Hoop Stress – Explanation, Calculator and Applications

What are the Hoop Stresses and Longitudinal Stresses?

Stress calculations have a very important place in mechanical engineering. For different applications, they developed different kinds of methods throughout the history of engineering. So, we use hoop stress calculations for different applications. Especially for safety calculations. 

What is Hoop And Longitudinal Stress at Tubes and Pipes?

Section of a pipe.
Section of a pipe or tube(Robert L. Moth: Machine Elements In Mechanical Design).

In pipes and tubes, there can be stress on the surface because of internal pressure. Because of this phenomenon, thickness, diameter, and other parameters of designed pipes or tubes must withstand these stresses. To design pipes or tubes in terms of internal pressure, you need to select the proper thickness, diameter, and material. So you need to do a stress calculation for external stress on the surface of the pipe.

Hoop Stress Calculator


Longitudinal Stress Calculator


Two types of surface stress originate from internal pressure in pipes or tubes; Longitudinal and Hoop stress. You need to calculate these stresses from obtained design parameters such as; the diameter and thickness of the pipe or tube. Then you need to compare the results with materials’ maximum stress values that we consider with safety factors. We calculate the longitudinal stresses with;

hoop stress formula.
Hoop stress formula.
longitudinal stress formula.
Longitudinal stress formula.

As you see the above formulas;

p: Internal pressure,

D: Diameter of pipe,

t: Thickness of pipe.

All these parameters are illustrated above illustration.

Take a look at other engineering calculators like this in Mechanicalland!

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How to Use Hoop and Longitudinal Stress Calculator?

As a good engineer or scientist, you need to TAKE CARE ABOUT YOUR UNITS in calculations. You need to select your proper units for the calculator to obtain the correct hoop and longitudinal stress results. Otherwise, all the calculations will be wrong because of improper unit set selection.

Also, what you need to do is very basic. Just enter the required parameters, internal pressure(P), diameter(D), and thickness(T) respective in the Longitudinal stress calculator.

Units can be; N/mm^2 for P, mm for D, mm for T, and N/mm^2 for example. Consistency of units for the stress calculator is the most important thing.

What is Hoop Stress in Engineering?

Iron straps are used to strengthen the thin tube railway bridge pillar.

Hoop stress is a type of circumferential stress that occurs at the surface of thin-walled structures, because of the inner pressure application. So, there are tons of engineering applications where these stresses take place. 

In Which Applications That Hoop Stress Used?

Hoop stresses on cylinders.
Effect of hoop stresses on thin cylinder walls(Image Source: https://www.trenchlesspedia.com/definition/2799/hoop-stress).

There are a bunch of mechanical applications that we must use hoop stress calculations to obtain a safe physical system when they use in full-load. So, hoop stress calculation is a very important engineering discipline. Engineers must take care of these calculations perfectly, for the applications mentioned below.

Steam Boilers

Tubings of a locomotive.
Inner tubings of a steam locomotive.

Steam boilers are commonly used on different sides of buildings. If we do not design properly and safely, it will be very dangerous to fail and will be very harmful to the environment and human life.

We can approximate the structure of the boilers as a thin-walled hollow structure filled with water or other fluid. And because of the heat and pressure of the fluid inside these steam boilers, we must design the outer wall to withstand these very high stresses. And also, these high stresses are hoop stresses that take place as tensile stresses that parallel the axis of the boiler geometry. This stress is caused by the internal pressure stress of the fluid.

In this case, we use the hoop stress calculations to obtain a safe design of the steam boilers.

Pressure Tanks and Containers

Gas containers.
Big pressure gas tanks in a refinery.

Pressure tanks and containers are used extensively in every part of human life such as big LNG tankers on LNG ships, fuel tanks beneath the fuel stations, and oxygen containers that are used in hospitals and welding departments… And there are other various examples that pressure tanks and containers are used both in engineering and in daily life. 

It is simple to imagine the hoop stresses occurring at the walls of the pressure tanks due to the pressure of the fluid, gas, or air inside the container. 

A safe design must be calculated for these pressure tanks and containers also. So, these calculations are made with hoop stress calculation formulae. 

Not Very Thick Wall, Optimized Thickness Of The Wall!

The thickness of the wall must be optimized. The thickness of the wall must be thick enough to be safe from failure because of the inner pressure. And the thickness of the wall must be thin as possible because of commercial concerns. 

As an engineer, you need to do this optimization for your company that produces pressure containers or tanks. There are other commercial opponents of your company that produces these products. Your product must compete with other products in terms of price/performance. 


So this is a very important phenomenon in engineering. We need to calculate them correctly to obtain good results.

Also, there are different kinds of applications that we use hoop stresses. So, we need to take care of these stresses to obtain strong pipe and hollow structures.

So, to obtain the optimum thickness of walls, you can use the calculator above.

Above all, Mechanicalland does not accept any responsibility for calculations made by users in calculators. A good engineer must check calculations again and again.

Also, You can find out much more calculators like this in Mechanicalland! Take a look at the other engineering calculators available in Mechanicalland!

Finally, do not forget to leave your comments and questions below about the hoop stress calculator and its applications.

Your precious feedbacks are very important to us.

FAQs About Hoop Stress

What is meant by hoop stress?

This is a very important phenomenon in engineering. It means the stress on the surface of pipes and tubes because of the internal pressure. So, to prevent the tears, we need to calculate the hoop stress at an engineering level.

What is the hoop stress equation?

The formula for this stress is very basic. You just need to use the pressure, diameter, and wall thickness of the pipes and tubes. You can find the equations in the article above.

What causes hoop stress?

The cause of this stress is the internal pressure of the tubes and pipes. The inflation effect of the internal pressure causes tearing stresses on the surfaces. So, we call this phenomenon hoop stress.

What is hoop stress on cylinders? 

This stress on cylinders is caused by the internal pressure of the fluid inside them. So, we can calculate the hoop stresses on the cylinder surfaces.

Can hoop stress be negative? 

To answer this question, we need to look at the general formula and parameters. So, the parameters are diameter, the thickness of the wall, and pressure. To obtain a negative value, one of these parameters must be negative. So, the thickness and the diameter can not be negative. But pressure is a vectorial feature that can be negative according to the direction. We call the negative pressures a vacuum. But in practice, we can not contain negative hoop stresses.

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