Pressure Vessel Stress Calculator
Calculate hoop stress, longitudinal stress, and Von Mises equivalent stress in thin-walled pressure vessels.
Enter internal pressure, vessel diameter, and wall thickness.
Pressure vessels — tanks, pipes, boilers, and cylinders — develop stress in their walls when pressurized. Two principal stresses arise from the geometry of a cylinder.
Thin-wall assumption. When the diameter-to-thickness ratio D/t exceeds 20, the thin-wall (membrane) equations are sufficiently accurate:
Hoop stress (circumferential): sigma_h = P x r / t = P x D / (2t)
Longitudinal stress (axial, for closed ends): sigma_l = P x r / (2t) = P x D / (4t)
where P is internal gauge pressure, r is the inner radius, and t is the wall thickness.
The hoop stress is always twice the longitudinal stress. This is why cylindrical pressure vessels typically fail by splitting along the longitudinal seam rather than at the end caps.
Von Mises equivalent stress combines the two principal stresses into a single scalar that can be compared to material yield strength:
sigma_vm = sqrt(sigma_h^2 - sigma_h x sigma_l + sigma_l^2)
Safety factor = material yield strength / Von Mises stress. ASME code typically requires a minimum safety factor of 3-4 for pressure vessels.
When thin-wall fails. If D/t < 20, use thick-wall (Lame) equations. The thin-wall formula increasingly underestimates the stress, and the calculator will warn you.
For spherical pressure vessels: sigma = P x r / (2t) in all directions — equal biaxial tension, which is why spheres are the strongest shape per unit material.