Hoop Stress Calculator

Hoop stress, also known as circumferential stress, is a fundamental concept in physics and engineering, particularly in the study of materials and structures. It refers to the stress in a pipe wall, under pressure, that is acting circumferentially in a plane perpendicular to the longitudinal axis of the pipe. The calculation of hoop stress involves parameters like internal and external pressures in the tube, internal and external radii in the tube, and the radius to a point in the tube. This tutorial delves into these calculations and the associated formulas.

Circumferential Stress of Cylinder Wall or Tube Calculator
Hoop Stress Calculator Results
Stress in Circumferential Direction = MPa

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Example Formula

The hoop stress (σ) in a thin wall pressure vessel can be calculated using the following formula:

σ = P × r / t


  1. σ: Represents the hoop stress.
  2. P: Represents the internal pressure in the tube.
  3. r: Represents the internal radius of the tube.
  4. t: Represents the wall thickness of the tube.

This formula assumes that the wall thickness is much less than the radius of the tube. If the tube has a considerable thickness, more complex formulas are used that involve both the internal and external radii and pressures.

Who wrote/refined the formula

The formula for hoop stress has been derived from the principles of mechanics and materials science. It is not attributed to a specific individual but is a result of collective progress in the understanding of material behavior under stress. It has significant relevance in fields beyond physics, including civil, mechanical, and aerospace engineering, where it is critical to understand and manage stress in structures.

Real Life Application

One of the primary applications of hoop stress is in the design and analysis of pressure vessels and piping systems. Engineers calculate hoop stress to determine the thickness required for a pipe wall to safely contain a certain pressure. For instance, gas cylinders, boilers, and airplane fuselages are designed considering the principles of hoop stress.

Key individuals in the discipline

While no one specific person can be singled out for the development of hoop stress concepts, several physicists and engineers have contributed significantly to the broader understanding of stress analysis. Notably, Augustin-Louis Cauchy, a French mathematician, made significant contributions to the theory of elasticity, which forms the basis for understanding stresses, including hoop stress.

Interesting Facts

  1. Hoop stress principles are used in the design of rockets. Engineers need to calculate the stress on the cylindrical fuselage due to the high internal pressure of the fuel tank.
  2. Hoop stress calculation plays a significant role in the oil and gas industry, where it's used in the design of long-distance pipeline systems.
  3. The understanding of hoop stress has revolutionized the field of civil engineering, allowing for the construction of dams and large storage vessels.


Understanding hoop stress and its associated calculations is crucial for anyone involved in the design or analysis of pressure vessels and similar structures. Its principles are widely applied in various fields, from physics to engineering, making it a fundamental concept to grasp for aspiring scientists and engineers.

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