Hoop Stress Calculator — Thin-Wall Pressure Vessel
Calculate the hoop and longitudinal stresses in a thin-walled cylindrical pressure vessel. Enter internal pressure, radius, and wall thickness — the calculator checks whether the thin-wall assumption applies.
MPa
mm
mm
Highest stress in a thin-walled pressure vessel — governs wall failure
20 MPa
hoop stress- 1
r ÷ t ratio (thin-wall check)
100 ÷ 5 = 20Thin-wall assumption is valid when r/t ≥ 10. - 2
Numerator P × r
1 × 100 = 100 - 3
Hoop stress σ_h = P × r ÷ t
100 ÷ 5 = 20
How does this calculator work?
Hoop stress in a thin-walled cylinder = P × r / t (MPa). Longitudinal stress is half that: P × r / (2t). The thin-wall assumption is valid when r/t ≥ 10. Enter internal pressure (MPa), internal radius (mm), and wall thickness (mm) to get both stresses.
Formula
How this is calculated
When a cylindrical vessel is pressurised internally, the wall must resist the outward force. The thin-wall (or "membrane") model treats the wall as a thin shell and computes two principal stresses. The hoop (circumferential) stress σ_h = P × r / t acts around the circumference and is the larger of the two — it governs wall thickness selection and failure mode. The longitudinal (axial) stress σ_l = P × r / (2t) acts along the axis for a closed-end vessel and is exactly half the hoop stress, which is why burst failures in pipes typically run along the length rather than across it.
The thin-wall assumption requires the radius-to-thickness ratio r/t to be at least 10 (some codes use 20). Below this threshold the stress distribution through the wall becomes nonlinear, and the more complex Lamé thick-wall equations should be used instead. The calculator flags this automatically.
Units are consistent: if pressure is in MPa and radius and thickness are in mm, the resulting stresses are in MPa. Use N/mm² = MPa or Pa/m² equivalently. This model assumes a perfectly cylindrical, uniform-thickness, isotropic wall under static pressure — no thermal stresses, no end-cap geometry effects, and no safety factors.
Frequently asked questions
The outward pressure acts on the full projected area of the cylinder wall in the circumferential direction but only on the end-cap cross-section in the axial direction. The ratio of these projected areas is exactly 2, so hoop stress = 2 × longitudinal stress. This is why pipes almost always split along a longitudinal seam when over-pressurised.
When r/t < 10 (or r/t < 20 for conservative applications such as ASME Boiler and Pressure Vessel Code), the stress varies significantly through the wall thickness and the thin-wall approximation over-predicts the inner-wall stress. Use the Lamé equations: σ_h = P(r_i² + r_o²)/(r_o² - r_i²) at the inner radius.
Pressure vessel codes (ASME VIII, EN 13445, PD 5500) prescribe specific design safety factors — typically 3–4 on ultimate tensile strength or 1.5–2 on yield strength, depending on the material and service class. Never use a calculator result directly for structural design without applying the relevant code's safety margin.
TG we-Calculate Editorial Team. (2026). Hoop Stress Calculator — Thin-Wall Pressure Vessel [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/hoop-stress-calculator
TG we-Calculate Editorial Team. "Hoop Stress Calculator — Thin-Wall Pressure Vessel." TG we-Calculate. 2026. https://we-calculate.com/calculator/hoop-stress-calculator.
TG we-Calculate Editorial Team, "Hoop Stress Calculator — Thin-Wall Pressure Vessel," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/hoop-stress-calculator
@misc{wecalculate_hoop_stress_calculator, title = {Hoop Stress Calculator — Thin-Wall Pressure Vessel}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/hoop-stress-calculator}}, year = {2026}, note = {TG we-Calculate} }
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