Torque

Torque is the rotational equivalent of force, it describes the tendency of a force to cause an object to rotate around a pivot point or axis. Rather than measuring straight-line push or pull the way ordinary force does, torque captures the twisting effect that occurs when force is applied at some distance from a fixed point, such as turning a steering wheel, tightening a bolt, or spinning a bicycle pedal.

The Torque Calculator computes this rotational effect from three inputs, the applied force, the length of the lever arm (the distance from the pivot to where the force is applied), and the angle between the force and the lever arm, returning the result in newton-meters. This is a distinct calculation from the separate bolt-torque-calculator, which instead looks up or applies manufacturer-specified fastener tightening specifications rather than computing torque from first principles; the Torque Calculator here is for general rotational mechanics problems in physics and engineering.

Torque plays a central role in rotating machinery, where it combines with angular velocity to determine power output, following the same underlying relationship that connects Work and Power in linear motion. It's also a direct application of the rotational form of Newton's laws, just as Newton's Second Law relates linear force to linear acceleration (F = ma), torque relates to angular acceleration through an object's rotational inertia.

τ = r × F × sin(θ)

Where τ (tau) is torque (in newton-meters, N·m), r is the lever arm length, the distance from the pivot to the point of applied force (in meters, m), F is the applied force (in newtons, N), and θ is the angle between the force vector and the lever arm.

When force is applied perpendicular to the lever arm (θ = 90°), this simplifies to τ = r × F.

A mechanic applies 150 N of force perpendicular to a wrench handle that is 0.3 meters long. The torque generated is:

τ = 0.3 m × 150 N × sin(90°) = 0.3 × 150 × 1 = 45 N·m

If the mechanic instead pushed at a 45-degree angle to the wrench handle rather than perpendicular to it, the torque would drop to 0.3 × 150 × sin(45°) = 0.3 × 150 × 0.707 ≈ 31.8 N·m, noticeably less effective, which is why applying force perpendicular to a wrench produces the most turning power.

• Maximized at a 90-degree angle: torque is greatest when force is applied perpendicular to the lever arm, since sin(90°) = 1 is the maximum value of the sine function.
• Longer lever arms multiply torque: doubling the distance from the pivot doubles the torque for the same applied force, which is why longer wrenches and longer wheelbraces make turning stubborn bolts easier.
• Distinct from the bolt-torque-calculator: that separate tool applies fastener-specific tightening specs (a manufacturer torque value for a given bolt size and material), while this general torque relationship (τ = rF·sinθ) applies to any rotational mechanics problem.
• Connects to rotational Power: in engines and motors, power equals torque times angular velocity (P = τ × ω), linking rotational force directly to energy delivery rate.
• Rotational analogue of Newton's Second Law: just as force causes linear acceleration via F = ma, torque causes angular acceleration via the rotational form of the same law, with rotational inertia replacing mass.