Torque

In plain English

Torque is a twisting or turning effort. Pushing on a spanner turns a nut; pushing harder, or pushing further from the nut, turns it more strongly. That turning strength is torque. Motors produce torque, shafts and gears carry it, and bolts are tightened by it.

Technical definition

Torque (moment of a force about an axis) is the product of a force and its perpendicular distance from the axis of rotation. Its SI unit is the newton metre (N·m). In vector form it is the cross product of the position vector and the force, T = r × F.

How it works and where it is used

Only the part of the force at right angles to the lever arm creates torque. A force pulling along the spanner, towards the nut, produces none. In rotating machinery, torque and speed together give power: a gearbox that reduces speed multiplies torque by almost the same ratio (less friction losses), because power is nearly unchanged.

Formula

T = F × r × sin θ    (θ = 90°: T = F × r)

P = T × ω = T × 2πn ÷ 60    T (N·m) = 9549 × P (kW) ÷ n (rpm)

T = torque (N·m), F = force (N), r = lever arm (m), θ = angle between the arm and the force, P = power (W), ω = angular speed (rad/s), n = speed (rpm).

Worked example

A 250 N push at the end of a 0.4 m spanner, at right angles: T = 250 × 0.4 = 100 N·m (about 73.8 lbf·ft).

A 7.5 kW motor running at 1450 rpm delivers T = 9549 × 7.5 ÷ 1450 = 49.4 N·m. Through a 3 : 1 gear reduction the output torque is about 148 N·m at 483 rpm (before friction losses).

In the workshop and in practice

In the workshop torque appears as bolt tightening torque, the torque a lathe spindle or drill must supply for a cut, the torque rating of a coupling or key, and the starting torque of a motor. Machine designers use the torque to size shafts against torsional stress and twist.

Common mistakes and misconceptions

• Confusing torque with power. A slow, high-torque shaft and a fast, low-torque shaft can carry the same power.
• Using the wrong lever arm. Use the perpendicular distance from the axis to the line of the force.
• Mixing up units. N·m, kgf·m and lbf·ft differ (1 lbf·ft = 1.356 N·m). The joule is also N·m but is used for energy, not torque.
• Assuming tightening torque sets an exact bolt force. Friction makes the clamp force from a given torque vary widely.

Related calculators

• Torque & Shaft Power Calculator — Torque from force × lever arm or from power and speed, and shaft power from torque and speed.
• Gear Ratio Calculator — Gear ratio from teeth or speeds, with output speed, torque and direction for a gear pair.
• Shaft Torsional Stress Calculator — Torsional shear stress and angle of twist of a round shaft, or the diameter needed.
• Bolt Tightening Torque Estimator — Tightening torque from preload (T = K·F·d), preload from torque, or a preload target from proof strength.

Related topics

• Stress and Strain — Internal force per unit area, and the stretch per unit length it causes.
• Cutting Speed — How fast the cutting edge moves across the work material, in m/min or SFM.

References

• ISO 80000-4: Quantities and units — Mechanics (moment of force, torque, power)
• Hibbeler, Engineering Mechanics: Statics (moments of a force)
• Shigley’s Mechanical Engineering Design (Budynas and Nisbett), power transmission and shafts