Hoop Stress Calculator
Calculate hoop stress, wall thickness, internal pressure, or diameter for thin-walled pressure vessels and pipes.
What Is Hoop Stress?
Hoop stress (circumferential stress) is the tensile stress in the wall of a thin-walled cylinder or pipe loaded by internal pressure. It acts around the circumference and is typically the dominant stress in pressure vessels, boilers, and pipelines.
Thin-Wall Hoop Stress Formula
$$\sigma = \frac{P \cdot D}{2t}$$\(P\) is internal pressure, \(D\) is inside diameter, and \(t\) is wall thickness. The formula assumes a thin wall where \(D/t \geq 10\). For thicker walls, Lamé or thick-cylinder theory gives better accuracy.
Engineering Applications
Mechanical and piping engineers use hoop stress to check whether a pipe wall is thick enough for a given operating pressure, or to estimate stress during hydrostatic testing. Compare the result to the material yield strength with an appropriate safety factor.
Related tools: Pressure Converter and Ductile Iron Pipe Calculator.
Frequently Asked Questions
When can I use the thin-wall formula?
Use it when the diameter-to-thickness ratio is at least 10. Below that, radial stress and through-wall variation matter more.
Is hoop stress the same as longitudinal stress?
No. Longitudinal stress in a closed cylinder is roughly half of hoop stress: \(\sigma_L \approx P D / (4t)\) for thin walls.
What units should I use?
Keep pressure, diameter, and thickness in consistent SI units (Pa and meters) or use the built-in unit selectors. The calculator converts internally.
Does this include safety factors?
No. This gives the theoretical hoop stress. Apply code-specific safety factors and material allowable stresses in your design.
Can I use this for external pressure?
This formula is for internal pressure. External pressure buckling requires a different analysis.
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