Longitudinal Stress Calculator

About this calculator

A thin-walled pressure cylinder — a pipe, tank or vessel where wall thickness is small relative to diameter — experiences two different internal stresses from the same pressure: hoop (circumferential) stress, which acts around the circumference and equals σ_hoop = P·d / (2t), and longitudinal (axial) stress, which acts along the cylinder’s length and equals σ_L = P·d / (4t), where P is internal pressure, d is inner diameter and t is wall thickness.

Because the longitudinal stress formula has a 4 in the denominator instead of a 2, it works out to exactly half the hoop stress for the same cylinder — which is why thin-walled pressure vessels typically fail by splitting lengthwise along the hoop-stress direction rather than by a circumferential fracture. Mechanical and piping engineers check both stresses against a material’s allowable stress under codes like ASME B31.3 or the Boiler and Pressure Vessel Code when sizing pipe walls and pressure vessels; enter internal pressure, inner diameter and wall thickness to get both stresses.