Torque Calculator

Torque is a rotational force. While force pushes or pulls an object in a straight line, torque causes an object to rotate around a pivot point. The same formula explains why a longer wrench makes it easier to loosen stubborn bolts and why electric cars accelerate so powerfully when they take off. This calculator allows you to calculate one of four quantities - torque, lever arm, force or angle. If you enter three values, the fourth value will be displayed.

What is torque?

Torque is represented by the Greek letter τ (tau) and represents the conversion of a force into rotational motion. Engineers who work with beams and connections often refer to this quantity as moment or moment of force. When an object begins to rotate, it is usually due to torque. This is determined by three values: the magnitude of the force, the distance between the point of application of the force and the pivot point, and the angle at which the force is applied. This explains why mechanics prefer long wrenches, and why it's easier to open a door if you push on the handle than if you push right next to the hinges.

How to use this calculator:

Enter the lever arm and force to read torque. The initial angle is 90 degrees. This corresponds to the case where the force acts perpendicular to the surface, which is the most common case and produces the greatest torque. If the applied force is not perpendicular to the lever arm, adjust the angle. Each field has a corresponding unit selector so that you can enter the lever arm in inches, the force in pounds, and if desired, the torque in newton meters. Conversely, any of these fields can be left blank. When you enter the target torque and two other values, the tool will directly calculate the missing lever arm, missing force, or missing angle.

Understanding of formula

Torque is the product of lever arm, force and sine of the angle between them.

where τ is the torque, r is the distance from the axis of rotation to the point where the force is applied, F is the magnitude of the force and θ is the angle between the direction of the force and the lever arm. Suppose you are using a wrench that is 0.3 meters long and you pull on it with a force of 100 Newtons perpendicular to the handle in order to loosen a bolt. Since the pulling force is perpendicular to the handle, the angle is 90 degrees.

Since the sine of 90 degrees is 1, this formula simplifies to a simple multiplication. If the screw still does not come loose, you do not need to increase the force. By extending the handle with a longer bar and making its length 0.6 meters, you will generate a torque of 60 Newton-meters using the same 100 Newtons of force, doubling the torque. The following table shows each symbol and example values for it.

Why Angle is Important

The sine term plays an important role though it is often overlooked. When you apply a force perpendicular to the lever arm then the sine value will be 1 so all of your force is converted into rotational motion. At an angle of 45 degrees only about 71% of the force can be used. If you point the force directly at the axis of rotation, the angle is 0 degrees and the sine value is zero, thus no effect is achieved. Only the component of the force that acts perpendicular to the lever arm, i.e. F times sin(θ), actually causes a rotation of the object. All other forces act along the lever arm and are therefore useless. If you open up the angle curve below then you can see the full change from 0 to 180 degrees.

Torque, power, energy

Torque is often confused with other physical quantities. Power indicates the rate at which a rotation does work, and its relationship to torque is such that power is equal to the product of torque and angular velocity. A tractor produces enormous torque at low speeds. A dental drill has almost no torque but rotates incredibly fast, and both are useful for completely different reasons. Energy is something else. One newton-meter of torque and one joule of energy are, in simplified terms, the same base unit, but they represent different things. Torque is a rotational vector, while a joule represents actual work done. Watch out for notation. If you use Newton-meters for torque and Joules for energy, then you can avoid treating them as interchangeable quantities and getting incorrect results. By opening up the power range, you can convert the torque into watts or horsepower, based on the specified rotational speed.

Where does the torque come from?

Torque is listed in the technical data of cars as it represents a value for driving force. Electric motors can produce their maximum torque from standstill which makes electric cars feel very powerful. Internal combustion engines only reach their maximum at higher revs. In a workshop, a torque wrench will click when a bolt has reached its target torque. If you tighten too much the threads can strip and if not tight enough there may be leaks in the connection. The same formula is used to determine the size of a crane. If a force of 5,000 Newtons acts on an arm and the point of application is 12 meters from the pivot then the torque at the pivot will be 60,000 Newton meters. Reversing it is just as simple. To calculate how much force is required to turn a wheel nut with a torque of 110 Newton meters using a wrench that's 0.35 meters long simply leave the field for force blank and the answer will be approximately 314 Newtons. This ratio determines calculations for all gearboxes, pulley systems and levers.

Units and Conversions

The SI unit for torque is the newton-meter. The U.S. customary unit is the pound-foot. One newton-meter equals approximately 0.7376 pound-feet and one pound-foot equals approximately 1.356 newton-meters. Engineering also uses kilogram-force meters, while small fasteners often use Newton millimeters. The unit scalers in each field do the conversions so you can enter values in one system of units and read results in another. Always check a field's unit before entering a value.