Bolt Tensile Force Calculator

When you tighten a screw, you are actually stretching a very stiff spring. The resulting tension is called preload and it keeps two parts together.

This calculator computes the preload based on the load and loaded area within the screw and can also convert arbitrary input values. By enabling additional functions, you can set the load based on the screw grade, compare it to a target preload or convert the force into a tightening torque.

What is the tensile strength of a screw?

Tensile strength is the axial tensile force that a bolt experiences in its longitudinal direction. Inside of the connection, the bolt stretches slightly and the metal tries to return back to its original shape. This restoring force is what holds all parts together. The magnitude of the tensile strength depends on two factors: how high the load inside the bolt is and how much material there is to support that load.

As the threads of a screw cut into the metal, they reduce the outside diameter of the thread. Engineers use not the nominal diameter but the published tensile area. The tensile area for an M12 bolt is about 84.3 square millimeters. On the other hand, the circular cross-sectional area of a 12 mm outside diameter is 113 square millimeters. The threads reduce the cross-sectional area by about one-quarter.

How to use this calculator:

Enter any two of the three values and the third will be calculated automatically. The tensile strength is the load inside the screw and is usually expressed in MPa (Megapascals), or Newtons per square millimeter. The tensile area comes from tables for metric or inch screws. The tension force is the resulting tightening force, and it's shown in newtons, kilonewtons, or pounds depending on which unit you select. If you want to convert a value, leave either load or area blank and enter the desired tension force.

Understanding of formula.

The tensile force is the product of stress and area.

Stress is force divided by area. So when you multiply it by the area, the area cancels out and you are left with just the force. The units work out as well. If you multiply N per square millimeter by square millimeters, you get an answer in Newtons (N). In SI units, a Pascal is equal to one Newton per square meter, so multiplying Pascals by square meters also gives an answer in Newtons.

Here is an example of a calculation: Let's take a bolt with the following parameters: M12, quality class 8.8, tension area 84.3 square millimeters, tensile stress 480 MPa. We substitute these values into the formula.

This is the resulting tensile force that this bolt will create. If you reduce the stress to 320 MPa then the tensile force also reduces accordingly to about 27 kN. As both quantities have a linear relationship with each other, halving the stress will halve the tensile force. Below are the input parameters and examples for each parameter:

The quality class of the bolt and target value for pre-tensioning.

In many cases the direct tension values are not known but only the screw size and an approximate target for the desired tightening pressure. The screw size is indicated on the head of the screw and is referred to as the ISO strength class. This determines the permissible stress. Permissible stress is the maximum stress that a bolt can withstand and return to its original length after unloading. For connections which may need to be loosened again, a common target value is 60 to 75 percent of the permissible stress.

When the "Tightness Level" function is enabled, you can select a tightness level, set a target percentage and check the recommended tension. The calculation tool also indicates where the entered tension stands in relation to the permissible tension so that you can judge whether the pre-tensioning is too low or if there is already a risk of permanent deformation.

Conversion of pull force to tightening torque:

On site, pre-tensioning is not adjusted with a measuring device but with a torque wrench. The simplified relationship between the two is as follows:

K is the thread coefficient, D is the nominal diameter and F_t is the desired tensile force. The K-value for dry steel threads is about 0.2, while it drops to 0.1 to 0.15 with lubricated threads. So an oil-lubricated thread will give a higher preload at the same torque setting. Since most of the torque is consumed by friction, the condition of the threads is just as important as the reading on the torque wrench. Also, the accuracy of torque wrenches in most cases is plus/minus 25 percent. If the "Torque" function is enabled, you can estimate the torque based on the tensile force.

This calculation is important for the following situations:

The wheel nuts on a car wheel are a typical example of an everyday application. When each nut is tightened to the required torque, tensile forces of several tens of kilonewtons are created. The elongation of the bolt is the reason why the wheel is fixed onto the hub body. However, if the nut is tightened beyond the yield strength, this will lead to permanent deformation and may even cause the bolt to break.

The success of bolted flange connections in piping or pressure vessels depends on the tightening force. The sum of the tightening forces produced by all bolts must exceed the separation load caused by internal pressure and have a safety factor. Engineers select appropriate sizes and grades of bolts so that the calculated tension force meets these requirements with sufficient margin. Even with torque wrenching, the result depends on the relationship between torque and tension force. Therefore, even a small amount of rust build-up on the threads can cause a connection to loosen, even if the torque wrench is set correctly.

Tips for accurate adjustment of the suit pressure:

Be sure to use the tensile stress areas given in the tables and not the nominal size of the bolt. The two values differ by 10 to 25 percent depending on thread pitch, and trying to save this lookup work can result in underestimating the strength of the connection. For reusable connections, the preload should be about 60 to 75 percent of the yield strength; higher values are appropriate only if permanent elongation is acceptable. If the specifications call for lubricating the threads, then it must be done. Even with very accurate torque settings, variability in friction is a major source of error in preload.