Thermal Stress Calculator

About this calculator

When a structural member is heated or cooled but is fully restrained — unable to expand or contract freely — the prevented dimensional change converts into internal stress instead. This calculator applies the standard engineering formula σ = E · α · ΔT, where E is the material's Young's modulus (stiffness), α is its coefficient of thermal expansion, and ΔT is the temperature change; the result is a compressive stress on heating or a tensile stress on cooling.

This is a critical calculation for anything rigidly fixed at both ends: pipelines welded between anchors, continuously welded rail track, bridge girders bonded to abutments, and multi-material assemblies where mismatched expansion rates create stress at the joint. Engineers use it to size expansion joints, select materials, and verify a restrained component won't yield or buckle under its expected temperature swing.