Thin Spherical Pressure Vessel Stress Calculator

How to use this calculator

1. Choose whether to find stress, internal pressure, radius, or wall thickness.
2. Enter the three known values; the sphere is assumed thin (t < 0.1 r).
3. Read the result in pascals or a prefixed unit.

Formula

σ = p r / (2 t)

σ is the membrane stress, p the internal gauge pressure, r the inner radius and t the wall thickness. This stress is biaxial and equal in all directions.

Worked example

Example: p=3 MPa, r=0.5 m, t=5 mm → σ=150 MPa

σ = p r / (2 t) = 3×10⁶ × 0.5 / (2 × 0.005) = 150 MPa.

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