Torque: How to Calculate Rotational Force with Force and Distance
Torque is force times the perpendicular distance from the pivot: push down with 200 N on a wrench handle 0.4 m from the bolt and you apply 80 N·m. The same push on a 0.6 m handle gives 120 N·m, which is why a longer wrench frees a bolt a short one cannot. This guide covers the formula, the angle and unit corrections that most often go wrong, and how torque is used for fasteners, levers and motors.
What Torque Is
Torque (also called moment) is a force's tendency to rotate an object about an axis. Where a force pushes in a straight line, torque twists. It captures two things at once: how hard you push and how far from the pivot you push. A small force far from the axis can out-turn a large force close to it, which is the principle behind levers, breaker bars and gearing. Engines are rated by torque alongside horsepower because torque is what accelerates a load; fastener makers publish torque values so bolts are tightened enough to hold and not so much that they stretch or snap.
How to Calculate Torque
For a force applied at right angles to the lever arm:
Torque = Force × Distance
Force in newtons and distance in meters give newton-meters (N·m); pounds-force and feet give pound-feet (lb·ft), and 1 lb·ft = 1.3558 N·m. The distance, or moment arm, is the perpendicular distance from the axis of rotation to the line along which the force acts.
Worked example. Tightening a bolt with a wrench, pushing down on the handle with 200 N at a point 0.4 m from the bolt's center:
1. Force: 200 N
2. Lever arm: 0.4 m
3. Torque: 200 × 0.4 = 80 N·m (about 59 lb·ft)
A longer wrench with the hand 0.6 m out gives 200 × 0.6 = 120 N·m from the same effort. The Torque Calculator multiplies force in newtons by distance in meters and returns N·m.
Angled forces. If the force is not perpendicular to the arm, only the perpendicular component counts: torque = force × distance × sin(angle between them). Pushing straight along the handle (angle 0°) produces no torque at all; at 60° you get about 87% of the perpendicular value.
Where Torque Is Used
Fasteners. Bolts and lug nuts have specified torque values. Too little and the joint loosens under vibration; too much and the bolt yields or shears. A torque wrench applies a repeatable value, and the Bolt Torque Calculator estimates the tightening torque for a target clamp load from bolt diameter, material strength and the friction condition of the threads.
Levers and tools. Breaker bars and cheater pipes exploit the distance term: a longer arm multiplies torque with no extra effort.
Motors and engines. Matching a motor to a load means checking it produces enough torque to start and sustain rotation against the resistance. For engines, power follows from torque and speed; the Horsepower from Torque Calculator uses HP = torque (lb·ft) × RPM ÷ 5,252.
Balance. A seesaw, crane or balance scale is in equilibrium when the torques on either side of the pivot are equal, which is how counterweights are positioned.
Common Mistakes
Ignoring the angle. Force × distance assumes a right angle. Use the perpendicular component otherwise.
Mixing units. N·m, lb·ft and in·lb are not interchangeable. A value meant as inch-pounds applied as foot-pounds is twelve times too high.
Measuring to the wrong point. The lever arm runs from the pivot to where the force acts, measured perpendicular to the force, not along the handle if the handle is bent or the grip is offset.
Over-torquing. Exceeding the specified value strips threads, cracks parts or weakens the bolt. Trust the published figure, not feel.
Equating wrench torque with clamp force. Most of the torque applied to a bolt is consumed by friction under the head and in the threads, so the same torque gives different clamp loads dry versus lubricated. Critical joints use angle-tightening or direct tension measurement for this reason.
Related guide: Beam Deflection: How to Calculate How Much a Beam Bends Under Load covers the bending moment that torque-like loading produces in a beam.