# Torque Calculator

 Torque J (N.m)MJkJmJuJWatt HourskW Hours Radius mpmnmmicrons (µm)mmcmkmmilinchesfeetyardsmilesPlanckBohrsAngstromlight-secondslight-yearsauparsecspointscubitsfathomsrodschainsleagues Force N (kg⋅m/s²)µNmNkNMNatomic unitdynepdllbfkg-forceton-force Angle degrees (°)milliradiansradiansgradarcsecondsarcminutescircles Please enter valid input

## Definition

Torque is a measure of how much a force acting on an object causes that object to rotate.

The object rotates about an axis, which we will call the pivot point, and will label ‘O’. We will call the force ‘F’. The distance from the pivot point to the point where the force acts is called the moment arm, and is denoted by ‘r’.

The direction of the torque is given be the right hand rule i.e If we put our fingers in the direction of r, and curl them to the direction of F, then the thumb points in the direction of the torque vector.

There may be more than one force acting on an object, and each of these forces may act on different point on the object. Then, each force will cause a torque. The net torque is the sum of the individual torques. In rotational equilibrium, the sum of the torques is equal to zero. In other words, Net torque on the object is zero.

## Formula

Torque is the cross product between the distance vector (the distance from the pivot point to the point where force is applied i.e. r) and the force vector i.e. F, ‘ θ ‘ being the angle between r and F.

T(Nm) = r(m) * F(N) * Sin θ

where :

T: The torque produced

θ: The acute angle between the radial and force lines

r: The radial distance from the axis to the point of application of the force

F: The force applied

Example:

1. Determine the torque on a bolt, if it is pull with a force of 100 N directed perpendicular to a wrench of length 10 cm?

Sol. :

F = 100N, r = 10 cm = 0.1 m , θ = 90º

τ = 0.1(m) * 100(N) * sin90

τ = 10 N

2. Calculate the force required to produce 10 Nm torque at an angle of 30º from along a 200 cm rod?

Sol. :

τ = 10 Nm , θ = 30º , r = 200 cm = 2 m

F= τ / (r*sinθ)

F= 10(Nm) / (2(m) * sin30º) = 10 / (2 x 0.5)

F = 10 N

## Units

The standard unit of measurement for torque is Newton-metre(i.e. N.m)

Note – Newton-metre is also a way of expressing a Joule (the unit for energy). But torque is not energy. The difference is that energy is a scalar quantity, whereas torque is a vector quantity.

Below is the conversion chart of various other units of Torque