Hoop Stress Calculator

Written by Great Medico

Updated September 25, 2026 •2 min read

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For hoop stress, a fast calculation is only useful when the setup is easy to audit. Stress, strain, stiffness, and section properties are tightly tied to geometry, so a correct formula can still give the wrong engineering answer when the wrong dimension is entered. The goal here is a result you can reproduce from the visible inputs, not a number that hides its assumptions.

What this calculator does

Use the Hoop Stress Calculator when you want hoop stress from Shape, Shell radius (r), Shell diameter (d) without building a broader simulation. Supporting cards, if present, expose useful consequences of the same equation rather than introduce unrelated assumptions.

How to use it

Use measured or specified values for Shell radius (r), Shell diameter (d), Thickness of the shell (t), Internal pressure (P), Young’s modulus (E). Let the page handle supported unit conversions, but keep the physical convention consistent across the fields. Choose Shape so the calculation path matches your case. If you are comparing two scenarios, change only the quantity you intend to test so the effect is easy to interpret.

How the calculation works

For a thin cylinder, hoop stress is σh = Pr/(tη); for a sphere it is σh = Pr/(2tη), with joint efficiency η. The page also reports radial stress −P, an out-of-plane shear measure, and a simple elastic diameter change when E and ν are supplied.

Example

Using the default example on the page (Shape = Cylinder; Shell radius (r) = 0.5 m; Shell diameter (d) = 1 m; Thickness of the shell (t) = 0.01 m), the calculator returns hoop stress of 50 MPa. The example is most useful as a consistency check; reproduce it first, then replace the defaults with your own measurements.

How to interpret the result

The hoop stress describes the modeled specimen or section, not every possible failure mode. A useful check is whether increasing a numerator term raises the answer and increasing a denominator term lowers it as the equation predicts.

Limitations and notes

The equations are thin-wall pressure-vessel relationships, so wall thickness must be small relative to radius and the shell must be reasonably uniform. Local nozzles, weld details, discontinuity stresses, thick-wall effects, external pressure, fatigue, and code-required allowables are not evaluated. Enter radius and diameter consistently because both are visible on the form.