# Torque Conversion Calculator

## What is Torque?

Torque is a measure of the force which can make an object rotate about an axis. In linear kinematics, the force causes an object to accelerate linearly, similarly, torque is what causes an object to acquire an angular acceleration. It’s a vector quantity, meaning it has both magnitude and direction. The direction of the torque vector depends on the direction of force acting on the rotational axis. In physics, torque is simply a twisting or a turning force. Different terminologies are used interchangeably to describe torque such as Moment or Moment of Force. We can say torque is a special case of Moment, as it relates to the rotational axis driving the rotation. On the other hand, for Moment to cause rotation, a driving external force is required.

For any object to experiences torque, it must have a pivot point. If you have ever opened a door, then you have an intuitive understanding of torque. Torque is what causes the door to open about its hinges, thus the hinges are the pivot point. Note, whenever you’re opening a door, you don’t exert a force at the hinges, as the door won’t move. Also, you would need to apply a lot of force if you’re pulling or pushing the door on the side closest to the hinges. Instead, the easiest way to open the door would be to push or pull it on the side that is far away from the hinges. That way, you’ll apply a force perpendicular to the line joining the hinges and the point of the force application. This maximizes the torque you exert at the hinges causing the door to open much more easily. Generally, people prefer to apply less force even if it’s over a larger distance (which is torque), hence the usual location of the door handle.

## Types of Torque

Torque can be classified as either dynamic or static.

• Dynamic Torque: This is the torque quantity related to the force on a mechanism that is rotating. For example, the propeller shaft of a racing car accelerates from the starting line exhibiting dynamic torque to produce an angular acceleration to the wheels; which causes the race car to accelerate along the track.
• Static Torque: This type of torque doesn’t produce an angular acceleration. For instance, when you pull a door handle, you apply a static torque to the door hinges; since the door doesn’t rotate about its hinges, in spite of the force applied. Moreover, when someone is pedaling a bicycle at a constant speed, they’re also applying static torque as there is no acceleration being is produced.

## Torque in our day-to-day Life

Whenever a force causes a rotating or turning movement, torque is bound to be produced. There are many real-life applications of torque that happen all around us-though we may not realize it. To give you an idea of torque in our daily lives, here are some interesting applications of torque:

A) Wrenches: When you use a wrench to loosen or tighten a nut around a bolt, you exert a 90o pulling force around the axis of the rotation axis of the nut. This allows torque to kick in and produce a turning effect. In such a case, several forces act simultaneously on the wrench, so, to get the amount of torque involved you’ll have to sum up all those forces and multiply the resultant force with the distance from the pivot to the point force application. You can increase the torque for turning the nut by increasing the force applied or the distance from the point of force application to the pivot point.

B) Seesaw: At one point when younger, you may have used a seesaw to play with your friends. A seesaw works in a quite simple way: As someone sits on one end and another person sits on its other end. If the two people have different weights, the heavier person can easily lift the lighter person. However, when the heavier person sits closer to the pivot, the moment arm length on their end decreases, resulting in less amount of exerted torque, and the person lighter in weight can now lift the heavier person. A shorter length of the lever arm results in a lower value of the exerted torque.

C) Torque in cars: You’ll often come across the word torque in the automobile industry, especially in the engine specifications. In cars, the engine’s crankshaft rotates about an axis, producing torque- it’s simply the engine’s rotational force. The more torque an engine’s crankshaft produces, the greater the ability of the engine to perform work. Hence, torque can be used as a measure of how powerful a vehicle is. Torque is what drives big trucks hauling heavy loads into motion. Torque is also what rockets a racing car from 0-60mph (miles per hour) in approximately 3 seconds.

D) Steering Wheel: The rotational force which is created when turning the steering wheel of a vehicle is torque. Have you ever noticed the steering wheel of an SUV (Sport Utility Vehicle) is smaller compared to that of an 18-wheeler truck, though they have the same functionality? Well, this is because maneuvering an 18-wheeler truck requires a lot more rotational force than doing so for an SUV. So, whenever the radius of the steering wheel from the fulcrum point is increased, the amount of force required to produce a turning effect will reduce. This torque concept in a larger steering wheel is what makes it easy for the truck driver to maneuver the 18-wheeler, otherwise, it would be very difficult to do so using a smaller steering wheel.

## How is Torque Calculated?

In order to find an unknown linear force, we only need to know the mass and acceleration of the object on which the force is acting. However, with torque, it is slightly different, due to the involvement of rotation. Because torque refers to the turning effect or the twisting force that causes motion around an axis of rotation. Note, the radius at which the twisting force acts is sometimes referred to as the moment arm. So, to find the magnitude of the torque, we not only need to know the linear force but also how far the applied force is from the axis of rotation.
A simple way of calculating the magnitude of torque is to first determine the length of the lever arm and multiply it with the value of the applied linear force. In other words, the amount of torque is defined by the magnitude of the linear force acting on an object and the distance of the applied force from the pivot point of the object. Mathematically torque can be expressed as: T = F × r × sinθ………(1.1)

T = Torque

F = Linear force

r = the distance between the point of linear force application and the pivot point (the axis of rotation), or simply the lever arm length

theta (𝜃) = the angle between F and r

Overall, torque depends on (i) the magnitude of the linear force; (ii) the distance between the point of force application and the rotational axis (the length of the moment arm); (iii) the orientation of the linear force in relation to the displacement from the axis of rotation to the point of the force application.

Torque being a vector quantity, it is calculated using a vector or cross product. Such that, the formula is given in Eq. (1.1) can be expressed in vector form; as a cross product of the force vector and the radius vector. So, torque as a vector product is given by the following formula:

τ→ = F→ × r→………(1.2)

Where,

𝜏→ = is the torque vector

F→ = is the force vector

r→ = is the radius vector

The equation for calculating the magnitude of a torque vector from Eqn. (1.2) is expressed as:

|τ| = ||r|| . ||F|| sinθ ………(1.3)

In which, (𝜃) is the angle between the radius vector and the force vector.

## Determining the Direction of Torque

The direction of the torque vector (𝜏→) depends on the direction of the force on the rotational axis. Conventionally, the direction of the torque vector is determined using the right-hand grip rule. If you curl your right hand around the axis of rotation of the object on which the torque is acting on, with your fingers pointing in the direction of force; then your thumb will point towards the direction of the torque vector. As illustrated in the diagram to the right:

From the diagram to the right, we can see that the applied torque is in the direction of the resulting angular velocity, so by changing the torque direction you also change the angular velocity. Alternatively, you can find the direction of torque using vector product notations in Eq. (1.2).

## What are the Units of Measurement of Torque?

The Greek letter tau (𝜏) is normally used to represent torque in calculations. Also, when torque is referred to as the moment of force, it is represented by M. From the formula of vector torque in Eq. (1.3); sin (𝜃) has no units, the units of F are Newtons(N), and r has units(m). Combining these together, the magnitude of torque can be measured in Newton-meter (Nm). In this case, N is the SI unit of force (Newton), and m is the meter, the SI unit of distance. Hence, the International System of Measurement units (SI units) used in torque calculations is Newton-meter (Nm). Note, although Nm is equal to joules- which is the SI unit for Work or Energy, torque is only measured in terms of Newton-meter.

In the imperial system, vector torque is measured in terms of pound-force-feet(lb-ft), which can simply be abbreviated as pound-foot, with the “force” being implied. For small torque values, pound-force-inch(lbf-in) can be used. Practitioners depend on the hyphen in the abbreviation and the context to determine whether the Imperial unit is used to refer to torque and not to moment of mass or energy. For example, it is easy to confuse pound-feet(lb-ft) with foot-pounds(ft-lb), as one ft-lb doesn’t refer to a twisting force, but to the amount of energy you’ll need to raise a 1pound(1lb) weight at a distance of 1foot(1ft). In addition, torque is dimensionally represented as force ×× distance, symbolically as M1L2T−2M1L2T−2. Where, M=Mass, T =Time, and L= Length.

## Examples of Torque Calculations

Example 1: An automobile mechanic applies a force of 800N to a wrench to loosen a nut with a bolt. He applies the force perpendicularly to the arm of the wrench. The distance from the nut to the mechanic’s hand is 0.40m. Determine the magnitude of the torque the mechanic is applying.

Solution: In this case, we can use the torque formula in Eqn. (1.3); keeping in mind that the angle between the force vector and the moment arm of the wrench is 90°

τ = F × r × sinθ = 800N  × 0.4m  × sin90°

τ = 800N × 0.4m × 1 = 320Nm

Hence, the magnitude of the torque applied by the mechanic to the nut is 320Nm.

Example 2: To open a door, a person is pulling the door handle with a force of 210N. If the door handle is located 72.0 cm from the hinges. And assuming that the person pulls straight back on the door handle, so the force is applied perpendicular to the door handle. Compute the torque applied.

Solution: In this case, the length of the lever arm is 0.720m, and θ=90°. So,

τ = F × r × sinθ = 210N × 0.720m × sin90°

τ = 210N × 0.720m × 1 = 151.20Nm

Note, pulling straight back on the door handle maximizes the torque applied when you pull against the handle at an angle. This will make it easier to open the door. Also, if the turning effect is clockwise then the torque will be negative (i.e., -151.20Nm for clockwise turning).

## Why is Calculating Torque Important?

From the applications mentioned previously, we can see that torque exists almost everywhere. If torque didn’t exist there could be no turn, no twist, and no spin; we all would only be able to do things linearly. Thus, torque is a key concept of physics that helps us to understand how things function around us. Most importantly, calculating torque values helps us to determine the magnitude and the direction of the rotational or twisting force applied to an object. This allows you to assess the results the force may generate.

Moreover, the direction of torque can assist you to determine whether the applied rotational force will result in a clockwise or counterclockwise motion. Also, the amount of torque can also help you predict the angular acceleration of the object being rotated.

## Torque Conversion Calculator

The magnitude of torque is measured by multiplying two factors- the amount of linear force applied and the distance from the point of force application to the axis of rotation. For this reason, the amount of torque can be written in different units of force and distance, as previously discussed. Also, the magnitude of torque can either be small or large, so it is measured in different units. And being able to easily convert the torque value in all those units is very important.

Carrying out torque conversions by hand tends to be inaccurate; given that most of the units don’t convert in whole numbers. The task can also be tedious, which could delay other important tasks especially in the design stage of equipment and machinery. For these reasons, a torque conversion calculator is preferred. A torque conversion calculator is a tool designed to convert between the different units of torque. Using the calculator, you can easily convert torque values from one type of unit measurement scale to another.

The torque conversion calculator can convert units in measurement size, such as from ozf-in (ounce force inch) to lbf-ft (pound-force foot). Or from one measuring system to another, such as from ozf-in (ounce force inch) to kgf-cm (kilogram-force centimeter). Outlined below are some of the International Torque Measuring Systems provided by most Torque Conversion Calculators:

## International Torque Measuring Systems

 Type of Unit of Measurement Description Abbreviation American Ounce force inch ozf-in American Ounce force foot ozf-ft American Pound force inch lbf-in American Pound force foot lbf-ft International Standard – S.I. Milli-Newton meter mN-m International Standard – S.I. Centi- Newton meter cN-m International Standard – S.I. Micronewton meter µN-m International Standard – S.I. Newton meter N-m International Standard – S.I. Kilonewton meter kN-m International Standard – S.I. Meganewton meter MN-m International Standard – S.I. Newton centimeter N-cm Metric gram force centimeter gf-cm Metric kilogram force centimeter kgf-cm Metric kilogram force meter kgf-m Metric dyne meter dyn-m Metric dyne centimeter dyn-cm Metric dyne millimeter dyn-mm Metric gram force meter gf-m Metric gram force centimeter gf-cm Metric gram force millimeter gf-mm

## Why Use a Torque Conversion Calculator?

As previously stated, torque is used in many aspects of our everyday lives, and it plays a key role in determining how much force you’ll need to apply and in which direction, to carry out a given task. There are many ways in which torque is making things happen around you; whether you’re opening a hinged door, riding a bicycle, using a wrench, or driving a car. Due to this diversity in torque applications, the magnitude of torque can be measured in a variety of units as outlined above. Luckily, we’ve provided a Torque Conversion Calculator which you can use to easily convert the torque values.

This calculator can provide accurate values and a wide range of torque conversion measurement options. For example, you can convert your torque value in all the units outlined above. For more information or to discuss which products might be best for your industrial needs, please visit our website here, or contact us at sales@dosupply.com or 1-800-730-0292.