
If the torque spec requires 25 N·m, they need either more force (100 N on the same wrench) or a longer wrench: r = τ/F = 25/40 = 0.625 m (62.5 cm)
Torque vs. horsepower: In vehicles, torque determines acceleration (“off the line” pull); horsepower (Horsepower = Torque × RPM / 5,252) determines sustained top-speed performance.