This all-in-one online Torque Calculator performs calculations using a formula that relates the torque produced by a force applied to an object and the respective lever arm. You can enter the values of any two known parameters in the input fields of this calculator and find the missing parameter.
Torque Formula
In physics and mechanics, torque (also called moment, moment of force or rotational force) is the ability of a force to cause a change in the rotational motion of a body. The concept of torque is used mainly in solving statics problems and problems related to the rotation of parts (levers, etc.) in technical mechanics.
Torque is a vector \(\overrightarrow{\tau}\) which is defined as the cross product of the radius vector of the point of application of the force \(\overrightarrow{r}\) and the applied force vector \(\overrightarrow{F}\):
$$\overrightarrow{\tau} = \overrightarrow{r} × \overrightarrow{F}.$$
The magnitude of the torque depends on the choice of the radius vector reference point. In the especially important case of rotation of a solid body around a fixed axis, the reference point is chosen on that axis. Then, instead of the torque itself, we consider its projection onto this axis, such a projection is called the torque relative to the axis.
So, the torque relative to the axis of rotation \(\tau\) is calculated as the product of the magnitude of the applied force \(F\) by the length of the radius vector \(r\) and the sine of the angle \(\theta \) between the radius vector and the force vector:
$$\tau = r \cdot F \cdot sin(\theta).$$
It is easy to see that \(r \cdot sin(\theta)\) is the lever arm, in relation to which the applied force \(F\) acts in the perpendicular direction. This very lever arm is one of the parameters in our calculator.
Torque has the dimension of force times distance, or M·L2·T−2. Although these fundamental dimensions are the same as those of energy or work, the official SI unit of torque is the newton-metre (N⋅m). In terms of SI base units we have:
$$1\ N⋅m = 1\ \frac{kg\cdot m^2}{s^2}.$$
The other most common units of torque, also used in our Torque Calculator, are:
• 1 Ncm = 0.01 Nm
• 1 kg-cm = 0.098066 Nm
• 1 ft-lb = 1.35582 Nm
• 1 J/rad = 1 Nm
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