Pressure Vessel Wall Thickness Calculator
Determines the minimum wall thickness required for cylindrical or spherical pressure vessels under internal pressure. Use it when designing tanks, boilers, or piping to meet safety codes.
About this calculator
The required wall thickness of a pressure vessel depends on the internal pressure, vessel geometry, material strength, and a safety factor. For a cylindrical vessel the formula is t = (P × D) / (2 × S × SF), where P is internal pressure, D is inner diameter, S is allowable stress, and SF is the safety factor. For a spherical vessel the denominator doubles: t = (P × D) / (4 × S × SF), because a sphere distributes hoop stress equally in all directions rather than concentrating it circumferentially. The allowable stress is typically derived from the material's yield or ultimate tensile strength divided by a code-specified factor. Higher safety factors and lower allowable stresses both demand thicker walls. These formulas align with thin-wall (membrane) theory and assume the wall thickness is small relative to the vessel radius.
How to use
Suppose you have a cylindrical vessel with an internal pressure of 10 bar (≈ 1 MPa), an inner diameter of 500 mm, an allowable stress of 150 MPa, and a safety factor of 2. Using the cylindrical formula: t = (P × D) / (2 × S × SF) = (1 MPa × 500 mm) / (2 × 150 MPa × 2) = 500 / 600 ≈ 0.833 mm. This is the theoretical minimum; in practice you would round up and add a corrosion allowance. Changing to a spherical vessel with the same inputs gives t = 500 / (4 × 150 × 2) = 500 / 1200 ≈ 0.417 mm, illustrating why spheres are structurally more efficient.
Frequently asked questions
What is the difference between cylindrical and spherical pressure vessel wall thickness calculations?
A cylindrical vessel develops circumferential (hoop) stress that is twice the longitudinal stress, so the wall must resist a larger force per unit area in one direction. The formula uses a factor of 2 in the denominator. A sphere distributes pressure uniformly in all directions, so the effective stress is halved compared to a cylinder of the same diameter, and the formula uses a factor of 4. For the same pressure, diameter, and material, a spherical vessel needs only half the wall thickness of a cylindrical one, making spheres more material-efficient for high-pressure storage.
How do I choose the correct allowable stress and safety factor for a pressure vessel?
Allowable stress is usually set by the governing design code (e.g., ASME Section VIII, EN 13445) and equals the lesser of the material's ultimate tensile strength divided by 3.5 or the yield strength divided by 1.5 at the design temperature. The safety factor—sometimes called the design factor—is also code-mandated and typically ranges from 1.5 to 4 depending on the application, fluid hazard, and inspection regime. Never use raw yield strength as the allowable stress without applying the code-specified reductions, and always check temperature-dependent material properties for elevated-temperature service.
When does thin-wall pressure vessel theory no longer apply?
Thin-wall (membrane) theory is valid when the wall thickness t is less than roughly one-tenth of the inner radius (t/r < 0.1). Beyond that ratio, the stress distribution through the wall becomes non-linear and the simplified formula underestimates the required thickness. Thick-wall vessels require the Lamé equations, which account for radial stress variation. Very high-pressure applications such as hydraulic cylinders, gun barrels, and autoclave reactors almost always fall into the thick-wall regime and should not be designed with the thin-wall formula alone.