Pressure Vessel Stress Calculator Formula

Understand the math behind the pressure vessel stress calculator. Each variable explained with a worked example.

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Formulas Used

Hoop (Circumferential) Stress

hoop_stress = pressure * radius / thickness

Axial (Longitudinal) Stress

axial_stress = pressure * radius / (2 * thickness)

D/t Ratio

dt_ratio = diameter / thickness

Variables

VariableDescriptionDefault
pressureInternal Pressure (P)(MPa)5
diameterInner Diameter (D)(mm)1000
thicknessWall Thickness (t)(mm)10
radiusDerived value= diameter / 2calculated

How It Works

Thin-Walled Pressure Vessel Stresses

For a cylindrical vessel where the wall thickness is much less than the diameter (D/t > 10), the stresses can be calculated using simplified thin-wall formulas.

Formulas

Hoop stress: sigma_h = P × r / t (circumferential, the larger stress)

Axial stress: sigma_a = P × r / (2t) (longitudinal, half the hoop stress)

The hoop stress is twice the axial stress, which is why pressure vessels fail along longitudinal seams (circumferential stress governs).

Worked Example

A vessel with 1000 mm diameter, 10 mm wall, at 5 MPa pressure.

pressure = 5diameter = 1000thickness = 10
  1. 01r = 1000 / 2 = 500 mm
  2. 02Hoop stress = 5 × 500 / 10 = 250 MPa
  3. 03Axial stress = 5 × 500 / (2 × 10) = 125 MPa
  4. 04D/t = 100 (thin-wall assumption valid)

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